NASA/CP—2011–216469

Meteoroids: The Smallest Solar System Bodies

W.J. Cooke, Sponsor

Marshall Space Flight Center, Huntsville, Alabama

D.E. Moser, and B.F. Hardin, Compilers

Dynetics Technical Services, Huntsville, Alabama

D. Janches, Compiler

Goddard Space Flight Center, Greenbelt, Maryland

July 2011

Proceedings of the Meteoroids 2010 Conference held 

in Breckenridge, Colorado, USA, May 24–28, 2010. 

Conference sponsored by the NASA Meteorid 

	

	
	 


	
		

	
 

Research, Los Alamos National Laboratory, and the 


	
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NASA/CP—2011–216469

Meteoroids: The Smallest Solar System Bodies

W.J. Cooke, Sponsor

Marshall Space Flight Center, Huntsville, Alabama

D.E. Moser and B.F. Hardin, Compilers

Dynetics Technical Services, Huntsville, Alabama

D. Janches, Compiler

Goddard Space Flight Center, Greenbelt, Maryland

July 2011

National Aeronautics and

Space Administration

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TABLE OF CONTENTS (Continued)

Origin of Short-Perihelion Comets ............................................................................................ 76

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Dynamical Evolution of Meteoroid Streams, Developments Over the Last 30 Years 

I. P. Williams1

Abstract As soon as reliable methods for observationally determining the heliocentric orbits of 

meteoroids and hence the mean orbit of a meteoroid stream in the 1950s and 60s, astronomers strived to 

investigate the evolution of the orbit under the effects of gravitational perturbations from the planets. At 

first, the limitations in the capabilities of computers, both in terms of speed and memory, placed severe 

restrictions on what was possible to do. As a consequence, secular perturbation methods, where the 

perturbations are averaged over one orbit became the norm. The most popular of these is the HalphenGoryachev method which was used extensively until the early 1980s. The main disadvantage of these 

methods lies in the fact that close encounter can be missed, however they remain useful for performing 

very long-term integrations. 

Direct integration methods determine the effects of the perturbing forces at many points on an 

orbit. This give a better picture of the orbital evolution of an individual meteoroid, but many meteoroids 

have to be integrated in order to obtain a realistic picture of the evolution of a meteoroid stream. The 

notion of generating a family of hypothetical meteoroids to represent a stream and directly integrate the 

motion of each was probably first used by Williams Murray & Hughes (1979), to investigate the 

Quadrantids. Because of computing limitations, only 10 test meteoroids were used. Only two years later, 

Hughes et. al. (1981) had increased the number of particles 20-fold to 200 while after a further year, Fox 

Williams and Hughes used 500 000 test meteoroids to model the Geminid stream. With such a number 

of meteoroids it was possible for the first time to produce a realistic cross-section of the stream on the 

ecliptic. 

From that point on there has been a continued increase in the number of meteoroids, the length of 

time over which integration is carried out and the frequency with which results can be plotted so that it 

is now possible to produce moving images of the stream. As a consequence, over recent years, emphasis 

has moved to considering stream formation and the role fragmentation plays in this. 

Keywords meteors · numerical integration · modeling 

1 Introduction 

Understanding the basic physics involved in meteoroid stream evolution is relatively easy. First, some 

model for the ejection of material from the parent body, that is time (location), speed and direction is 

needed. From this the initial orbit of each meteoroid can be calculated. Some means of calculating the 

effects of gravity from the Sun and Planets on the orbits of these meteoroids is then required which 

should also incorporate the effects of Solar Radiation (Pressure and the Poynting-Robertson effect). 

Hence the orbit of each meteoroid can be calculated at any desired time after the initial formation. 

Finally if the meteoroid position coincides with that of the Earth, there is a need to understand the 



I. P. Williams ( ) 

Queen Mary University of London, Mile End Rd, E1 4NS, UK. E-mail: i.p.williams@qmul.ac.uk


interaction between the meteoroids and the atmosphere so that the observed meteor shower can be tied 

in with the meteoroid stream. 

Walker (1843) drew attention to the similarity, in terms of eccentricity, between meteor and 

comet orbits, but it was left to Kirkwood (1861) to propose that shower meteors were debris of ancient 

comets. At that time, the standard model for comets was essentially the flying sandbank model, so that 

initially the velocity of the meteoroids were essentially the same as that of the comet, there was no need 

for an ejection model. LeVerrier (1867) correctly pointed out that, given sufficient time, planetary 

perturbations would spread the meteoroids all around the orbits. Newton (1864 a, b) showed that the 

node of the Leonid orbits advanced relative to a fixed point in space at 52.4 arc seconds per year and 

Adams (1867) showed that a 33.25 year period was the only period that was consistent with the 

observed nodal advancement. Thus, early workers were incorporating the principles laid down above 

into their thoughts but computers were human assistants rather than machines and of necessity rather 

slow. 

2 New Techniques and Thoughts 

Nagaoka (1929) had suggested that meteors could affect the propagation of radio waves, a suggestion 

also made by Skellet (1931, 1932), but little was done. Hey realized that radar could be used as a tool to 

investigate meteors and at the end of the war ensured that military radar equipment became available for 

civil use allowing astronomers to start meteor work. There was a strong storm of Draconid meteors in 

1946. This resulted in several papers being published on radar observations of the Draconids (Clegg et. 

al. 1947, Hey et. al. 1947, Lovell et. al. 1947). Radar can detect smaller meteoroids (down to submillimetre size) and so detected many more meteors. Radar also had the advantage of working in the day 

as well as by night, thus doubling the coverage and discovering many new streams (Ellyett 1949) and 

orbits of thousands of meteors were obtained. 

Whipple (1950) proposed a new model for a comet, replacing the flying sandbank model. 

According to this model, a comet had an icy nucleus with dust grains embedded within it, the dirty 

snowball model. As a comet approaches the sun, solar heating causes the ices to sublimate and the 

resulting gas outflow carries away small dust grains with it, the larger ones becoming meteoroids and 

the very small ones forming the dust tail. Whipple, (1951) modelled this and produced an expression for 

the ejection velocity, V of the meteoroids relative to the cometary nucleus at a heliocentric distance r as 

    	

  	

  

	


where is the bulk density of the meteoroid and r the heliocentric distance in astronomical units. Rc is 

the nucleus radius in kilometers and all other quantities are in cgs units. Others (e.g. Gustafson 1989, 

Crifo 1995, Ma et al, 2002), have modified this model, but the general result is the same, namely that the 

outflow speed of the meteoroids is much less than the orbital speed of the comet. Thus there is little 

change in the specific energy and momentum of these meteoroids and so they move on similar orbits to 

that of the comet, in other words, they form a stream. If the ejection velocity is known relative to the 

nucleus, then the heliocentric velocity can be calculated and from this, the initial orbit. The mathematics 

involved in this and the relevant equations are given in detail in Williams (2002). 

Initially, computing capabilities were too limited to allow direct integration of a significant set of 

meteoroids and so secular perturbations were commonly used, generally based on an algorithm by 


Brouwer (1947) that could be applied to orbits with high eccentricity, all previous methods relied on 

using a series expansion that was valid only for low values of e. This mathematical development 

allowed Whipple & Hamid (1950) to follow the evolution of the mean Taurid stream over an interval of 

4700 years. Secular perturbation methods were the prime method of investigation and became quite 

sophisticated, the most popular being the Halphen-Goryachev method described in Hagihara (1972). 

This was used by Galibina & Terentjeva (1980) to determine the effect of gravitational perturbations on 

the stability of a number of meteoroid streams over a time interval of tens of thousands of years. 

Babadzhanov & Obrubov (1980, 1983) also used the Halphen-Goryachev method to investigate the 

evolution of both the Geminid and the Quadrantid streams. The major draw-back of any secular perturbation method is that it deals with the evolution of orbits rather than determining the position of 

individual meteoroids (that is, no account is taken of true anomaly). Hence, the method may show that 

the orbits of meteoroids intersect the Earth’s orbit, but unless meteoroids are present at that location at 

that time, no meteors will be seen. This consideration is particularly important for showers like the 

Leonids as was discussed by Wu & Williams (1996), Asher et. al. (1999). 

3 Direct Integration Methods 

Direct integration methods integrate the path of each individual meteoroid and this was done by Hamid 

& Youssef (1963) for the six meteoroids then known to belong to the Quadrantid stream. The diculty 

is that as there are at least 1016 meteoroids in a typical stream so that the six observed meteors are almost 

certainly not a representative sample of the whole stream. However, a smaller sample has to be taken to 

represent the stream, in reality a set of test particles have to be generated to represent the stream. This 

was done 30 years ago by Williams et. al. (1979), who represented the Quadrantid stream by 10 test 

particles, spread in uniformly in true anomaly around the orbit and integrated over an interval of 200 

years using the self adjusting step-length Runge-Kutta 4th order method. 

 Four years later, Fox et al. (1983) were using 500 000 meteoroids and were able to produce a 

theoretical cross section on the ecliptic for the Geminid stream which gives vital information about the 

properties of the resulting shower. Jones (1985) used similar methods to produce a stream cross section. 

In four years computer technology had advanced from allowing only a handful of meteoroids to be 

integrated to the situation where numbers to be used did not present a problem. 

 By the mid eighties, complex dynamical evolution was being investigated, Froeschlé and Scholl 

(1986), Wu & Williams (1992) were showing that the Quadrantid stream, experiencing close encounters 

with Jupiter, was behaving chaotically. A new peak in the activity profile of the Perseids also caused 

interest with models being generated by Wu & Williams (1993) for example. Williams & Wu (1994) 

were able to show how the cross-section of the Perseid shower should vary from year to year. 

Babadzhanov et al. (1991) looked at the possibility that the break-up of comet 3D/Biela was caused 

when it passed through the most heavily populated part of the Leonid stream. 

 By now calculating from models the likely cross-section at any given time has become routine 

(Jenniskens & Vaubaillon 2008, 2010). 

4 A Problem Emerges 

The Quadrantid shower is a prolific and regular shower seen at Northern latitudes around the beginning 

of January. It is arguably the only major meteor shower that does not have a body that is generally 


accepted as being its parent. Part of the problem of identifying the parent undoubtedly lies in the fact 

that orbits in this region of the Solar System evolve very rapidly so that claims can be made based on a 

similarity of orbits at some epoch in the past. Equally, a similarity of orbits at the current time alone is 

not a proof of parenthood. The history of the Quadrantid meteoroid stream, including a discussion of 

most of the suggested parent bodies can be found in Williams & Collander-Brown (1998). 

 One of the suggestions for the parent of the Quadrantids is comet C/1490 Y1 (Hasegawa, 1979), 

the claim being based on orbital similarity around 1490 AD. In the Quadrantid shower there is both a 

strong narrow peak and a broad background showing the existence of both an old stream and a new one 

(Jenniskens et. al. 1997). There is an asteroid, 2003 EH1 with an orbit that is currently almost identical 

to the mean orbit of the Quadrantids and it has been argued that this asteroid may be a surviving remnant 

of the comet of 1491, following its catastrophic break-up (Jenniskens 2004, Williams et. al. 2004). We 

now know that comet break-up is fairly common and so one might expect meteor streams with such an 

origin to be also common. The Taurid complex is also generally considered to consist of comet 2P/ 

Encke, a significant number of asteroids and of course the Taurid meteor streams, suggesting a past 

fragmentation (Babadzhanov et. al. 2008, Napier 2010). 

5 Conclusions 

In the last 30 years, the field appears to have gone full circle. In the beginning it was generally agreed 

that we knew how meteor streams formed, but were struggling to follow the effects of perturbations on 

the orbits. Now we are confident that we can follow the evolution of any given set of orbits but are 

struggling to model the stream formation process when partial or total disintegration takes place. 

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The Working Group on Meteor Showers Nomenclature: a History, Current Status 

and a Call for Contributions 

T. J. Jopek1• P. Jenniskens2

Abstract During the IAU General Assembly in Rio de Janeiro in 2009, the members of Commission 22 

established the Working Group on Meteor Shower Nomenclature, from what was formerly the Task

Group on Meteor Shower Nomenclature. The Task Group had completed its mission to propose a first 

list of established meteor showers that could receive officially names. At the business meeting of 

Commission 22 the list of 64 established showers was approved and consequently officially accepted by 

the IAU. 

A two-step process is adopted for showers to receive an official name from the IAU: i) before 

publication, all new showers discussed in the literature are first added to the Working List of Meteor 

Showers, thereby receiving a unique name, IAU number and three-letter code; ii) all showers which 

come up to the verification criterion are selected for inclusion in the List of Established Meteor 

Showers, before being officially named at the next IAU General Assembly. Both lists are accessible on 

the Web at www.astro.amu.edu.pl/jopek/MDC2007. 

Keywords meteor shower · meteoroid stream · methods: nomenclature 

1 Introduction 

The naming conventions for celestial objects, and the method of announcement of their discovery, has 

been the prerogative of the International Astronomical Union (IAU) since years. At its inaugural 

meeting in Rome in 1922, the IAU standardized the constellation names and abbreviations. More 

recently the IAU Committee on Small Body Nomenclature has certified the names of asteroids and 

comets, e.g. see Kilmartin (2003), Ticha et al. (2010) or enter the website 

www.ss.astro.umd.edu/IAU/csbn/. 

Until 2009, however, the IAU has never named a meteor shower. The need to settle on official 

nomenclature rules was widely discussed, but the problem was not settled by the community of meteor 

astronomers. As a result, there was much confusion in the meteor shower literature. Some well defined 

showers had multiple names (Draconids, Giacobinids, ...), while many showers were given a different 

name in each new detection. 

This situation changed during the IAU General Assembly in Prague in 2006, when Commission 

22 established a Task Group on Meteor Shower Nomenclature. The task of this group was to formulate a 

descriptive list of established meteor showers that could receive official names during the next IAU 

General Assembly in Rio (Jenniskens 2007; Spurný et al. 2007, 2008). Task Groups are established for 



T. J. Jopek ( ) 

Institute Astronomical Observatory UAM, Sloneczna 36, 60-286 Pozna£, Poland. E-mail: jopek@amu.edu.pl 

P. M. Jenniskens 

SETI Institute, 515 N. Whisman Road, Mountain View, CA 94043, USA 


periods of three years, and serve until the next General Assembly. The members of the first Task Group 

on Meteor Shower Nomenclature were: Peter Jenniskens (chair), Vladimír Poruban, Pavel Spurný, 

William J. Baggaley, Juergen Rendtl, Shinsuke Abe, Robert Hawkes and Tadeusz J. Jopek. 

2 Nomenclature Rules and the Working List of Meteor Showers 

To make this task possible, the traditional meteor shower nomenclature practices were formalized, and a 

set of nomenclature rules was adopted: 

a meteor shower should be named after the constellation of stars that contains the radiant, using 

the possessive Latin form of the constellation and replacing the Latin declension for ”id” or 

”ids”, 

if in doubt, the radiant position at the time of the peak of the shower (at the year of discovery) 

should be chosen, 

to distinguish among showers from the same constellation: 

the shower may be named after the nearest (brightest) star with a Greek or Roman letter 

assigned (“ Lyrids”, “c Andromedids”), 

the name of the month (months) may be added (May Lyncids, September-October 

Lyncids), 

for the shower with a radiant elongated less than 32 degrees from the Sun, one should add 

“Daytime” before the shower name (“Daytime Arietids”, “Daytime April Piscids”), 

by adding “South” and “North” one refers to the branches of a single meteoroid stream, both 

branches are active over about the same period of time. The radiants of these branches are 

located south and north of the ecliptic plane, 

showers that move through two constellations can be named by giving the two constellations in 

successive order using a ”-” symbol, e.g., Librids-Luppids, 

a composed name of a shower is allowed (Northern Daytime  Cetids), 

In case of confusion, The Task Group on Meteor Shower Nomenclature will select among the proposed 

names a unique name for each shower. For further details related to all above rules see (Jenniskens 

2006a, 2008). 

The second part of the task to create a descriptive list of established meteor showers is a 

much more complicated issue. As a starting point a Working List of  230 showers was compiled using 

data collected and published in the book by Jenniskens (2006b). Each shower was given a name, a 

unique number and a three-letter code to be used in future publications ( Aquariids, 31, ETA). The 

Working List, and the list of nomenclature rules, was posted on a newly established IAU Meteor Data 

Center website (Jopek 2007). 

During the Meteoroids 2007 meeting in Barcelona, the Task Group worked out the logistics of 

adding new streams to the Working List, and of adding new information on streams already in the 

Working List: 

the institute responsible for maintaining the Working List is the IAU Meteor Data Center, 

managed currently by Vladimír Poruban of SAS, Slovakia, 

already known and newly discovered streams should be reported in the literature only with a 

designated IAU name, number and code, 


Tadeusz J. Jopek of the UAM Astronomical Observatory, Poland, is the person currently 

responsible for: 

maintaining the shower part of the IAU MDC website, 

reporting new streams and new data on existing streams, 

giving out new IAU numbers and codes. To obtain new numbers and codes the author 

should contact T.J. Jopek directly3

, 

the International Meteor Organization takes a role in coordinating the reporting of newly 

discovered showers. It facilitates the inclusion of showers that are recognized by amateur 

astronomers, for example from visual observations. 

To inform the scientific community of newly discovered showers, the IAU’s Central Bureau for 

Astronomical Telegrams (CBAT) issues an electronic telegram (CBET) with a brief summary of each 

new nd. Those telegrams are prepared by the Task Group, as a part of the process of reporting new 

streams, when new showers are added to the working list. Following this CBET, all publications 

discussing that new shower should use the newly established name, number, and shower code. 

 During the 2006-2009 triennium, the Working List was updated several times (Kashcheev et al. 

1967; Uehara et al. 2006; Brown et al. 2008; Molau and Kac 2009; Molau and Rendtel 2009; SonotaCo 

2009; Brown et al. 2010; Jopek et al. 2010). In July of 2009, the Working List of all Meteor Showers 

consisted of 365 meteor showers. 

 

3 The List of Established Meteor Shower 

The Task Group met again at the May 2009 Bolides Meeting in Prague, where the Task Group settled on 

the list of established meteor showers. Established showers are those meteor showers that have certainly 

manifested. 64 meteor showers from the Working List were moved to the List of Established Showers. 

As the main grounds for this action, two factors were considered — definite shower activity (for 

example because of a strong meteor outburst) or confirmation from the detection of a shower in at least 

two recent meteor orbit surveys. The decision to move a shower into the list of established showers was 

to some extend subjective and border cases were decided by the democratic process of voting in the 

Task Group. Goal was to leave out any showers that were not certain to exist. The list was subsequently 

posted on the Meteor Data Center website for review. 

In August of 2009, during the Commission 22 business meeting held in Rio de Janeiro, the 

content of the List of Established Showers was approved without changes (Watanabe et al. 2010), and 

this decision was confirmed by the subsequent Division III business meeting, see Bowell et al. (2010). 

As a result, for the first time in the history of meteor astronomy, meteor showers were officially named 

by the IAU. All these showers are listed in Table 1. 

4 The Working Group for Meteor Shower Nomenclature 

To facilitate the future update of the Working List and the List of Established Showers, Commission 22 

(C22) has accepted a two step process: 



3 Email: jopek@amu.edu.pl, web:http://www.astro.amu.edu.pl/~jopek/JopekTJ/.)


Table 1. Geocentric data of 64 showers officially named during XXVII IAU General Assembly held in Rio de 

Janeiro in 2009. For each shower, the solar ecliptic longitude S, the radiant right ascension and declination g, g are 

given for J2000.0. 

No IAU Stream name S g g Vg 

 No & code (deg) (deg) (deg) (km/s) 

1 1 CAP § Capricornids 127 306.6 -8.2 22.2 

2 2 STA Southern Taurids 224 49.4 13 28 

3 3 SIA Southern  ̈ Aquariids 131.7 339 -15.6 34.8 

4 4 GEM Geminids 262.1 113.2 32.5 34.6 

5 5 SDA Southern © Aquariids 125.6 342.1 -15.4 40.5 

6 6 LYR April Lyrids 32.4 272 33.3 46.6 

7 7 PER Perseids 140.2 48.3 58 59.4 

8 8 ORI Orionids 208.6 95.4 15.9 66.2 

9 9 DRA October Draconids 195.1 264.1 57.6 20.4 

10 10 QUA Quadrantids 283.3 230 49.5 41.4 

11 12 KCG a Cygnids 145.2 284 52.7 24 

12 13 LEO Leonids 235.1 154.2 21.6 70.7 

13 15 URS Ursids 271 219.4 75.3 33 

14 16 HYD « Hydrids 265.5 131.9 0.2 58 

15 17 NTA North. Taurids 224 58.6 21.6 28.3 

16 18 AND Andromedids 232 24.2 32.5 17.2 

17 19 MON December Monocerotids 260.9 101.8 8.1 42 

18 20 COM December Comae Berenicids 274 175.2 22.2 63.7 

19 22 LMI Leonis Minorids 209 159.5 36.7 61.9 

20 27 KSE a Serpentids 15.7 230.6 17.8 45 

21 31 ETA ¬ Aquariids 46.9 336.9 -1.5 65.9 

22 33 NIA North.  ̈ Aquariids 147.7 328 -4.7 27.6 

23 61 TAH ­ Herculids 72 228.5 39.8 15 

24 63 COR Corvids 94.9 192.6 -19.4 9.1 

25 102 ACE § Centaurids 319.4 210.9 -58.2 59.3 

26 110 AAN § Antliids 313.1 140 -10 42.6 

27 137 PPU ® Puppids 33.6 110.4 -45.1 15 

28 144 APS Daytime April Piscids 30.3 7.6 3.3 28.9 

29 145 ELY ¬ Lyrids 49.1 292.5 39.7 45.3 

30 152 NOC North. Daytime  ̄ Cetids 46.7 2.3 17.8 33 

31 153 OCE South. Daytime  ̄ Cetids 46.7 22.5 -3.6 36.6 

32 156 SMA South. Daytime May Arietids 55 33.7 9.2 28.9 

33 164 NZC North. June Aquilids 86 298.3 -7.1 36.3 

34 165 SZC South. June Aquilids 80 297.8 -33.9 33.2 

35 170 JBO June Bootids 96.3 222.9 47.9 14.1 

36 171 ARI Daytime Arietids 76.7 40.2 23.8 35.7 

37 172 ZPE Daytime ° Perseids 78.6 64.5 27.5 25.1 

38 173 BTA Daytime ± Taurids 96.7 84.9 23.5 29 

39 183 PAU Piscis Austrinids 123.7 347.9 -23.7 44.1 

40 187 PCA 2 Cassiopeiids 106 389.4 71.5 40.3 

41 188 XRI Daytime 3 Orionids 117.7 94.5 15 44 

42 191 ERI ¬ Eridanids 137.5 45 -12.9 64 

43 198 BHY ± Hydrusids 143.8 36.3 -74.5 22.8 

44 206 AUR Aurigids 158.7 89.8 38.7 65.7 

45 208 SPE September  ́ Perseids 170 50.2 39.4 64.5 


Table 1 (continued). Geocentric data of 64 showers officially named during XXVII IAU General Assembly held in 

Rio de Janeiro in 2009. For each shower, the solar ecliptic longitude S, the radiant right ascension and declination 

g, g are given for J2000.0. 

 

No IAU Stream name S g g Vg 

 No & code (deg) (deg) (deg) (km/s) 

46 212 KLE Daytime a Leonids 181 162.7 15.7 43.6 

47 221 DSX Daytime Sextantids 188.4 154.5 -1.5 31.2 

48 233 OCC October Capricornids 189.7 303 -10 10 

49 246 AMO § Monocerotids 239.3 117.1 0.8 63 

50 250 NOO November Orionids 245 90.6 15.7 43.7 

51 254 PHO Phoenicids 253 15.6 -44.7 11.7 

52 281 OCT October Camelopardalids 193 166 79.1 46.6 

53 319 JLE January Leonids 282.5 148.3 23.9 52.7 

54 320 OSE  ̄ Serpentids 275.5 242.7 0.5 38.9 

55 321 TCB μ Coronae Borealids 296.5 232.3 35.8 38.66 

56 322 LBO ¶ Bootids 295.5 219.6 43.2 41.75 

57 323 XCB 3 Coronae Borealids 294.5 244.8 31.1 44.25 

58 324 EPR  ́ Perseids 95.5 58.2 37.9 44.8 

59 325 DLT Daytime ¶ Taurids 85.5 56.7 11.5 36.4 

60 326 EPG  ́ Pegasids 105.5 326.3 14.7 29.9 

61 327 BEQ ± Equuleids 106.5 321.5 8.7 31.6 

62 328 ALA § Lacertids 105.5 343 49.6 38.9 

63 330 SSE « Serpentids 275.5 242.8 -0.1 42.67 

64 331 AHY § Hydrids 285.5 127.6 -7.9 43.6 

before being published, each new shower will obtain a unique name, the IAU number and three 

letter code. After publication, the shower will be added to the Working List of Meteor Showers 

and the discovery announced, 

all showers which come up to the verification criterion will be included in the List of Established 

Showers, and after their approving by the C22 business meeting during the next General 

Assembly, all new established showers will from thereon be known by their official name. 

This makes the naming of meteor showers an ongoing effort. During the business meeting in 

Rio, the present members of Commission 22 agreed that the Task Group on Meteor Shower 

Nomenclature should be transformed into the Working group on Meteor Shower Nomenclature. The 

current members of the Working Group in the 2009-2012 triennium are: Peter Jenniskens (chair), 

Tadeusz J. Jopek (vice-chair), Vladimír Poruban, William J. Baggaley, Juergen Rendtl, Shinsuke Abe, 

Peter Brown and Pavel Koten. The main goal of the Working Group is similar to that in the previous 

triennium: maintaining and improving the Working List of meteor showers on the IAU Meteor Data 

Center website; assigning new names, numbers and three letter codes for the showers discovered in new 

surveys; and decide which new showers can be moved to the List of Established Showers, and thus 

obtain official names during the next IAU General Assembly in Beijing in 2012. 


5 Conclusions and Call for Contributions 

In 2009 for the first time in history of the Meteor Astronomy, 64 showers were officially named by the 

IAU. Their names are given in Table 1, and are posted on the IAU MDC website, see Jopek (2007). The 

current Working List of Meteor Showers has already 301 candidate showers that could receive official 

names if their existence can be confirmed. 

 Meteor astronomers can contribute to minimizing the confusion in the literature by checking the 

correct name of a shower when minor showers are discussed and by adhering to the newly adopted 

names (e.g., ”© Aquariids”, not ”© Aquarids”). Showers that are not yet in the Working List should be 

reported before they are mentioned in new (amateur or professional) literature. 

 Nomenclature is important in astronomy because it regulates the language used by astronomers. 

In our meteor community we started with this task quite recently. Our first experiences taught us that 

there is a real need to assign a particular name to a particular shower, but that this task alone is not 

simple. We needed to check, and check again, that those names were unique and did not lead to 

confusion. The task to establish if a new shower is a real entity or only ill defined, is even more difficult. 

To establish a shower is the end of a long process that can take many years. At the beginning of the 

process, no one can predict all problems that wait for a solution in a given case. 

 In the near future, the Working Group on Meteor Shower Nomenclature has several tasks to 

solve. At this moment, we are expanding the information on meteor showers included in the Working 

List to make the list more descriptive. As a very important next step, we consider developing more 

objective criteria to be used for verification whether a given shower can be considered an established 

one. More precise and regular meteor observation can be of invaluable help in this task. In addition, our 

community needs new theoretical concepts and studies that can make us more confident in recognizing 

meteor showers among a sporadic meteor background. 

Acknowledgements 

TJJ work on this paper was partly supported by the MNiSW Project N N203 302335. 

 

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Large Bodies Associated with Meteoroid Streams 

P. B. Babadzhanov1• I. P. Williams2• G. I. Kokhirova1,3

Abstract It is now accepted that some near-Earth objects (NEOs) may be dormant or dead comets. One 

strong indicator of cometary nature is the existence of an associated meteoroid stream with its 

consequently observed meteor showers. The complexes of NEOs which have very similar orbits and a 

likely common progenitor have been identified. The theoretical parameters for any meteor shower that 

may be associated with these complexes were calculated. As a result of a search of existing catalogues 

of meteor showers, activity has been observed corresponding to each of the theoretically predicted 

showers was found. We conclude that these asteroid-meteoroid complexes of four NEOs moving within 

the Piscids stream, three NEOs moving within the Iota Aquariids stream, and six new NEOs added to 

the Taurid complex are the result of a cometary break-up. 

Keywords near-Earth object · dormant comet · meteoroid streams · meteor showers · orbital evolution · 

Piscids stream · Iota Aquariids stream · Taurid complex 

1 Introduction 

Though there had been some prior speculation that Near Earth Asteroids could be responsible for some 

minor meteoroid streams, the first definite association was between the Geminid stream and asteroid 

3200 Phaethon (Whipple 1983, Fox et al. 1984). A number of Near Earth Asteroids were also found to 

be moving on orbits within the Taurid complex, though comet 2P/Encke also moves in this complex 

(Asher et al. 1993). More recently asteroid 2003EH1 was identified as moving on the same orbit as the 

Quadrantids (Jenniskens 2003, Williams et al. 2004) and the generally accepted hypothesis is that these 

are the result of the fragmentation of a larger comet so that these ‘asteroids’ are in reality comet 

fragments that are dormant or dead. All the associations mentioned above are based on the similarity of 

the orbits of the NEO and the meteor stream that gives rise to the observed shower at roughly the present 

time. 

2 Orbital Evolution 

Gravitational perturbations from the planets change all orbits over a period of time. However in the 

region of the Solar system that is of interest to us (the Earth-Jupiter region),  (the argument of 

 

P. B. Badadzhanov 

Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan 

I. P. Williams 

Astronomy Unit, Queen Mary University of London, E1 4NS, UK 

G. I. Kokhirova ( ) 

Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan. E-mail: kokhirova2004@mail.ru 


perihelion) passes through the range of values from 0 to 2 in a period of several thousand years. We 

call this one cycle of . Though there may be short term variations, the changes in the three orbital 

elements q (perihelion distance), e (eccentricity) and i (inclination) over one cycle of  are all 

essentially sinusoidal. The nodal distances, Ra and Rd also show the same characteristic variation. This 

variation is shown in Figure 1 for the three NEOs, 2002JS2, 2002PD11 and 2003 MT9. Some time ago 

(Babadzhanov and Obrubov 1992) pointed out that as the nodal distance will be equal to 1 AU at four 

different values of  during one cycle (clearly seen in Figure 1), four meteor showers originating from a 

single meteoroid stream can be formed. These four meteor showers consist of a night-time shower with 

northern and southern branches and of a day-time shower also with northern and southern branches. 

Figure 1. The variation in the nodal distances for three NEOs. 

 With a large number of NEOs currently being discovered, the probability that one has an orbit 

that is similar to a meteoroid stream at the present time by chance is high and, in order to establish a 

relationship with a stream, similarity of orbital evolution must be shown. This was carried out by 

Porubcan et al. (2004) through numerically integrating both the orbital evolution of the NEO and the 

meteoroid stream. Integrating the evolution of a meteoroid stream can be expensive due to the large 

number of particles involved and here we describe an alternative, and computationally cheaper, 

approach to the problem. 

 If the break-up of a comet was part of its history, then one might expect several large fragments 

to be present within the meteoroid stream. Such fragments should show the same evolutionary pattern as 

the stream. We thus integrate only the orbits of NEOs that might be suspected of being such fragments 

and calculate the characteristics of a theoretical meteor shower that would be formed at each location 

where the nodal distance of the NEO is 1 AU, assuming the orbital elements to be those of the NEO. We 

then have to ascertain whether a known meteor shower has these characteristics. 

3 ‘Asteroids’ Associated with Meteor Showers and Meteorite Streams 

Babadzhanov et al. (2008a, 2008b, 2009) have used the procedure described above in order to identify 

NEOs that can be associated with meteor showers that are related to three well know showers, the 

Piscids, the Taurids and the Iota Aquariids. Such associations indicate that they are likely to be 

fragments of a comet. The results are summarized in Tables 1, 2 and 3. In Tables 1-3 the values of the 


D-criterion which quantifies the similarity between the orbits of a meteor shower and an NEO are also 

given, calculated using the formula given by Steel et al. (1991) namely 

( ) ( ) 
  2sin 	  / 2 .

2

1 2

2

1 2

2

1 2

2 D 
 q q  e e  i i

All the determined values of the D-criterion satisfy D < 0.3 showing that the meteor showers and the 

NEOs under investigation move on very similar orbits implying that the meteoroid stream also contains 

large fragments of the parent comets. 

Table 1. Orbital elements for NEOs and showers in the Piscid Complex. 

Name q e i    D 

N.Piscids 0.40 0.80 6 174 3 8 - 

1997GL3 0.49 0.78 7 178 0 8 0.09

2000PG3 0.34 0.88 12 172 0 10 0.14

2002JC9 0.38 0.85 6 169 357 4 0.05

S.Piscids 0.44 0.82 3 179 7 -1 - 

1997GL3 0.45 0.80 6 173 3 -6 0.06

2000PG3 0.37 0.87 14 174 6 -1 0.21

2002JC9 0.38 0.83 6 167 0 -6 0.08

Ass.25 0.34 0.78 6 31 13 10 - 

1997GL3 0.45 0.80 6 21 10 11 0.11

2000PG3 0.36 0.87 13 37 19 20 0.15

2002JC9 0.38 0.83 6 30 16 13 0.06

Ass.30 0.27 0.83 11 30 14 3 - 

1997GL3 0.49 0.78 7 17 14 -2 0.24

2000PG3 0.35 0.88 13 38 28 1 0.10

2002JC9 0.38 0.85 5 28 19 3 0.15

Table 2. Orbital elements for NEOs and showers in the Taurid Complex. 

Name q e i    D 

N.Taurids 0.36 0.86 2.4 231 59 22 - 

16960 0.27 0.88 18.2 200 31 25 0.29 

1998VD31 0.49 0.81 6.7 244 65 29 0.16 

1999VK12 0.46 0.79 7.3 230 52 27 0.15 

1999VR6 0.53 0.76 7.9 231 50 28 0.22 

2003UL3 0.41 0.82 3.7 239 65 25 0.07 

2003WP21 0.45 0.80 1.5 239 63 23 0.11 

2004TG10 0.31 0.86 3.2 224 55 22 0.05 

S.Taurids 0.37 0.81 5.2 221 51 14 - 

16960 0.30 0.87 19.9 202 41 1.4 0.27 

1998VD31 0.52 0.81 9.4 247 70 11 0.17 

1999VK12 0.50 0.78 9.4 233 59 9 0.15 

1999VR6 0.49 0.78 9.1 228 53 8 0.14 

2003UL3 0.44 0.81 5.9 241 68 16 0.07 

2003WP21 0.49 0.79 3.8 242 66 17 0.12 

2004TG10 0.29 0.87 5.0 221 54 16 0.10 

°-Perseids 0.34 0.79 0.0 79 62 23 - 

16960 0.29 0.87 19.5 85 64 35 0.30 


Table 2. (continued) Orbital elements for NEOs and showers in the Taurid Complex. 

Name q e i λ α δ D 

1998VD31 0.52 0.81 9.3 76 69 33 0.24 

1999VK12 0.50 0.78 9.3 70 61 31 0.23 

1999VR6 0.49 0.78 9.1 66 56 30 0.22 

2003UL3 0.44 0.81 6.0 91 82 29 0.15 

2003WP21 0.48 0.79 3.8 81 75 27 0.15 

2004TG10 0.33 0.85 5.4 99 86 28 0.11 

β-Taurids 0.33 0.85 6.0 97 87 19 - 

16960 0.31 0.86 18.0 83 68 9 0.21 

1998VD31 0.49 0.81 6.6 79 74 15 0.17 

1999VK12 0.47 0.79 7.1 74 67 14 0.15 

1999VR6 0.53 0.76 7.8 62 59 11 0.22 

2003UL3 0.41 0.82 3.5 94 85 20 0.10 

2003WP21 0.45 0.80 1.4 85 77 21 0.15 

2004TG10 0.31 0.86 2.9 101 87 21 0.06 

Table 3. Orbital elements for NEOs and showers in the Iota Aquariid complex. 

Name q e i λ α δ D 

N.ι-Aquariids 0.26 0.86 8 132 330 -5 - 

2002PD11 0.32 0.85 7 150 342 -2 0.06 

2002JS2 0.38 0.83 8 150 341 -1 0.12 

2003MT9 0.16 0.94 4 116 319 -14 0.15 

S. ι-Aquariids 0.26 0.86 8 134 337 -13 - 

2002PD11 0.29 0.87 7 146 344 -12 0.04 

2002JS2 0.34 0.84 7 147 344 -13 0.08 

2003MT9 0.29 0.88 2 133 330 -13 0.11 

April Piscids 0.31 0.80 4 29 10 8 - 

2002PD11 0.29 0.87 7 29 11 10 0.09 

2002JS2 0.33 0.84 7 22 5 8 0.07 

2003MT9 0.16 0.94 4 323 10 2 0.21 

April Cetids 0.28 0.83 9 29 10 1 - 

2002PD11 0.32 0.86 7 26 13 0 0.06 

2002JS2 0.36 0.83 8 18 8 -4 0.08 

2003MT9 0.30 0.88 2 13 -1 1 0.13 

4 Conclusions 

In all three cases a number of NEOs were found that could have formed observable meteor showers. We 

thus conclude that the break up of a comet nucleus, leaving a number of fragments as well as a 

meteoroid stream, is common, supporting the view of Asher et al. (1993), and Jenniskens and Vaubillion 

(2008). We also conclude that a number of objects, currently classified as asteroids, are in fact cometary 

fragments. 


References 

D.J. Asher, S.V.M. Clube, D.I. Steel, Asteroids in the Taurid Complex. R.A.S. Monthly Notices 264, 93-105 (1993) 

P.B. Babadzhanov, Yu.V. Obrubov, Evolution of short-period meteoroid streams. Celestial Mech. Dyn. Astron. 54, 111-127 

(1992) 

P.B. Babadzhanov, I.P. Williams, G.I. Kokhirova, Near-Earth asteroids amongst the Piscids meteoroid stream. Astron. & 

Astrophys. 479, 149-255 (2008a) 

P.B. Babadzhanov, I.P. Williams, G.I. Kokhirova, Near-Earth asteroids in the Taurid complex. R.A.S. Monthly Notices 386, 

1436-1442 (2008b) 

P.B. Babadzhanov, I.P. Williams, G.I. Kokhirova, Near-Earth asteroids amongst the Iota Aquariid meteoroid stream. Astron. 

& Astrophys. 507, 1067-1072 (2009) 

K. Fox, I.P. Williams, D.W. Hughes, The Geminid asteroid (1983TB) and its orbital evolution. R.A.S. Monthly Notices 208, 

11-15 (1984) 

P. Jenniskens, 2003EH1 is the Quadrantid Shower parent comet, Astrophys. J. 127, 3018-3022 (2003) 

P. Jenniskens, J. Vaubaillion, Minor Planet 2008ED69 and the Kappa Cygnid meteor shower. Astrophys. J. 136, 725-730 

(2008) 

V. Porubcan, I.P. Williams, L. Kornos, Associations between asteroids and meteoroid streams. Earth Moon Planets 95, 697-

712 (2004) 

D.I. Steel, D.J. Asher, S.V.M. Clube, The Structiure and evolution of the Taurid complex. R.A.S. Monthly Notices 251, 632-

648 (1991) 

F.L. Whipple, 1983 TB and the Geminid Meteors. IAU Circular 3881, 1W (1983) 

I.P. Williams, G.A. Ryabova, A.P. Baturin, A.M. Chernitsov, The parent of the Quadrantid meteoroid stream and asteroid 

2003EH1. R.A.S. Monthly Notices 355, 1171-1181 (2004) 


Stream Lifetimes Against Planetary Encounters 

G. B. Valsecchi1• E. Lega2• Cl. Froeschlé2

Abstract We study, both analytically and numerically, the perturbation induced by an encounter with a 

planet on a meteoroid stream. Our analytical tool is the extension of Öpik’s theory of close encounters, 

that we apply to streams described by geocentric variables. The resulting formulae are used to compute 

the rate at which a stream is dispersed by planetary encounters into the sporadic background. We have 

verified the accuracy of the analytical model using a numerical test. 

Keywords meteoroid streams · planetary close encounters 

1 Introduction 

Meteoroids stream orbits can intersect, in specific phases of their evolution, the orbit of the Earth, 

leading to meteor showers. This causes not only the removal of particles from the stream due to 

collisions, but also potentially large perturbations of the remaining stream members due to planetary 

encounters. 

 We here examine the role of planetary encounters on the dispersion of streams using results from 

the analytical theory of close encounters. The reason for an analytical approach, which is inevitably 

affected by some approximations, is to be able to generalize the results to most orbits of interest. 

 To this purpose, we use the extension of Öpik’s theory of planetary close encounters [Öpik 1976] 

developed in recent years [Valsecchi et al. 2003]. In it, the gravitational model is a restricted, circular, 3-

dimensional 3-body problem in which, far from the planet, the small body moves on an unperturbed 

heliocentric keplerian orbit. The encounter with the planet is modeled as an instantaneous transition 

from the incoming asymptote of the planetocentric hyperbola to the outgoing one, taking place when the 

small body crosses the b-plane, the plane centered on the Earth and normal to the incoming asymptote of 

the planetocentric hyperbola (i.e., normal to the unperturbed geocentric velocity U of the small body). 

The direction of the latter is defined by two angles, (U, a)and (a, e, i) (see Figure 1), such that 

 	      !

" #$% &

and 

 '   %( ) %( *+

  ,   !

"  	  



G. B. Valsecchi ( ) 

IASF-Roma, INAF, Roma (Italy). E-mail: giovanni@iasf-roma.inaf.it 

E. Lega • Cl. Froeschlé 

Observatoire de la Côte d’Azur, Nice (France)


Figure 1. The geometric set up of Öpik’s theory: the Earth is at the origin of axes and moves in the direction of the 

y-axis, while the Sun is on the negative x-axis; the geocentric velocity vector of the small body is U,  is the angle 

between U and the y-axis, and  is the angle between the plane containing U and the y-axis, and the y-z plane. 

  	  

-   #$% )

 #$% &  	

.   %( ) *

 ,	 

#$%

  %( & 

) 

!/01/2

3

and 

 #$%

0

%( *  , /2

3/"!/41

 /2

3/"!/41
5617

 #$% *  ,  !/41 "  89: 7

 /2

3/"!/41
5617

where the upper sign in the expressions for Uz and cos  apply to encounters at the ascending node, and 

ns for Ux and sin  apply to post-perihelion encounters, while a is in AU and U is in 

units of the orbital velocity of the Earth. 

th remove me a stream. For a given stream, the 

ollisional cross-section of the Earth on the b-plane is 	b;

2

 with 

   < =

in the expressio

2 Earth Cross-section 

As already noted, collisions with the Ear teoroids from

c

; ; ;>

; U of the stream orbits are 

 [Jopek et al. 1999]. 

where r; is the radius of the Earth in AU, c = m/U2

 and m is the mass of the Earth in solar masses. The 

values of c and b are tabulated for various streams in Table 1; the values of 

taken from


Table 1. Values of c and b;, in Earth radii, for various streams of interest. 

Stream c b;

Leonids 0.013 1.01

Perseids 0.018 1.02

Lyrids 0.029 1.03

Quadrantids 0.038 1.04

Southern © quariids 0. 8 -A 03 1.04

Geminids 0.052 1.05

Northern Taurids 0.070 1.07

Northern §-Capricornids 0.12 1.11

Starting from [Valsecchi 2006], [Valsecch al. 2005] derived an algorithm to pass from bplane coordinates, close to a col et, to p o ents (assuming that all the 

other elements are kept consta te Öpik’s theory. The algorithm 

eglects second and higher order the origin. 

We here apply it to meteoroid streams encountering the Earth, keeping fixed a, e, i, 
 (and thus 

, , 

Figure 2. Left: the collisional cross-section of the Earth on the b-plane for the Northern 

Taurids; right: the same cross-section in the -M plane. 

 An explicit computation, along the lines of [Valsecchi et al. 2005], shows that the area of the 

ellipse in the 

?@;A  B;

C D %( & %( ) E%( *E

i et 

lision with the plan airs of 

t

rbital elem

nt), in the framework of

 terms in the distance from

he ex nded

n

U , ), and computing in the -M plane the area of the ellipse corresponding to a circle centered in 

the origin of the b-plane. 

 Figure 2 shows the collisional cross-section of the Earth on the b-plane for the Northern Taurids 

and the corresponding ellipse, computed analytically, in the -M plane, where  and M are the 

displacements in the respective angles relative to a central collision with the Earth. 

-M plane is 



>

where we take the values for a, i, ,  for the stream from [Jopek et al. 1999]. 


 To test the validity of the analytic approach, we have set up the following numerical experiment: 

in the restricted, circular, 3-dimensional 3-body problem, we start a suitable number of meteor particles 

t a large distance from the Earth; all the parti le orbits have the same a, e, i, 
, while , M are 

unter with the Earth, and 

mum geocentric distance 

long the perturbed trajectory is les equal to r;); interpolating in the grid, we can then find the initial 

Figure 3. The collisional cross-section of the Earth in the -M plane for the Northern Taurids (top left), the 

Geminids (top right), the Northern §-Capricornids (bottom left), and the Quadrantids (bottom right); superimposed 

on the analytical estimates (green lines) are the results of a numerical computation (red dots).

a c

distributed on a regularly spaced grid. We follow the particles through an enco

heck which of them actually collide with it (i.e., those for which the mini

s or 

c

a

values of , M for which the minimum geocentric distance is exactly r;. 

 We have used a fourth order Runge-Kutta integrator on the equations of motion regularized 

through Kustaanheimo-Stiefel regularization [Kustaanheimo and Stiefel 1965]. The reader can find in 

[Froeschlé 1970] a detailed derivation of the regularized equations of motions using the Lagrangian 

formalism and in [Celletti 2002] a review of regularization theory. As recently shown in [Celletti et al. 

2010] and in [Lega et al. 2010], when integrating orbits undergoing close encounters or even collisions, 

the existence of the singularity cannot be canceled, neither by changing the integration scheme, nor 

through a better precision computation; by singularity we mean that the solution does not behave as a 

power series about the point, while usual integration schemes are based on the development in power 

series of the solution. 

 The results of these computations are compared to those of our analytical approach in Figure 3 

and, as the plots show, are definitely satisfactory. 


3 Stream Dispersion 

The agreement between the analytic computation and the numerical check encourages us in the use of 

the former in order to study the dispersion induced in a stream by its passage close to the Earth. To get a 

quantitative description of stream dispersion, we start by recalling the orbital similarity criterion based 

on U, cos ,  and , the longitude of the Earth at the time of the meteor fall, introduced by [Valsecchi 

et al. 1999] to classify meteoroids in streams; it is based on the quantity DN defined by: 

FG

  H  !I

 < H#$% )  #$% )!I < JK

where 

nd 

%(*  *!



JK  L(+HMN

 < MON> MNN < MONN I

a

M*P   ++++MPP   %( B<*  *!



Q  Q! MQP   %(  ++++++MOPP   %( B<Q  Q!

As discussed in [Valsecchi et al. 1999], this criterion basically uses the geocentric speed, the 

anti-radiant coordinates (in a frame rotating with the Earth about the Sun) and the date of meteor fall, 

instead of the usual orbital elements. Of these quantities, encounters with the Earth affe

ina

ct only the antidiant coord tes, and therefore , , since U is an invariant; we disregard changes in , since they are 

far smaller than those in  and . 

In the approximation c

2

 << b2, valid for all of the streams we examined, we have that an 

ter with the Earth at unperturbed distance b rotates the geocentric velocity vector by an angle 

y: 

%( R S

=



ra

encoun

given b



Thus, in order to turn the direction of U (i.e., to change the radiant) by a significant quantity, say by  ¿ 

0.1 rad, we need an encounter with the Earth taking place at: 

TUV! W

=


	  

Table 2 gives the values of b ¿ 0.1 for the same streams of Table 1; note that for all the tabulated streams, 

with the exception of the Northern Taurids and the Northern §-Capricornids, the collisional crosssection is larger than the deflection cross-section. 


Table 2. Values of b¿0.1 and of b;, in Earth radii, for various streams of interest. 

Stream c bÀ¿0.1 b;

Leonids 0.013 0.25 1.01

Perseids 0.018 0.36 1.02

Lyrids 0.029 0.57 1.03

Quadrantids 0.038 0.75 1.04

Southern ©-Aquariids 0.038 0.75 1.04

Geminids 0.052 1.03 1.05

Northern Taurids 0.070 1.4 1.07

Northern §-Capricornids 0.12 2.3 1.11

 For a generic, not too large value of b, the area A(b) on the -M plane covered by the ellipse 

corresponding to a circle of radius b centered in the origin of the b-plane is given, as seen before, by: 

?  B

CX %( & %( ) E%( *E

 



Every year, when the Earth crosses a stream, a fraction of the latter will be removed, either by collision 

or by deflection b arth crossing the 

meteoroids have, in general, Á 2	, while the values of re racterized by ()min Á  Á 

()max, with values of ()m )max different for tr a tion of, among other things, 

the age of the stream itself. 

 Thus, the fraction f(b a stream, either by collision or by 

Y  ?

BJZ

y an angle larger than a suitable threshold. On the othe and, at the E r h

 0 Á M  a cha

in and ( each s eam, s func

) removed each year from

>

where  = ()max Â ()mi

Table 3 gives the fraction, to be divided by a suitable value of  for each stream, eliminated 

early by collisions and/or close encounter with the Earth; as it is readily seen, the Earth seems not to 

Table 3. Values of f(b¿0.1)· and of f(b;·, in Earth radii, for various streams of interest. 

Stream f(b

n. 

y

have a major effect in dispersing streams. Note, however, that some of the tabulated streams intersect 

the orbit of Jupiter, something that would greatly accelerate their dispersion. 

¿0.1)· f(b;·

Leonids Â 1.9·10-9

Perseids Â 6.8·10-11

Lyrids Â 4.1·10-12

Quadrantids Â 3.1·10-9

S -10 outhern ©-Aquariids Â 5.7·10 

Geminids Â 1.7·10-9

Northern Taurids 1.1·10 6.6·10 -8 -9

Northern §-Capricornids 1.2·10-8 2.5·10-9


4 Conclusion 

We have presented an analytic formula relevant for the rate of dispersion of a meteoroid stream induced 

by encounters and collisions with the Earth, and have checked its validity by numerical computations in 

the restricted, circular 3-body problem. 

 We plan to pursue this work, extending it to encounters with more than one planet, and 

vestigating the coupled effects of planetary close encounters and of secular perturbations. 

References 

A. Celletti, Singularities, collis regularization theory, in Si larities tional Systems. Applications to 

Chaotic Transport in the So enest and C. Froeschl ds.), Le in Physics 590, Springer Verlag, 

Heidelberg, Germany, pp. 1

A. Celletti, L. Stefanelli, E. Leg s on the g al dyna regularized restricted three-body 

problem with dissipation, su & Dynam. A 10) 

Cl. Froeschlé, Numerical Study s with Th s of Freedom. I. Graphical Displays of FourDimensional Sections, Astro 0) 

. J. Jopek, G. B. Valsecchi and Cl. Froeschlé, Meteoroid stream identication: a new approach. II. Application to 865 

photographic meteor orbits, Mon. Not. R. Astron. Soc. 304, 751-758 (1999) 

nd E. Stiefel, Perturbation theory of Kepler motion based on spinor regularization, J. Reine Angew. Math. 

(1965) [Lega et al. 2010] E. Lega, M. Guzzo and Cl. Froeschlé, Close encounters and resonances detection 

in three body problems through Kustaanheimo Stiefel regularization, preprint (2010) 

heory, Astron. 

Astrophys. 408, 1179-1196 (2003) 

. B. Valsecchi, A. Rossi, A. Milani and S. R. Chesley, The size of collision solutions in orbital elements space, in Dynamics 

ons of Planetary Systems (Z. KnezeviÃ and A. Milani, eds.), I.A.U. Colloquium 197, Cambridge Univ. Press, 

4 (2005)

in

ions and ngu in Gravita

lar System (D. B é e cture Notes 

-24 (2002) 

a Cl. Froeschlé, Some result

bmitted to Ce

lob

on. 

mics of the

l. Mech. 

 of Dynamical System

str (20

ree Degree

n. Astrophys. 4, 115-128 (197

T

P. Kustaanheimo a

218, 204-219 

E. J. Öpik Interplanetary Encounters, Elsevier, New York (1976) 

G. B. Valsecchi, Geometric Conditions for Quasi-Collisions in Öpik’s Theory, in Dynamics of Extended Celestial Bodies 

And Rings (J. Souchay ed.), Lecture Notes in Physics 682, Springer Verlag, Heidelberg, Germany, pp. 145-158 (2006) 

G lsecchi, T. J. Jope . B. Va k and Cl. Froeschlé, Meteoroid stream identication: a new approach. I. Theory, Mon. Not. R. 

Astron. Soc. 304, 743-750 (1999) 

G. B. Valsecchi, A. Milani, G. F. Gronchi and S. R. Chesley, Resonant returns to close approaches: analytical t

G

of Populati

pp. 249-25


Numerical Modeling of Cometary Meteoroid Streams Encountering Mars and 

Venus 

A. A. Christou1• J.Vaubaillon2

Abstract We have simulated numerically the existence of meteoroid streams that encounter the orbits 

of Mars and Venus, potentially producing meteor showers at those planets. We find that 17 known 

comets can produce such showers, the intensity of which can be determined through observations. Six of 

these streams contain dense dust trails capable of producing meteor outbursts. 

Keywords Mars · Venus · meteoroid streams · meteors · meteor showers · meteor outbursts 

1 Introduction 

Although no meteor showers have yet been observed at Venus and Mars, the undertaking of projects 

such as the U.S. rover Curiosity and the JAXA orbiter Akatsuki leads one to expect that such 

observations will be made, serendipitously or otherwise, in the near future. In support of these and 

follow-on missions with some meteor-detecting capability we carried out numerical simulations of 

cometary streams identified by previous work as potentially Mars- or Venus-encountering. We hope that 

these results will be used to guide future meteor surveys but also to interpret observations. 

2 Method 

Our method is that of Vaubaillon et al (2005a; 2005b). The motion of test particles initially ejected from 

the comet near perihelion according to the model of Crifo and Rodionov (1997) is propagated forward in 

time by numerical integration. The software then records all particles that approach the planet to within 

a few hundredths of an AU within the period 2000-2050. The initial sample of cometary candidates, 

either Intermediate Long Period Comets (ILPCs; P > 200 yr) or Halley Type Comets (HTCs; P < 200 

yr), is taken from Christou (2010). Cometary orbits from HORIZONS (Giorgini et al, 1996) were backintegrated in time, to simulate past perihelion passages. Relevant physical and orbital characteristics of 

the comets themselves may be found in Tables 2 and 4 of the work by Christou. As these comets’ orbital 

periods span two orders of magnitude, we have varied the number of perihelion passages considered for 

particle ejection on a case-by-case basis as shown in Table 1. In some cases, we have considered nonconsecutive perihelion passages (eg one out of every five) in order to extend the time period over which 

the comet’s, and hence the stream’s, orbital evolution can be investigated. 



A. A. Christou ( ) 

Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland, UK. E-mail: aac@arm.ac.uk

J. Vaubaillon 

IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris, France 


Table 1. Characteristics of all ILPCs and HTCs from Christou (2010) that satisfied the “shower” criterion in the 

numerical simulations. Column 2 gives the orbital period in years. Column 3 identifies the relevant planetary body 

as Venus (V) or Mars (M). Column 4 gives the number of perihelion passages where test particles where ejected 

from the comet. In cases where a mixture of consecutive and non-consecutive perihelion passages were considered 

for particle ejection we provide the number of said passages x and the increment y in the format (y)x in Column 5. 

Column 6 gives the date of the earliest perihelion passage considered in the simulations. 

Comet Period

(yr) 

Planet Number of per. 

pass. considered

Step Start 

Year

13P/Olbers 70 M 11 1 1313

27P/Crommelin 27 V 30 5(10) + 1(20) 326

35P/Herschel-Rigollet 155 V 17 1 Â6160

161P/Hartley-IRAS 21 M 21 5(6) + 1(15) 1104

177P/Barnard 119 M 10 1 1038

P/2005 T4 (SWAN) 29 V 11 1 1720

P/2006 HR30 (Siding Spring) 22 M 11 1 1751

C/1769 P1 (Messier) 2100 M 9 1 Â12087

C/1857 O1 (Peters) 235 V 8 1 Â336

C/1858 L1 (Donati) 2000 V 9 1 Â18372

C/1917 F1 (Mellish) 145 V 16 1 Â5496

C/1939 B1 (Kozik-Peltier) 1800 V 5 1 Â4689

C/1964 L1 (Tomita-Gerber Honda) 1400 V 4 1 Â3600

C/1984 U2 (Shoemaker) 270 M 10 1 11

C/1998 U5 (LINEAR) 1000 M 5 1 Â1989

C/2007 H2 (Skiff) 348 M 4 1 1016

5335 Damocles 41 M 18 5(8) + 1(10) 6

 The simulation of the generation and evolution of these meteoroid streams was run on 5 to 50 

parallel processors at CINES (France). Three size bins, equally log-spaced from 0.1 mm to 100 mm 

were considered. Ten thousand (104

) particles per size bin and per perihelion passage were simulated. In 

the analysis reported in this work, we do not discriminate between the different particle sizes. 

3 Results 

The results of the numerical simulations consist of state vectors of planet-encountering particles as 

defined in the previous Section. If the distribution of the particle orbit nodes on the planetary orbital 

plane encompasses the planetary orbit then we can say that a shower is present at that planet. This 

condition was quantified by highlighting all those test particles (TPs) that approached the planetary orbit 

to within 0.005 AU and binning them in the direction parallel to the planetary orbit in units of time. Bins 

of angular width corresponding to one hour of time were used. In the resulting distribution plot, the 

comet tests positive for a shower if any one of the bins contains more than one particle. 17 comets in our 

sample satisfied this criterion, which we will hereafter refer to as the “shower” criterion. 

 We separate those into two groups. The first group consists of those streams which exhibit a 

smooth distribution of particles on the planetary orbit plane, in other words a smooth “background” flux 

of meteoroids. An example of such a stream is shown in Figure 1. The left panel shows the spatial 

distribution of Venus-encountering particles from comet C/1858L1 (Donati). The orbit of Venus, 


indicated by the black curve, passes well within the distribution of particles in its orbit plane, indicating 

that this planet samples the core of the Donati stream. The right panel shows the distribution of particles 

that satisfy the shower criterion along the Venusian orbit as a function of the astronomical solar 

longitude S .The profile of this shower, and all other showers in Group I, appears to be well-behaved, in 

the sense that the distribution is fairly symmetric with a gradually varying slope and a single maximum. 

From this information, basic properties of the shower can be predicted. 

 

Figure 1. Left panel: Distribution of test particles ejected from comet C/1858 L1(Donati) that encountered Venus 

between the years 2000 and 2050. The points represent the locations of the particles, in cartesian heliocentric J2000 

coordinates and units of AU, as they cross the orbital plane of the planet. The black curve represents the orbit of 

Venus, with the direction of motion of the planet being from bottom to top. Right panel: Histogram of those 

particles shown on the left panel that approach the planet’s orbit to within 0.005 AU as a function of solar longitude 

in units of degrees. The size of each bin corresponds to one hour of time. 

 In Table 2 we provide such properties in the form of the solar longitude of the peak of the 

histogram (Column4), the shower duration in terms of the solar longitudes at which the first and last bins 

with more than one TP are encountered (Column5), the peak count of test particles per bin (Column6) 

and the total number of TPs that satisfied the shower criterion for that comet (Column7). 

Group II, also listed in Table 2, consists of those cometary streams, six in total, containing 

multiple density enhancements orders of magnitude higher than the background value. The fact that 

these enhancements only appear on certain years lead us to conclude that they correspond to individual 

dust trails which can yield meteor outbursts at the corresponding planet. An example of such a case, for 

comet C/2007 H2 (Ski), is shown in Figure 2. A number of planet-approaching trails are embedded in 

the background (left panel) resulting in at least two maxima in the corresponding shower density 

histogram (right panel). For two cases belonging to this group, that of 13P/Olbers and C/1998 U5 

(LINEAR), the background component is not well defined as its particle density is too low. These are 

indicated by a question mark (?). 


Table 2. Simulation results for all ILPCs and HTCs from Christou (2010) that satisfied the “shower” criterion. Whether a 

stream tested positive for membership in Group I or II as defined in the text is indicated in Columns 2 and 3 respectively. 

Comet Back

ground

Out 

bursts

Peak

S (°) 

Width 

(°), (hr) 

Peak

Count

Total

Count

13P/Olbers Y? Y 256.0 255.8-256.6 (33) 20 175

27P/Crommelin Y N 251.7 250.0-253.2 (47) 12 205

35P/Herschel-Rigollet Y N 175.1 175.0-175.2 (4) 2 11

161P/Hartley-IRAS Y Y 176.9 176.7-177.4 (31) 20 124

177P/Barnard Y Y 100.1 100.1-100.4 (16) 20 57

P/2005 T4 (SWAN) Y Y 210.5, 213.4 210.1-213.8 (56) 130 869

P/2006 HR30 (Siding Spring) Y N 303.1 Â (1) 2 30

C/1769 P1 (Messier) Y N 175.6 Â (1) 2 6

C/1857 O1 (Peters) Y N 207.6 206.6-208.0 (22) 28 273

C/1858 L1 (Donati) Y N 166.1 165.6-166.9 (21) 25 143

C/1917 F1 (Mellish) Y N 271.7 270.2-272.6 (35) 5 30

C/1939 B1 (Kozik-Peltier) Y N 289.1 288.8-289.6 (12) 25 133

C/1964 L1 (Tomita-Gerber Honda) Y N 139.2 137.8-139.8 (27) 6 43 

C/1984 U2 (Sho ma e ker) 

C/2007 H2 (Ski

Y N 214.6 214.3-214.6 (11) 10 51 

C/1998 U5 (LINEAR) Y? Y 235.7 235.4-235.9 (21) 100 524 

) Y Y 32.7 32.2-32.8 (28) 420 1526 

5335 Damocles Y N 308.7 308.4-308.8 (18) 5 35 

Figure 2. As Figure 1 but for Mars-encountering test particles ejected from comet C/2007 H2 (Ski). In the lefthand panel, the direction of the planet’s motion is from top to bottom. Note the numerous concentrations of particles 

within the stream’s cross-section. These result in multiple maxima well above the background intensity of the 

shower in the histogram on the right-hand side. 


4 Conclusions and Future Work 

In this work we have simulated numerically the structure of meteoroid streams that encounter the orbits 

of Mars and Venus. We have highlighted seventeen of those streams where the planet-encountering 

density of test particles is sufficiently high to allow estimation of the solar longitude of maximum 

meteor activity, constrain the duration of said activity and determine whether the stream cross-section as 

sampled by the planet contains denser trails of particles that could give rise to meteor outbursts. 

 To convert the density histograms into actual meteor activity profiles would require observations 

of these showers at Venus and Mars (Vaubaillon et al, 2005b). In the meantime, we intend to use the 

information in Tables 1 and 2 in combination with available knowledge of the properties of these comets 

from observations and dynamical studies to calibrate these histograms in the relative sense and conduct 

intra-sample comparisons. 

 We also intend to follow up on our discovery of outburst activity from some of these comets by 

initiating a new series of numerical experiments to model any such outbursts occurring in the near 

future. These would be prime targets for meteor searches at those planets in coming years. 

Acknowledgements 

The authors wish to thank the CINES team for the use of the super-computer. Part of the work reported 

in this paper was carried out during JV’s visit to Armagh Observatory in May 2009 funded by Science & 

Technology Facilities (STFC) Grant PP/E002242/1. Astronomical research at the Armagh Observatory 

is funded by the Northern Ireland Department of Culture, Arts and Leisure (DCAL). 

References 

Christou, A. A., 2010. Annual meteor showers at Venus and Mars: lessons from the Earth. MNRAS, 402, 2759–2770. 

Crifo, J.F.,Rodionov, A.V., 1997. The dependence of the circumnuclear coma structure on the properties of the nucleus. 

Icarus 129, 72–93. 

Giorgini, J.D., Yeomans, D.K., Chamberlin, A.B., Chodas, P.W., Jacobson, R.A., Keesey, M.S., Lieske, J. H., Ostro, S. J., 

Standish, E. M., Wimberly, R. N., 1996. JPL’s on-line solar system data service. Bull. Am. Astron. Soc. 28, 1158. 

Vaubaillon, J., Colas, F., Jorda, L., 2005. A new method to predict meteor showers I. Description of the model. Astron. 

Astrophys. 439, 751–760. 

Vaubaillon, J., Colas, F., Jorda, L., 2005. A new method to predict meteor showers II. Application to the Leonids.. Astron. 

Astrophys. 439, 761–770. 


Meteor Shower Activity Derived from “Meteor Watching Public-Campaign” in 

Japan 

M. Sato1• J. Watanabe • NAOJ Campaign Team 

Abstract We tried to analyze activities of meteor showers from accumulated data collected by publiccampaigns for meteor showers which were performed as outreach programs. The analyzed campaigns 

are Geminids (in 2007 and 2009), Perseids (in 2008 and 2009), Quadrantids (in 2009) and Orionids (in 

2009). Thanks to the huge number of reports, the derived time variations of the activities of meteor 

showers is very similar to those obtained by skilled visual observers. The values of hourly rates are 

about one-fifth (Geminids 2007) or about one-fourth (Perseids 2008) compared with the data of skilled 

observers, mainly due to poor observational sites such as large cities and urban areas, together with the 

immature skill of participants in the campaign. It was shown to be highly possible to estimate time 

variation in the meteor shower activity from our campaign. 

Keywords meteor showers · Geminids · Perseids · Orionids · public-campaign 

1 Introduction 

The public-campaign is one of the outreach programs which we perform in Japan, such as “Watch a 

comet”, “Watch planets”, “Watch a meteor shower” and “Watch an eclipse”. This is widely announced 

to the public by the National Astronomical Observatory of Japan, and we received more than a few 

thousands of reports every time. The main purpose of the campaigns is to interest the general public in 

astronomical phenomena. However, we have noticed that we might be able to extract some scientific 

results from these reports because of its huge numbers, for example, over 5,000. Therefore we tried to 

derive the hourly rate of meteor showers from accumulated data of some campaigns, which resulted in 

the success described in this paper. 

2 Report Form 

We recommend participants in the campaigns monitor the night sky more than 10 minutes when 

observing meteors by naked-eye. The participants are also recommended to report their results via the 

internet. We use a very simple form of questionnaire for this report because the main purpose is the 

outreach to the general public, including children. The participants in the campaigns answer questions 

about observation epoch, observation time duration, number of counted meteors, distinction of meteor 

shower from sporadic meteors, location, and so on. 

 

M. Sato ( ) • J. Watanabe • NAOJ Campaign Team 

National Astonomical Observatory of Japan; 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan. Phone: +81-422-343966; Fax: +81-422-

343810; E-mail: Mikiya.Sato@nao.ac.jp 


About observation epoch, participants are asked to choose the range of observed hour, for 

example, before 21h, 21-22h, 22-23h, ... 3-4h, after 4h on every day within the campaign period. About 

observation time duration, the choices are prepared as follows: less than 10 minutes, 11-20 minutes, 21-

30 minutes, 31-40 minutes, 41-50 minutes, 51-60 minutes. The number of counted meteors is also 

divided into nine levels which are 0, 1, 2, 3-5, 6-10, 11-20, 21-30, 41-50 and more than 51. Although 

each report is not as precise as those coming from the skilled visual observers, the huge number of 

reports gives us good reason to look into the data in detail on the scientific aspect. 

3 Method of Analysis 

We try to analyze the collected data in order to derive activity profiles of each meteor shower. Because 

we set the discrete steps in our campaign, we have uncertainty in the actual observation time for each 

participant. We adopted the median value of each step when we analyzed data. For example, in case of 

the range of 11-20 minutes for the time of observation duration, we considered that it was 15.5 minutes 

in average. We applied the same way in the case of the meteor numbers; if the report of the number of 

observed meteors is the range of 6-10, we regarded this data as 8. The derived hourly rate (HR) is 

expressed as 

HR =É (Nm*Nn) / É (Dm*Dn) * 60, 

where Dm (minutes) is the median of observation duration time, Dn is the number of corresponding 

reports collected within the specified time epoch, Nm is the median of the number of counted meteors, 

and Nn is the number of the corresponding reports. We could remove contribution of the sporadic 

meteors on the basis of the judgment of each participant in the report. 

4 Results 

We analyzed data collected during four campaigns: Geminids in 2007 and 2009, Perseids in 2008 and 

Orionids in 2009. The following figures show the results plotted together with the data obtained by 

skilled Japanese observers (NMS; Nippon Meteor Society) for comparison. It is clear that the time 

profiles of the meteor showers in the campaigns are similar to those obtained by skilled observers. In 

order to show the similarity, the vertical axis of the NMS data in each figure is multiplied by one fourth 

or one fifth, of which the values are shown in the vertical axis in the right of the figure. This factor is 

thought to originate from the poor observational condition in the participants in the campaign. Most of 

the participants are in the large city or urban area where they have heavy light pollution in general. 

 In the case of the Geminids in 2007 (Figure 1), the derived HR of the campaign was about onefifth of the data of NMS (Uchiyama 2007), while the time profile of the activity is similar to the NMS. 

On the other hand, the derived value of the HR in the campaign was one-fifth. This corresponds to the 

difference of a limiting magnitude of the observational condition between the campaign and NMS 

corresponds to 2.3 magnitude as population index (r) = 2.0 (IMO 2007). 

 In the case of the Perseids in 2008 (Figure 2), time variation of the hourly rate deduced from the 

campaign was also very similar to NMS (Uchiyama 2008), especially on August 12-13. The derived 

value of the HR was about one-fourth of the data of NMS. This corresponds to the difference of a 

limiting magnitude 1.9 magnitude as r = 2.1 (IMO 2008). 


0

10

20

30

-20h

22h

0h2h

5h-

-20h

22h

0h2h

5h-

-20h

22h

0h2h

5h-

-20h

22h

0h2h

   	



0

50

100

150

   


Campaign (left axis)

NMS* (right axis)

Dec 13-14 16-17 14-15 15-16 Time

(JST)

Figure 1. Hourly Rate of Geminids in 2007. The solid line with diamond marks is the results of our campaign and 

the dashed line with triangle marks is the results of the NMS (Nippon Meteor Society, Uchiyama 2007). 

0

5

10

15

20

-20h

22h

0h2h

4h-

-20h

22h

0h2h

4h-

-20h

22h

0h2h

4h-

-20h

22h

0h2h

4h-

   	



0

20

40

60

80

   


Campaign (left axis)

NMS (right axis)

Aug 11-12 14-15 12-13 13-14 Time

(JST)



Figure 2. Hourly Rate of Perseids in 2008. The solid line with diamond marks is the results of our campaign and 

the dashed line with triangle marks is the results of the NMS (Uchiyama 2008). *The number of data was very few. 

(n = 2) 

 In the case of the Orionids in 2009 (Figure 3), the derived HR of campaign was also about onefourth of the data of NMS (Iiyama 2009) like the case of the Perseids in 2008. The corresponding 

difference of a limiting magnitude is thought to be 2.0 magnitude when we apply the population index as 

r = 2.0 (IMO 2009). It should be noted that the time variation of the activity derived from our campaign 

seems to be smoother than the one by the NMS. Although this is mainly due to the huge number of 

reports, about 7,000, it may imply that the result by the huge number of observers may be better than 

that performed by a small number of skilled observers. We need further careful discussion on this point 

in the future. 


0

5

10

-22h

23h

0h1h2h3h

4h-

-22h

23h

0h1h2h3h

4h-

-22h

23h

0h1h2h3h

4h-

-22h

23h

0h1h2h3h

4h-

   	



0

20

40

   


Campaign (left axis)

NMS (right axis)

Oct 19-20 22-23 20-21 21-22 Time

(JST)

Figure 3. Hourly Rate of Orionids in 2009. The solid line with diamond marks is the results of our campaign and 

the dashed line with triangle marks is the results of the NMS (Iiyama 2009). 

 In case of the Geminids in 2009 (Figure 4), the derived HR of campaign was one-fifth of the data 

of NMS (Uchiyama 2009) from December 11 to 14. However, it changed to about one-seventh of the 

data of NMS from December 14 to 15. This corresponds to the variation of the limiting magnitude from 

2.3 to 2.8, when we assume the population index is r = 2.0 (IMO 2009 No.2). The reason for this change 

may be due to the change of the sky condition of participating observers who reported to the campaign. 

0

10

20

30

-21h

0h2h

4h-

-21h

0h2h

4h-

-21h

0h2h

4h-

-21h

0h2h

4h-

   	



0

50

100

150

   


Campaign (left axis)

NMS (right axis)

Dec 11-12 14-15 12-13 13-14 Time

(JST)

Figure 4. Hourly Rate of Geminids in 2009. The solid line with diamond marks is the results of our campaign and 

the dashed line with triangle marks is the results of the NMS (Uchiyama 2009). 


5 Conclusion 

We analyzed the data collected in public campaigns for four meteor showers, and confirmed that the 

derived time variation of the activities of meteor showers is very similar to those obtained by skilled 

visual observers. 

 On the other hand, the derived values of the HR in the campaigns are about one-fifth (Geminids 

in 2007 and 2009, except for from December 14 to 15) or about one-fourth (Perseids in 2008 and 

Orionids in 2009) compared to the data of the NMS. This is mainly due to poor observational sites for 

participants in the campaign, and probably partly due to immature skill of participants in the campaign. 

The difference of the limiting magnitude is estimated to be 1.9 ~ 2.3, as the average observational 

condition between the campaigns’ participants and skilled observers. Even if we should have such 

difference, it is clear that we have a potential to extract scientific results from such outreach programs 

related to the meteor showers mainly due to the huge number of reports. 

References 

O. Iiyama, Report of visual observation on Octover in 2009, Astron. Circ., J. Nippon Meteor Soc., 810, 4 (2009) 

IMO, Geminids 2007: Visual data quicklook, http://www.imo.net/live/geminids2007/ (2007) 

IMO, Perseids 2008: Visual data quicklook, http://www.imo.net/live/perseids2008/ (2008) 

IMO, Orionids 2009: Visual data quicklook, http://www.imo.net/live/orionids2009/ (2009) 

IMO, Geminids 2009: Visual data quicklook, http://www.imo.net/live/geminids2009/ (2009 No.2) 

S. Uchiyama, Quick results of Geminids in 2007, http://homepage2.nifty.com/s-uchiyama/meteor/shwr-act/12gemact/gemact.html, 4 (2007) 

S. Uchiyama, Quick results of Perseids in 2008, http://homepage2.nifty.com/s-uchiyama/meteor/shwr-act/08peract/peract.html, 3 (2008) 

S. Uchiyama, Quick results of Geminids in 2009, http://homepage2.nifty.com/s-uchiyama/meteor/shwr-act/12gemact/gemact.html, 1 (2009) 


Observations of Leonids 2009 by the Tajikistan Fireball Network 

G. I. Kokhirova1• J. Borovika2

Abstract The fireball network in Tajikistan has operated since 2009. Five stations of the network

covering the territory of near eleven thousands square kilometers are equipped with all-sky cameras with 

the Zeiss Distagon "fish-eye" objectives and by digital SLR cameras Nikon with the Nikkor "fish-eye" 

objectives. Observations of the Leonid activity in 2009 were carried out during November 13-21. In this 

period, 16 Leonid fireballs have been photographed. As a result of astrometric and photometric 

reductions, the precise data including atmospheric trajectories, velocities, orbits, light curves, 

photometric masses and densities were determined for 10 fireballs. The radiant positions during the 

maximum night suggest that the majority of the fireball activity was caused by the annual stream 

component with only minor contribution from the 1466 trail. According to the PE criterion, the majority 

of Leonid fireballs belonged to the most fragile and weak fireball group IIIB. However, one detected 

Leonid belonged to the fireball group I. This is the first detection of an anomalously strong Leonid 

individual. 

Keywords observations · fireball · atmospheric trajectory · radiant · orbital elements · light curve · 

density · porosity 

1 Introduction 

Leonids are a well known meteor shower capable of producing meteor storms around November 17. The 

parent body is comet 55P/Tempel-Tuttle. Complex observations of Leonids were performed both by 

ground-based and aircraft facilities during 1998-2002 and in 2006 in connection with the high activity of 

the shower at this period. Owing to extensive observational data, very important results were obtained 

which significantly complemented meteor physics and dynamics and physical properties of cometary 

meteoroids. For the first time, extraordinary high beginning altitudes of the luminosity of the Leonid 

meteors were registered, among which some reaching the limit of almost 200 km, and are a result of 

both physical-chemical features of Leonid meteoroids and conditions of ablation at such altitudes 

(Spurny et al. 2000a, Spurny et al. 2000b, Koten et al. 2006). 

 According to several authors (Vaubaillon et al. 2005, Maslov 2007, Lyytinen and Nissinen 

2009), high activity of the Leonids was predicted also in 2009. 

In this work, the results of the photographic observations of the meteor shower Leonids in 2009 

in Tajikistan are presented. 

 

G. I. Kokhirova ( ) 

Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan. E-mail: kokhirova2004@mail.ru 

J. Borovika 

Astronomical Institute of the Academy of Sciences of the Czech Republic, OndÌejov Observatory 


2 Observational Data 

The photographic observations of the Leonids activity in 2009 were carried out during November 13-21, 

by the fireball network which consists of 5 stations situated in the south part of the Tajikistan territory 

and covering the area of near eleven thousands square kilometers (Babadzhanov and Kokhirova 2009b). 

The mutual distances between them range from 53 to 184 km. All stations of the network are equipped 

with all-sky cameras with the Zeiss Distagon "fish-eye" objectives (f = 30 mm, D/f = 1:3.5) using sheet 

films 912 cm and by digital SLR cameras "Nikon D2X" and "Nikon D300" with the Nikkor "fish-eye" 

objectives (f = 10.5 mm, D/f = 1:2.8). 

 As a result of observations, 16 Leonid fireballs have been photographed, from which 9 were 

registered on the night of maximum activity of November 17/18. Among all, 3 fireballs have been 

photographed from five stations, 1 – from four, 2 – from three, 7 – from two, and 3 – from one station. 

 The time of fireball appearance was determined by the method of combination of fireball images 

obtained by fixed and guided cameras, or by the digital fireball image. During the maximum night, 

double station video observations were performed simultaneously (Koten et al., in preparation). For six 

fireballs reported here, more precise times of appearance could be extracted from the video tapes. Here 

we present precise data of only 10 photographed fireballs for which the coordinates of radiants, heights, 

velocities, light curves, and orbital elements were determined. The geometrical conditions for the other 

three double-station fireballs were not good enough to compute reliable trajectories. Fireball 

photographs were measured using the Ascorecord device. Digital fireball images were measured using 

the Ascorecord measuring software “FISHSCAN” developed by J.Borovika for measurements of 

scanned photographs of fireballs registered by all-sky cameras. 

 Astrometric reduction procedures are the same as that used by the European Fireball Network, 

which allows determination of the position of an object at any point of photographic frame with the 

precision of one arc minute or better (Borovika et al. 1995, Babadzhanov et al. 2009).

3 Atmospheric Trajectories 

The basic parameters of atmospheric trajectories of fireballs are given in Table 1, which contains the 

following data: the number of the fireball; the number of stations whose fireball photographs were 

involved in reduction; the type of camera which registered a fireball; date, the time of the fireball 

passage in UT; 

 Lis the longitude of the Sun corresponding to the time of the fireball passage (J2000.0); 

 vB and vE are the velocities at the beginning and at the end of the luminous trajectory; 

 hB and hE are the beginning and the terminal heights of the luminous trajectory above the sea 

level; 

 l is the total length of the luminous trajectory; 

 MP is the maximum absolute magnitude of the fireball;

 m
 is the initial mass of the meteoroid; 

 mE is the terminal mass of the meteoroid; 

 PE is the empirical end height criterion for fireballs; the type of fireball according to Ceplecha 

and McCrosky (1976) classification. The standard deviations given for the beginning and the 

terminal points reflect the precision in computing the heights and positions of fireballs in the 

atmosphere. In Table 1, FC means fireball camera and DC – digital ones.


Table 1. Data of the atmospheric trajectories of the fireballs. 

Fireball No. TN171109A TN171109B TN171109C TN171109D TN171109E TN171109F TN171109G TN131109 TN191109 TN211109 

Number of 

stations, 

type of camera 

5 stations FC 

2 stations DC 

(5 total) 

5 stations 

FC 

3 stations FC 

1 station DC 

(3 total) 

2 stations 

DC 

2 stations 

DC 

4 stations 

FC 

5 stations 

FC 

2 stations FC

1 station DC

(2 total) 

2 stations FC 

2 stations DC 

(3 total) 

2 stations FC 

1 stations 

DC 

(2 total) 

Date, 2009 

November 

17 

November 

17 

November 

17 

November 

17 

November 

17 

November 

17 

November 

17 

November 

13 

November 

19 

November 

21 

Time (UT) 

20h39m09s 

±10s 

20h49m56s 

±2s 

21h10m25s 

±2s 

21h24m05s 

±2s 

22h17m14s 

±2s 

22h37m37s 

±2s 

23h35m27s 

±2s 

22h09m01s 

±15s 

22h14m41s 

±15s 

21h47m39s 

±15s 

Lo235.504 235.511 235.526 235.535 235.572 235.590 235.627 231.535 237.589 239.590 

v
 (km s-1) 71.84±0.05 72.07±0.17 71.45±0.38 71.77±0.18 71.71±0.60 71.59±0.53 70.57±0.49 71.80±0.16 70.38±0.36 71.78±0.03 

hB (km) 111.21±0.01 112.38±0.02 107.66±0.09 114.56±0.02 114.06±0.01 106.45±0.29 106.68±0.01 108.50±0.04 104.26±0.01 110.33±0.02 

vE (km s-1) 71.84±0.05 72.07±0.17 71.45±0.38 71.77±0.18 71.71±0.60 71.59±0.53 70.57±0.49 71.80±0.16 70.38±0.36 71.78±0.03 

hE (km) 91.03±0.00 91.51±0.04 91.05±0.07 98.91±0.02 77.84±0.01 89.04±0.28 87.01±0.01 91.14±0.03 91.05±0.02 98.20±0.01 

l (km) 51.2 50.3 32.9 29.9 55.1 24.7 23.8 26.4 19.9 21.2 

Mmax -7.2 -8.5 -8.3 -3.7 -3.4 -9.1 -8.3 -8.0 -6.3 -7.5 

m
 (kg) 0.007 0.019 0.020 0.0002 0.00025 0.017 0.007 0.008 0.002 0.004 

mE (kg) 0 0 0 0 0 0 0 0 0 0 

PE -5.64 -5.90 -5.99 -5.76 -4.40 -5.98 -5.75 -5.82 -5.67 -6.34 

Type IIIA IIIB IIIB IIIB I IIIB IIIB IIIB IIIA IIIB 


 Note that for all fireballs it was impossible to determine decelerations along the trajectories 

reliably. The cameras are not particularly suitable for studying velocities of very fast meteors like 

Leonids, since the shutter frequency is relatively low (12–15 breaks per second). In some cases we had 

to rely on 3 or 4 shutter breaks. Therefore, only average velocities were computed and were assumed to 

be equal to the initial velocities. 

 One digital camera was equipped with symmetrical two-blade shutters rotating with the 

frequency 370 rotations per minute in front of the objective. In the fireball cameras, the shutter is placed 

near the focal plane. 

4 Photographic Beginning and End Heights of Visible Fireball Trajectories 

It is undoubted now that the limit of beginning heights of photographic high-velocity meteors reaches 

200 km. This fact was confirmed due to observations of the Leonids storm and outbursts during 1998-

2002. Use of the more sensitive than photographic techniques provided a large number of meteors 

registered at the beginning heights between 130-200 km (see, e.g., Spurny et al. 2000a, Spurny et al. 

2000b, Koten et al. 2006). 

 Our observational equipment does not allows us to record meteors at such heights because for 

the film’s sensitivity I = 125 ISO units the limiting magnitudes of registration of meteors is equal to 

about -4 magnitudes. While, as was shown by Spurny et al. (2000a) and Koten et al. (2006), a brightness 

of meteors at heights above 130 km is more than 0 magnitude, as a rule. 

 The range of beginning heights of fireballs under investigation photographed by all-sky cameras 

is between 112-104 km. On observations from the same point it is revealed that the beginning height 

registered by the digital camera is equal to 128-114 km. This difference is caused by greater sensitivity 

of the digital camera. The standard range of terminal heights is 98-87 km for all-sky cameras and is 

practically the same for digital ones. One case of terminal height of 77.8 km was fixed only by digital 

camera. 

 From all-sky photographic records of Leonid fireballs Shrbeny and Spurny (2009) obtained the 

value 111 ± 5 km for beginning height for the range of maximum absolute magnitudes from -3 to -14, 

and concluded that this is the limiting altitude of all Leonids registration by the all-sky cameras. 

 Spurny et al. (2000b), investigating photographic and TV heights of high-altitude Leonid 

meteors (Hb > 116 km), found that photographic beginning height of a meteoroid weakly depends on its 

initial mass or maximum absolute magnitude. But they revealed relatively strong correlation on end 

heights, namely, very bright Leonid meteors, and consequently with greater mass, penetrate more than 

20 km deeper than the faintest ones. 

 We plotted the same graphs using our data (Figures 1 and 2). The greatest magnitude and initial 

mass of described fireballs are Mmax = -9.0 and m
 = 0.02 kg i.e. our data represents a half of the data 

range used by Spurny et al. (2000b). 


Figure 1. The Leonid beginning and terminal heights as a function of maximum absolute magnitude. 

Figure 2. The Leonid beginning and terminal heights as a function of initial mass. 

Nevertheless, gradual dependences of beginning and terminal heights on maximum absolute magnitude 

and initial mass can be seen clearly. However, the fireball TN171109E with maximal magnitude –3.4 

and initial mass of only 2.510-4 kg was quite anomalous in this respect because it penetrated to the 

terminal height of 77.8 km, much deeper than more massive bodies. 

5 Radiants and Heliocentric Orbits of Fireballs 

Table 2 gives the results of determination of the coordinates of radiants and heliocentric orbits of the 

Leonid fireballs with their standard deviations. Here: 

 R, R are the right ascension and declination of the apparent radiant of fireball at the time of 

observation;

 zR is the zenith distance of the apparent radiant; 

 Qp is the convergence angle between two planes (for multi-station fireballs the largest angle 

from all combinations of planes); 

 v
 is the initial (preatmospheric) velocity; 

 g, g are the right ascension and declination of the geocentric radiant of fireball in J2000.0 

equinox; 


 vg is the geocentric velocity; 

 vh is the heliocentric velocity; 

 a, e, q, Q , , 
, i are the orbital elements in J2000.0 equinox. 

 The results of determination of the coordinates of radiants of Leonid fireballs photographed 

during November 13-21, 2009, in dependency on longitude of the Sun, are illustrated in Figure 3 and 

compared with previously published radiant drifts. Using only our data, the daily radiant drift was found 

to be  = 0.78Î

 and  = -0.53Î. Maximum activity of Leonids occurred on the night of November 

17/18 at the Solar longitude near 235.55o. The enhanced activity was predicted to be produced by two 

meteoroid trails ejected from the parent comet in 1466 and 1533, respectively. The annual Leonid 

shower was expected to peak approximately at the same time but with much lower activity. 

231 232 233 234 235 236 237 238 239 240

Solar Longitude (deg)

150

151

152

153

154

155

156

157

158

Right Ascension (deg)

19

20

21

22

23

24

25

Declination (deg)

Lindblad et al. (1993)

Kresák & Poruban (1970)

Cook (1973)

This work

J2000.0

Figure 3. Drift of Leonid radiant as a function of Solar longitude. Our observations are compared with three 

published drifts as quoted in the book of Jenniskens (2006). Linear fit to our data is also shown. All coordinates are 

given in the equinox J2000.0. 

Figure 4 shows the radiant positions of Leonids observed that night together with the predicted radiants 

for the 1466 and 1533 trails (Vaubaillon et al. 2009), the radiant of the annual shower according to 

various authors, and the so-called filament circle along which the radiants were spread during 2006 

Leonids (Jenniskens et al. 2008). The radiants of two Leonids (D and F) have too large error to judge 

their origin. The radiant C, with moderate error, lies in between the annual radiant and the 1466 trail. 

Quite precise radiants A, B, and G lie closer to the annual shower or to the filament circle. Radiant E is 

the only one, which can be attributed with some confidence to the 1466 trail. None of the seven fireballs 

can be firmly attributed to the 1533 trail. 


Table 2. Coordinates of radiants and heliocentric orbits of the fireballs. 

Fireball No. TN171109A TN171109B TN171109C TN171109D TN171109E TN171109F TN171109G TN131109 TN191109 TN211109 

oR

oR

153.87±0.04 

21.76±0.01 

153.77±0.02 

21.65±0.03 

153.70±0.14 

21.96±0.21 

153.73±1.11 

21.58±1.03 

154.17±0.01 

22.18±0.01 

154.42±0.58 

22.44±1.81 

154.51±0.03 

21.73±0.06 

151.04±0.09 

24.23±0.07 

155.26±0.07 

20.85±0.03 

157.51±0.07 

19.99±0.02 

cos zR 0.390 0.412 0.503 0.523 0.655 0.705 0.828 0.658 0.663 0.572 

Qop 74 55 25 5 33 17 74 51 62 58 

og

og

154.07±0.04 

21.66±0.01 

153.95±0.02 

21.56±0.03 

153.81±0.15 

21.89±0.21 

153.81±1.12 

21.52±1.04 

154.14±0.02 

22.16±0.01 

154.33±0.59 

22.40±1.83 

154.29±0.03 

21.71±0.06 

151.02±0.09 

24.21±0.08 

155.21±0.07 

20.81±0.03 

157.54±0.07 

19.92±0.02 

v
 (km s-1) 71.84±0.05 72.07±0.17 71.45±0.38 71.77±0.18 71.71±0.60 71.59±0.53 70.57±0.49 71.80±0.16 70.38±0.36 71.78±0.03 

vg (km s-1) 70.64±0.05 70.87±0.17 70.26±0.38 70.59±0.18 70.56±0.60 70.47±0.54 69.50±0.50 70.66±0.16 69.22±0.37 70.61±0.04 

vh (km s-1) 41.35±0.05 41.56±0.17 40.99±0.38 41.26±0.25 41.34±0.60 41.31±0.60 40.24±0.50 41.64±0.16 39.85±0.36 41.23±0.04 

a (AU) 10.44±0.49 13.15±2.80 7.73±2.11 9.61±2.12 10.40±6.04 10.05±5.66 5.05±1.15 14.91±3.38 4.28±0.60 9.21±0.28 

e 0.906±0.004 0.925±0.016 0.873±0.035 0.897±0.023 0.905±0.055 0.902±0.055 0.805±0.044 0.934±0.015 0.770±0.032 0.893±0.003 

q (AU) 0.984±0.000 0.984±0.000 0.985±0.001 0.985±0.004 0.985±0.000 0.984±0.003 0.983±0.000 0.983±0.000 0.986±0.000 0.984±0.000 

Q (AU) 19.90±0.98 25.32±5.59 14.48±4.23 18.23±4.24 19.81±12.08 19.11±11.32 9.12±2.30 28.85±6.76 7.58±1.20 17.44±0.56 

o 171.78±0.13 172.13±0.11 172.81±0.58 172.46±3.78 172.48±0.30 172.26±3.19 170.94±0.35 170.80±0.30 173.85±0.29 172.98±0.21 


o 235.50±0.00 235.51±0.00 235.53±0.00 235.53±0.00 235.57±0.00 235.59±0.00 235.63±0.00 231.53±0.00 237.59±0.00 239.59±0.00 

io 162.35±0.03 162.63±0.06 162.09±0.35 162.72±1.77 161.53±0.11 161.01±2.89 161.94±0.14 160.04±0.13 162.80±0.09 163.07±0.06 


155.5 155.0 154.5 154.0 153.5 153.0 152.5

Right Ascension (deg)

20.5

21.0

21.5

22.0

22.5

23.0

Declination (deg)

1533

1466

A

B

C

D

E

F

G

LPS

PG

KP+SS C

Observed radiants

Theoretical radiants for two trails

Annual Leonid radiants from different papers

2006 filament

 circle

Figure 4. Leonid radiants during the maximum on November 17, 2009. The observed radiants are shown with their 

errors and compared with theoretical radiants for the 1466 and 1533 trails (Vauballion et al. 2009), with the annual 

Leonid radiant at Solar longitude 235.55° according to Cook (1973) (C), Kresák and Poruban (1970) (KP), 

Lindblad et al. (1993) (LPS), Poruban and Gavajdová (1994) (PG), and Shrbený and Spurný (2009) (SS), radiant 

almost identical to (KP). The filament circle as observed in 2006 (Jenniskens et al. 2008) is also shown. All 

coordinates are given in the equinox J2000.0. 

 

 

 The mean geocentric radiant of Leonid fireballs on November 17/18, 2009 is  = 153.66o ± 0.17Î

and  = 22.11 o ± 0.31Î

, and is very close to the mean radiant values of Leonid fireballs in 1998  = 

153.63o,  = 22.04 o for L= 235.1Î (Betlem et al. 1999) and in 1999–2006  = 153.6o ± 0.4Î,  = 22.0o ± 

0.4Î for L= 235.1Î

 (Shrbeny and Spurny 2009). 

6 Light Curves of Fireballs 

The photometry of Leonid fireballs was performed by the method developed for photographs taken by 

the Czech fish-eye camera (Ceplecha 1987). This method allows determine a brightness of fireball with 

the photometric precision of ±0.2 stellar magnitudes in the whole field to a zenith distance to 70o

. 

Negatives, where fireball images have the best quality and the greater number of breaks, were used for 

photometry. The photometry of two fireballs observed only by the digital cameras was performed with 

the FISHSCAN program. 

 Maximum absolute magnitudes and initial photometric masses are given in Table 1. The 

maximum absolute magnitude ranges between –3.4 and -9.1, the masses are between 0.2 and 20 grams. 

The typical observed light curve of the fireball TN171109B is presented in Figure 5. We also present the 

light curve of deeply penetrating fireball TN171109E in Figure 6. All registered fireballs have smooth 

light curves with no significant flares. Almost all curves have asymmetric shape and the maximum 

points shifted towards to the end of luminosity. 


-9

-8

-7

-6

-5

114 112 110 108 106 104 102 100 98 96 94 92 90

Absolute magnitude

Height [km]

Figure 5. Observed light curve of Leonid fireball TN171109B. 

130 120 110 100 90 80 70

Height [km]

-4

-3

-2

-1

0

1

2

Absolute magnitude

Figure 6. Observed light curve of Leonid fireball TN171109E. The empty circles are approximate 

magnitudes from the spectral video camera. 

7 Physical Properties of Leonid Meteoroids 

The values of the PE criterion given in Table 1 and calculated by the following expression: 

E R PE 
 lg 0.42lgm 1.49lgv 1.29lgcosz    , 

where  – is the air density (g/cm3

) at the hE – the terminal height of the fireball visible trajectory, 

indicate the penetration ability of a meteoroid; m is given in grams and v in km/s. For the majority 

of fireballs the PE values are typical for the fireballs of type IIIB according to Ceplecha and McCrosky 

(1976) classification or they lie close to the IIIA/IIIB boundary (PE = –5.70). The fireballs of group IIIB 

are produced by the meteoroids with the lowest bulk density equal to © = 0.2 g/cm3

, and represent the 

weakest cometary material. The fireball TN171109E was classified as type I, which is the absolute 

exception among Leonids and quite unusual for fireballs on cometary orbits. Type I fireballs are 


normally associated with stony meteoroids of density about 3.5 g/cm3

. The existence of different fireball 

types among the Leonid fireballs was also confirmed by Shrbeny and Spurny (2009). They recognized 

fireballs corresponding to types II, IIIA, and IIIB according to the PE criterion and made a conclusion 

on non-homogeneity of the parent comet. 

 Babadzhanov and Kokhirova (2009a) on the basis of photographic observations of Leonids 

determined mean bulk density equal to © = 0.4 ± 0.1 g/cm3

, and mean mineralogical density of ©m = 2.3 

± 0.2 g/cm3

 of these meteoroids. Using the relation between these densities, the porosity of Leonid 

meteoroids was calculated to Ï = 83%. These confirm the very porous and fragile (weak) structure of the 

Leonid meteoroids. It turned out that density and porosity of Leonid meteoroids are very similar to those 

of Draconid meteoroids, which also were found to be porous aggregates of constituent grains with bulk

density of © = 0.3 g/cm3 and porosity of p = 90% (Borovicka et al. 2007). 

 The value of mean bulk density © = 0.2 g/cm3

 of Leonid meteoroids under investigation obtained 

according to the calculated values of PE criterion and fireball type, is in good agreement with mentioned 

results of investigation of density and porosity of cometary meteoroids. The nature of TN171109E with 

likely much larger bulk density is puzzling in this context. Nevertheless, small strong constituents 

penetrating much deeper than the majority of the meteoroid were observed in Leonids before (Spurný et 

al. 2000a, Borovika and Jenniskens 2000). TN171109E is the first case where a whole Leonid 

meteoroid was so strong that it was classified as type I meteoroid. 

8 Conclusions 

As a result of photographic observations by the Tajikistan fireball network during November 13-21, 

2009, 16 Leonid fireballs were registered, from which 9 fireballs were captured at the night of maximum 

on November 17/18. This number confirms the forecasted enhanced activity of Leonids in 2009. 

 The results of determination of precise atmospheric trajectories, velocities, initial masses and 

orbits of 10 Leonid fireballs are presented in this study. 

 The daily radiant drift of Leonids was found to be  = 0.78Î

 and  = -0.53Î. The radiant 

positions during the maximum night suggest that the majority of the fireball activity (i.e. the majority of 

flux of Leonid meteoroids larger than 0.2 g) was caused by the annual stream component with only 

minor contribution of the 1466 trail. According to the PE criterion, the majority of Leonid fireballs 

belonged to the most fragile and weak fireball group IIIB, corresponding to the meteoroid mean bulk

density of about 0.2 g/cm3

 and porosity of 80–90%. However, one detected Leonid of a size of about 5 

mm belonged to the fireball group I and likely had a bulk density of few g/cm3

. This is the first detection 

of an anomalously strong Leonid individual. 

Acknowledgments

The authors would like to express gratitude to specialists of the Institute of Astrophysics of Tajik

Academy of Sciences M.I.Gulyamov, A.Sh. Mullo-Abdolov, A.O.Yulchiev, U.Kh.Khamroev, 

S.P.Litvinov, and to Dr. P. Koten (Astronomical Institute of the Academy of Sciences of the Czech 

Republic) who participated in the observations and data reduction. This work was supported by the 

International Science and Technology Centre Project Ñ-1629. 


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System Research 43 No. 4, 353-363 (2009) 

P.B. Babadzhanov and G.I. KokhirÎva, Densities and porosities of meteoroids, Astron. & Astrophys. 495, Issue 1, 353-358 

(2009a) 

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(2009b) 

H. Betlem, P. Jenniskens P., J. van’t Leven, et al., Very precise orbits of 1998 Leonid meteors. Meteoritics & Planetary 

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J. Borovika, P. Spurny, J. Keclikova, A new positional astrometric method for all-sky cameras. Astron. & Astrophys. Suppl. 

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J. Borovika, P. Spurny, P. Koten, Atmospheric deceleration and light curves of Draconid meteors and implications for the 

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P. Jenniskens, Meteor Showers and their Parent Comets. Cambridge Univ. Press, New York, 790 p. (2006) 

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P. Koten, P. Spurny, J. Borovika, S. Evans et al., The beginning heights and light curves of hight-altitude meteors. 

Meteoritics & Planetary Sciences 41 No. 9, 1305-1320 (2006) 

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CHAPTER 2: 

ASTEROIDS AND METEOR SHOWERS: 

CASE OF THE GEMINIDS 


Multi-Year CMOR Observations of the Geminid Meteor Shower 

A.R. Webster1• J. Jones1

Abstract The three-station Canadian Meteor Orbit Radar (CMOR) is used here to examine the Geminid 

meteor shower with respect to variation in the stream properties including the flux and orbital elements 

over the period of activity in each of the consecutive years 2005 – 2008 and the variability from year to 

year. Attention is given to the appropriate choice and use of the D-criterion in the separating the shower 

meteors from the sporadic background. 

Keywords meteor · orbital elements · radar · D-criterion 

1 Introduction 

Located near Tavistock, Ontario (43.26N, -80.77E) and operating at a frequency of 29.85 MHz, the 

three-station Canadian Meteor Orbit Radar (CMOR) has been in place for over a decade accumulating a 

considerable amount of data relating to meteor orbits, sporadic and shower (Jones et al, 2005). Here, 

observations of the Geminid meteor shower are used from an extended four year period (2005 – 2008) to 

cover the full range of solar longitude over which there is significant activity. The shower is known for 

its consistent return each year and the objective here is to look for variability in the waxing and waning 

stages in a given year and from year-to-year. 

2 Observational Data 

The radar is a back-scatter system and, aside from the occasional down-time for maintenance or weather 

events, operates continuously with a wide-angle all-round view of the sky. While sporadic meteors are 

widely spread in elevation and azimuth, the position of a detected shower meteor is governed by the 

shower radiant direction resulting in an effective “echo-line” on which the observed meteor lies (Kaiser, 

1960). As the radiant rises, passes through transit and sets, the echo-line moves with it in a perpendicular 

fashion and with a minimum range which increases with the radiant elevation. As a result of this motion, 

the observed radar echoes move in range over the period when the radiant is above the horizon leaving a 

characteristic range-time “signature”; this is illustrated in Figure 1 for the Geminid shower. It will be 

noted that from the latitude of the radar site, this signature covers a total period of about 16 hours with a 

gap of about 3 hours centred on transit time. 

In developing and applying the analysis routines, data from the year 2008 were first used 

over the anticipated period of significant activity, 251° to 267° in Solar Longitude (S.L.); the routines 

were then applied to the years 2005 – 2007 to complete the picture. The approach taken is illustrated in 

 

A. R. Webster ( ) • J. Jones 

Meteor Physics Group, The University of Western Ontario, London, ON. N6A5B9, CANADA. E-mail: awebster@eng.uwo.ca 


Figure 2. The first filter employed (rather generous) restrictions on the values of Right Ascension (RA), 

Declination (Dec) eccentricity (e) and semi-major axis (a). The final selection of Geminid meteors made 

use of the D-criterion. 

The application of the first filter to the 2008 data is shown in Figure 3, where the “range-time’ 

signature of the Geminids is apparent, as is the peak in shower activity around 261° S.L. 

 

Figure 1. The “range-time” signature of the Geminid shower; the sharp minimum range will be noted. 

 

Figure 2. Extraction of Geminid meteors from the total observed. 

261.0 261.5 262.0 S. L., deg.

Range, 

km.

50

100

150

200

250

300

Geminids

Transit

07:26 U.T.


December 2008

250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Range, km

50

100

150

200

250

Solar Longitude, deg.

250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Range, km.

50

100

150

200

250

1st filter - Geminids

All meteors 44697 meteors

4674 meteors

Figure 3. Total observed meteor echoes over the period 251° to 267° in S.L. in 2008 (top) and those extracted by 

the 1st filter (bottom). 

The limits imposed in this first cut were deliberately made fairly wide to ensure that a high 

fraction of the Geminids present were selected, in the expectation that some sporadic meteors would be 

included. With this in mind, the application of the oft-used D-criterion was thought to be appropriate in 

reducing this contamination. The three versions based on the 5 orbital elements, q, e, i, ,  commonly 

used were examined; Southworth and Hawkins (1963), Drummond (1981) and Jopek (1993) shown 

below (DSH, DD and DJ respectively), i.e., 

(1a) 

(1b) 

(1c) 

where 21 and  involve i, , and . Application in turn of these to the data from the 1st filter results 

in the D values shown in Figure 4. The reference values used for the orbital elements were the mean 

values of the accepted meteors except for the longitude of the ascending node where the solar longitude 

at the time of occurrence is appropriate. 

   2

21

2

1 2

2

2 21

1 2

2

1 2

2

2

2sin

2 2

2sin 



 



  



 



   



 



 
  

I e e

DSH e e q q

2

0

21

2

1 2

2

0

21

2

1 2

1 2

2

1 2

2 1 2

2 180 180 



 



  



 



   



 



 

 













 



 













 




 I e e

q q

q q

e e

e e DD

  2

21

2

1 2

2

21

2

1 2

2 1 2

1 2

2

2

2sin

2 2

2sin 



 



  



 



   



 



 

 













 




 I e e

q q

q q D e e J


250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Drummond, DD

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Southworth/Hawkins, DSH

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Solar Longitude, deg

250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Jopek, DJ

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 4. The D-criteria values as applied to the meteor orbital elements after the application of the 1st filter. The 

90% cut-off values of DSH = 0.24, DD = 0.21 and DJ = 0.30 will be noted (see text and Figure 5.). 

 As can be seen in Figure 4, while the distributions are similar, the appropriate cutoff value to be 

used would be somewhat different. A better idea of this may be obtained from Figure 5 showing the 

differential and cumulative distributions for each of the criteria. In deciding what value of D to use for 

accepting the data, visual examination of Figure 4 suggests that at the time of the Geminid maximum, a 

significant number of shower meteors have D value higher than that normally used in this kind of 

application. Further, the waxing and waning of the activity in Figure 4 suggests that most of the meteors 

belong to the Geminid shower. Given the evidence in Figures 4 and 5, it was decided to apply a value of 

0.21 to the Drummond data corresponding to the acceptance of ~90% of the meteors. This resulted in 

the reduction of presumed Geminids from 4674 to 4272 (Figure 6). 


D value

0.0 0.1 0.2 0.3 0.4 0.5

Density (number in 0.01 interval)

0

100

200

300

400

D value

0.0 0.1 0.2 0.3 0.4 0.5

Cumulative (number > D), %

1

10

100

D

S/H

J

D

S/H

J

Figure 5. The differential (left) and cumulative (right) distributions of the three D-criteria DSH, DD and DJ. 

Solar Longitude, deg.

250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Range, km

50

100

150

200

250

1st filter + DD 4272 meteors

Figure 6. The range-time distribution of selected meteors after applying the 1st filter and the Drummond D-criterion 

with DD = 0.21 cut-off (2008 data). 

 These remaining 4272 meteors in 2008 were assumed to represent a good estimate of the total 

observable Geminids with little contamination from other sources. The resulting echo rate, that is the 

total number of Geminid meteors seen by the radar over the period of significant activity, is presented in 

Figure 7, expressed in terms of the rate before and after transit and the total for a given night’s 

observation. It will be remembered that the effective observing periods amounted to about 6.5 hours 

each before and after transit and the numbers presented represent a total for these periods. 


Geminids, December 2008

250 252 254 256 258 260 262 264 266 268

Number of echoes

0

100

200

300

400 # before transit

# after transit

Solar Longitude, deg.

250 252 254 256 258 260 262 264 266 268

Total number of echoes

0

200

400

600

800

Figure 7. The echo rate seen by the radar over the period of significant activity; the rate before and after transit 

(top) and the total rate for each night (bottom). 

 The same routines were then applied to the data from the years 2005-2007 and the results 

consolidated into the activity shown in Figure 8. Again, for clarity, the total results for each night also 

are presented here. Since the transit time repeats every year, the fractional 0.25 day in the year causes a 

regression in the transit about 0.25° in Solar Longitude from year-to-year resulting in the “filling-in” 

seen in Figure 8. The classic rise to a maximum at about 261° in S.L. followed by a rapid fall in activity 

is apparent with little in the way of fluctuations. The residual activity at both ends of the observing 

period appears to be genuine. 


Solar Longitude, deg.

250 252 254 256 258 260 262 264 266 268

Number of echoes

0

200

400

600

800

1000

yr2008 4272

yr2007 3943

yr2006 3953

yr2005 3765

250 252 254 256 258 260 262 264 266 268

Number of echoes

100

200

300

400

500

Figure 8. The activity of the Geminid shower over the four year period 2005 – 2008 showing: (top) the individual 

rates before and after transit; (bottom) the total number on a given night in each year for clarity. 

 The remarkable consistency from year-to-year is evident; it will be noted also that results are 

missing for 3 days in 2005, but were they available and in line with the trend, a further 200 or so would 

be added to the 2005 total. 


 The next step was to look at the variations in the various stream parameters including the orbital 

elements, velocities etc. All of these were available for each of the 15933 Geminid meteors selected, and 

linear regression was applied to plots of each parameter versus Solar Longitude. Examination of Figure 

8 suggests that activity peaks at about SL = 261° and this was used as the reference point. Figure 9 gives 

an example of this procedure showing the variation in orbital inclination. Similar results of this exercise 

for all the parameters are summarized in Table 1; the quoted uncertainties are standard errors. 

(S.L. - 261), deg.

-10 -8 -6 -4 -2 0 2 4 6 8

inclination, i

0

10

20

30

40

50

60

Figure 9. The variation in orbital inclination with Solar Longitude with SL = 261° as the reference. The linear 

regression line is shown. All the 15933 selected Geminid meteors over the 4 year period are included. 

Table 1. Mean Values and Variations with Solar Longitude 

y = b0 + b1*(SL-261) 

y b0 b1

 Semi-major axis, a, AU. 1.426 ± 0.003 +0.003 ± 0.001 

 Eccentricity, e 0.8964 ± 0.0003 +0.0007 ± 0.0003 

 Inclination, i, deg. 23.13 ± 0.05 -0.13 ± 0.02 

 Argument of perihelion, deg. 324.9 ± 0.04 -0.06 ± 0.01



 Right Ascension, deg. 112.64 ± 0.02 +1.07 ± 0.01 

 Declination, deg. 31.93 ± 0.02 -0.18 ± 0.01 

 Geocentric, vg, km/s 34.35 ± 0.05 -0.02 ± 0.02 

 Heliocentric, vh, km/s 33.79 ± 0.04 +0.01 ± 0.01 


3 Discussion and Comments 

The results presented here are part of the ongoing and continuous operation of CMOR over extended 

periods with stable properties. This allows confidence in comparative studies encompassing several 

years. As with any such system, there are uncertainties in the measured quantities, but the extensive 

numerical data gathering properties of CMOR allow meaningful answers to be drawn. 

Examining the data from a 4 year period, with separated samples before and after transit, allows 

~ 8 samples per degree in Solar Longitude. Although not entirely unexpected, the consistency of the 

flux of Geminid meteors from year-to-year is notable as are the relatively smooth variations from dayto-day. Given that, there is a suggestion of fluctuations in activity around the peak at SL ~261° which 

may be consistent with the more frequently sampled results presented by Rendtel (2005) using visual 

observations. The residual activity at each end of the period in this study is believed to represent 

Geminid meteors; a separate study using CMOR suggests that such activity may extend from late 

November to early January (Brown et al, 2010). 

 The changes in the orbital elements over the duration of the shower are notably small. For 

example, given the evidence in the literature for decreasing magnitude distribution exponent, generally 

associated with the Poynting-Robertson effect, a more significant increase in the semi-major axis, a, 

might be expected as the Earth moves from the inside to the outside of the stream. 

 The D-criterion has been, and is, used extensively in looking for connections between bodies 

orbiting the Sun and the three versions considered here have been use with differing cut-off values 

depending on the observing system used. In his paper, Drummond suggested values of DD = 0.105 and 

DSH = 0.25 in linking meteor streams and parent bodies based on the visual, photographic and radar data 

presented by Cook (1973) and Marsden (1979). Williams and Wu (1993) used the Drummond version 

with DD again equal to 0.105. Galligan (2001) investigated the three criteria using the AMOR system in 

New Zealand and suggested a 90% recovery using DSH = 0.20, DD = 0.18 and DJ = 0.23. It might be 

remarked that different magnitude ranges can be involved in such studies which may influence the 

effectiveness; for example, AMOR has a limiting magnitude of around +13.5, CMOR of ~ +8.5 with 

visual and photographic usually brighter than ~ +6.0. We believe that the choice depends on the system, 

the interactions being studied and the quality of the data and that the use of DD = 0.21 is appropriate 

here. 

 A further version of the D-criterion was introduced by Valsecchi et al (1999) which has found 

much favour in some applications. Instead of using the five orbital elements for comparison, the 

geocentric velocity (speed and direction in Earth oriented coordinates) is used. This is particularly useful 

when the data is available as direct, rather than derived, measurements. In the case of CMOR, all of the 

elements are derived from interferometric and time-delay measurements, though we are looking into this 

approach and developments. It is noted that Galligan (above) also considered this method and found it to 

be comparable and preferable in some circumstances. 

Acknowledgements 

The authors would like to acknowledge the many helpful discussions with those involved with the 

operation and data handling of CMOR, P. Brown, M. Campbell-Brown, Z. Krzemenski and R. Weryk, 

and the substantial support from the NASA Meteoroid Environment Office. Thoughtful insights from 

discussions with G. Valsecchi at Meteoroids 2010 are also acknowledged. 


References 

Brown, P., Wong, D., Weryk, R. and Wiegert. P., 2010, Icarus, 207(1), 66-81. 

Cook, A.F., 1973, Evolutionary and Physical Properties of Meteoroids, U.S. Gov. Printing Office, NASA SP-319, 183-319. 

Drummond, J.D., 1981, Icarus, 45, 545-553. 

Galligan, D.P., 2001, Mon. Not. R. Astron. Soc., 327, 623-628. 

Jopek, T.J., 1993, Icarus, 106, 603. 

Jones, J., Brown, P., Ellis, K.J., Webster, A.R. Campbell-Brown, M.D., Krzemenski, Z. and Weryk, R.J. : 2005, Planetary 

and Space Science, 53, 413 – 421. 

Kaiser, T.R., 1960, Mon. Not. R. Astron. Soc, 121, 3, 284–298. 

Marsden, B.G., 1979, Catalogue of Cometary Orbits, 3rd ed., Cent. Bureau Astron. Telegrams, I.A.U., SAO, Cambridge, 

Mass. 

Rendtel. J., 2004, Earth, Moon and Planets, 95 (1-4), 27-32, DOI10.1007/sl1038-004-6958-5. 

Southworth, R.B. and Hawkins, G.S., 1963, Smithson. Contrib. Astrophys., 7, 262-285. 

Valsecchi, G.B., Jopek, T.J. and Froeschle, C., 1999, Mon. Not. R. Astron. Soc., 304, 743-750. 

Williams, I.P. and Wu, Z., 1993, Mon. Not. R. Astron. Soc., 262, 231-248. 


The Distribution of the Orbits in the Geminid Meteoroid Stream Based on the 

Dispersion of their Periods 

M. Hajduková Jr.1

Abstract Geminid meteoroids, selected from a large set of precisely-reduced meteor orbits from the 

photographic and radar catalogues of the IAU Meteor Data Center (Lindblad et al. 2003), and from the 

Japanese TV meteor shower catalogue (SonotaCo 2010), have been analyzed with the aim of 

determining the orbits’ distribution in the stream, based on the dispersion of their periods P . The values 

of the reciprocal semi-major axis 1/a in the stream showed small errors in the velocity measurements. 

Thus, it was statistically possible to also determine the relation between the observed and the real 

dispersion of the Geminids. 

Keywords meteoroid · meteor showers · meteoroid streams 

1 Introduction 

One of the most intense annual meteor showers, Geminids are produced by a meteoroid stream unusual 

in having small orbits with aphelia well inside the orbit of Jupiter and perihelia close to the Sun. The 

Geminid’s parent body, asteroid (3200) Phaethon, with a perihelion distance of only 0.14 AU and semimajor axis 1.27 AU, appears to be an inactive cometary nucleus (Gustafson 1989, Beech et al. 2003). 

The Phaethon‘s active period was determined by Gustafson (1989) as not more than 2000 years ago. 

This is in agreement with the age of the meteoroid stream, calculated dynamically, and which 

corresponds to a few thousand years (Ryabova 1999, Beech et al. 2002). The model for the formation of 

the Geminid meteor stream was developed by Fox and Williams (1982). Later, Williams and Wu (1993) 

produced a theoretical model showing that meteoroids ejected from Phaethon could have evolved, under 

the influence of planetary perturbations and radiation pressure, into Earth crossing orbits. The orbits of 

the Geminid meteoroids with aphelia far inside the orbit of Jupiter lead to the fact that the gravitational 

effects of the other outer planets are negligible. Furthermore, there have not been any close encounters 

significantly affecting their orbits during at least the last ten thousand years (Ryabova 2007). Thus, the 

orbital elements of most stream meteoroids vary little; furthermore, the spread in these elements is 

approximately invariant with the passage of time (Jones and Hawkes, 1986). Therefore, the structure of 

the Geminid meteoroid stream is dominated by the initial spread of meteoroid orbits. Ryabova (2001, 

2007) developed a model explaining the two branches of the stream as being formed by the disintegration of the parent body, due to differences in orbital parameters of the individual particles ejected 

from the parent body before and after perihelion. The small perihelion distance may cause an intense 

thermal processing, which affects the physical properties of the meteoroids (Beech et al. 2003) and the 

higher density of Geminids, in comparison with other meteoroids (Babadzhanov and Konovalova, 

2004). 



M. Hajduková Jr. ( ) 

Astronomical Institute of the Slovak Academy of Sciences, 84504 Bratislava, Slovakia. E-mail: astronomia@savba.sk


The present paper, based on a statistical analysis of a large set of precisely-reduced meteor 

orbits, shows the dispersion in the orbital elements of Geminid meteoroids for different mass ranges of 

the particles. For the analysis, data from the photographic and radar catalogues of the IAU Meteor Data 

Center (Lindblad et al. 2003) were used. Among the 4,581 photographic orbits, 385 meteoroids 

belonging to the Geminid meteor shower were identified using Southworth-Hawkins D-Criterion for 

orbital similarity (Southworth and Hawkins, 1963) and fulfilling the condition DSH Á 0.20. Similarly, 

we applied a limiting value of DSH = 0.25 to 62,906 radar orbits and obtained 887 Geminids. The 

photographic data in the MDC catalogues are limited to the mass range of 10-4 kg (3m) and radar data to 

10-7 kg (5m); for more powerful radars to 10-9 kg (15m). To cover a broad mass range of the particles, 

quality orbits from the reduced database of 8,890 meteoroid orbits (Vereš and Tóth, 2010) of the 

Japanese TV meteor shower catalogue (SonotaCo 2009) were also used, giving 1,442 Geminids for the 

limiting value of DSH = 0.20, detected mostly up to +2 magnitude. 

2 Observed Dispersion of Orbital Elements 

It is obvious that examination of the structure of meteoroid streams by means of the period of the 

individual particles is possible only for the short period meteoroid streams. The meteoroid streams with 

long periods of several decades to centuries, e.g. Lyrids, Perseids, Orionids, Leonids and Eta Aquarids, 

have heliocentric velocities close to the parabolic limit. The observational errors of those meteor streams 

greatly exceed the real deviations from the parent comet’s orbit. Given that errors in the heliocentric 

velocity are a significant source of uncertainty in semi-major axes determination, it should be mentioned 

that errors in velocity determination in the IAU MDC can reach the value vH  10 km s-1. The errors 

differ both for individual catalogues and for individual meteor showers. The largest spread was found 

for the Perseids from the catalogues with a lower precision, reaching values of 10 Â 15 km s-1

(Hajduková 1993, 2007). But this is certainly not the case with the Geminids, the mean heliocentric 

velocity of which is only 36.6 km s-1. The values of the reciprocal semi-major axis in this stream show 

small errors in the velocity measurements. The different precision of measurements, depending on the 

observation technique as well as on the quality of observations, causes a natural spread in the orbital 

elements. Figure 1 shows the dispersion in eccentricities, perihelion distances and semi-major axes. For 

the sake of comparison, we also plotted the orbital element of Geminid’s parent body, which was 

obtained using the computer program Dosmeth (Neslušan et al. 1998). 

Figure 1. Observed spread in the orbital elements of the 835 photographic (+) and 887 radar (Ô) Geminids of the 

IAU MDC, and of the 1442 TV Geminids from the Japanese meteor shower catalogue ([). For the sake of 

comparison, we also plotted the orbital elements of the Geminid’s parent body (Õ).


 The observed dispersion of the orbit periods is shown in Figure 2 (left), separately for all three 

investigated data, obtained by different techniques. The mean period of the Geminids was found to be 

1.59 and 1.48 years, derived from the photographic and video orbits, with a standard deviation of 0.37 

and 0.24 respectively. The mean period of the fainter particles from the radar observation is 1.69 years, 

but the period determination from individual orbits varies from 0.53 to 7.54. It is clear that we are not 

dealing with a stream all of whose meteors have exactly the same period, but obviously the last observed 

spread in the values exceeds the real deviations. 

Figure 2. Comparison of observed dispersion of the period of revolution (left) and of the reciprocal semimajor axes 

(right) of Geminids from three dierent sets of data in term of mass particles, obtained using dierent techniques 

and dierent measurement methods. The observed dispersion is greater for radar Geminids in comparison with both 

other sets of data. 

 A complete study about the real dispersion of orbital periods in meteor streams was made by 

Kresák (1974), which showed that the observed dispersion of the semi-major axes involves the real 

orbital dispersion plus errors, which are greater by a factor of 104 for the orbits of the meteoroids than in 

the case of well-determined cometary orbits. Poruban (1984), in his study of the dispersion of the 

orbital elements of meteor orbits, analyzing 153 photographic Geminids determined the mean orbital 

period at 1.66 years. The widely-observed dispersion is also seen in distributions of the reciprocal semimajor axes (Figure 2 right). The radar data in general are of a lower precision, which is obvious from the 

greater spread in the values of the semi-major axes in comparison with both other catalogues, in which 

the precision is comparable. The observed dispersion of the semi-major axis, defined by the standard 


deviation, is 0.079 for the photographic and 0.158 for the radar Geminids from the IAU MDC. The 

smallest standard deviation of 0.071 was derived from the Japanese video data, probably because we 

used a strict selection (Vereš and Tóth, 2010) of high quality video meteor orbits. 

3 The Accuracy of the Semi-major Axes and their Dispersion 

We tried to estimate the real dispersion of the semi-major axis within the meteor stream by comparing 

the observed dispersions in different catalogues of orbits, where the observational errors are different. 

However, for each observation technique, there are different sources of errors, which produce the 

observed dispersion in semi-major axis determination. On the basis of this fact, we chose in our analysis 

the median aM as the most representative value of semi-major axis a, because the arithmetic mean value 

a is strongly affected by extreme deviations caused by gross errors. It was shown (Kresáková 1974) that 

the medians of (1/a)M in several major meteor showers do not differ from those of their parent comets 

beyond the limits of statistical uncertainty. The dispersion of the semi-major axis within the meteor 

stream is described by the median absolute deviation M in term of 1/a: M (1/a) = | (1/a)1/2 Â (1/a)M |, 

where (1/a)1/2 are limiting values of the interval, which includes 50 percent of all orbits. The probable 

range of uncertainty is determined by ± n

-1/2M (1/a), where n is the number of the meteor orbits used for 

the median determination (1/a)M . For the sake of comparison, we also derived the deviation of the 

median 1/a from the parent body: (1/a)Ph =| (1/a)M Â (1/a)Ph |, where the (1/a)Ph is the reciprocal semimajor axis of Geminid’s parent body Phaethon. 

 The results of our analysis are shown in Table 1 as in Figure 3. Table 1 summarizes the 

numerical results obtained separately for the three different sets of Geminids. The mean value, the 

standard deviations and the median semi-major axis a are listed in the first part of the Table. The second 

part contains the mean value, the standard deviations and the median reciprocal semi-major axis 1/a. 

The median absolute deviation M in term of 1/a, and the deviation of the median 1/a from the parent 

body, are listed in the last part of the Table. For comparison, we also list the chosen orbital elements 

from 3200 Phaethon. 

Table 1. Numerical data obtained separately for the three different sets of Geminids observed by different 

techniques. n – number of meteors; , 	/a – the mean values; a, 1/a – the standard deviations; aM , (1/a)M – the 

median a, 1/a respectively; M (1/a) – the median absolute deviation; (1/a)Ph – deviation of the median 1/a from 

the parent body. 

 aM a 	/a (1/a)M 1/a M (1/a) (1/a)Ph

nphot = 835 1.361 1.356 0.180 0.744 0.737 0.079 0.040 0.049 

ntv = 1442 1.302 1.285 0.185 0.777 0.778 0.071 0.029 0.008 

nrad = 887 1.402 1.351 0.343 0.749 0.740 0.159 0.081 0.047 

Phaethon 1.271 0.787 

The dispersion, described by the median absolute deviation M in terms of 1/a obtained from the 

photographic, video and radar catalogues, are 0.040, 0.029 and 0.081 AU-1 respectively. This 

corresponds to a deviation of ±0.01 years for the Geminid’s period obtained from the precise 

photographic measurements. This is in agreement with a study by Kresáková (1974), which analyzed 

meteor orbits obtained from the most precise double-station photographic programs; it was shown that 

the dispersion of the 157 analyzed Geminids is moderate and the period can be put into narrow limits, 

between 1.62 and 1.64 years. 


 

Figure 3. Dispersion in terms of 1/a for Geminids observed by three different techniques. Bold line – the deviation 

of the median 1/a from the parent body (1/a)Ph; thin line – the absolute median deviation M in terms of 1/a; 

vertical line – Phaethon. 

 The deviation of the median reciprocal semi-major axis from the parent body, obtained from 

Japanese video orbits, is only 0.008 AU-1, whereas for the orbits from the IAU MDC catalogues, it is 

approximately five times greater. For the video and radar orbits, (1/a)Ph is considerably smaller than M

(1/a), but for photographic orbits, it is slightly bigger. 

4 Conclusions 

The analysis of a sufficient number of meteor orbits of chosen catalogues of meteors observed with 

different techniques allowed us to estimate the dispersion of semi-major axes within the Geminid meteor 

stream. It was shown that the dispersion differs considerably between the three different sets of data in 

terms of the different masses of the particles. This may be a consequence of different measurement 

errors for different observation techniques, as well as of different dispersions in the orbital elements for 

particles belonging to different mass ranges. The dispersion was found to be higher for small particles 

obtained by radars in comparison with the results of video and photographic observations of large 

meteoroid particles. It was found that the real dispersion of the Geminids is at least 2 times smaller than 

indicated by the observations, based on all three investigated catalogues. The deviations in terms of 1/a

determined from the investigated catalogues range from ±0.029 to ±0.081 AU-1. This corresponds to a 

deviation of ±0.01 years for the Geminid’s period obtained from the precise measurements and of ±0.02 

years using data of lower accuracy. 

Acknowledgements 

This work was supported by the Scientic Grant Agency VEGA, grant No 0636. 


References 

Babadzhanov, P. B. and Konovalova, N. A.: 2004, Astron. Astrophys. 428, 241 

Beach, M.: 2002, Mon. Not. R. Astron. Soc. 336, 559 

Beach, M.: 2003, Meteoritics and Planetary Science 38, No.7, 1045 

Fox, K. and Williams, I. P.: 1983, Mon. Not. R. Astron. Soc. 205, 1155 

Gustafson, B. A. S.: 1989, Astronom. Astrophys. 225, 533 

Hajduková, M. Jr.: 2007, Earth, Moon and Planets 102, Issues 1-4, 67 

Hajduková, M. Jr.: 1994, Astronom. Astrophys. 288, 330 

Jones, J. and Hawkes, R. L.: 1986, Mon. Not. R. Astron. Soc. 223, 479 

Kresák, L. and Kresáková, M.: 1974, Bull. Astron. Inst. Czech. 25, No.6, 336 

Kresáková, M.: 1974, Bull. Astron. Inst. Czech. 25, No.4, 191 

Lindblad, B., Neslušan, L., Poruban, V. and SvoreØn, J.: 2003, Earth, Moon, Planets 93, 249 

Neslušan,L., SvoreÙ, J., Poruban, V.: 1998, Astron. Astrophys. 331, 411 

Poruban, V.: 1978, Bull. Astron. Inst. Czech. 29, No.4, 218 

Ryabova, G. O.: 1999, Solar System Research 33, 258 

Ryabova, G. O.: 2001, Proc. Meteoroids 2001 Conf. ESA Pub. Div., Noordwijk, 77 

Ryabova, G. O.: 2007, Mon. Not. R. Astron. Soc. 375, 1371 

Southworth, R. R. and Hawkins, G. S.: 1963, Smithson. Contr. Astrophys. 7, 261 

SonotaCo: 2009, WGN, Journal of the IMO 37, 55 

Vereš, P. and Tóth, J.: 2010, WGN, Journal of the IMO 38, 1 

Williams, I. P. and Wu, Z.: 1993, Mon. Not. R. Astron. Soc. 262, 231 



CHAPTER 3: 

SPORADIC AND INTERSTELLAR METEOROIDS 


Inferring Sources in the Interplanetary Dust Cloud, from Observations and 

Simulations of Zodiacal Light and Thermal Emission 

A.C. Levasseur-Regourd1• J. Lasue1

Abstract Interplanetary dust particles physical properties may be approached through observations of 

the solar light they scatter, specially its polarization, and of their thermal emission. Results, at least near 

the ecliptic plane, on polarization phase curves and on the heliocentric dependence of the local spatial 

density, albedo, polarization and temperature are summarized. As far as interpretations through 

simulations are concerned, a very good fit of the polarization phase curve near 1.5 AU is obtained for a 

mixture of silicates and more absorbing organics material, with a significant amount of fluffy 

aggregates. In the 1.5-0.5 AU solar distance range, the temperature variation suggests the presence of a 

large amount of absorbing organic compounds, while the decrease of the polarization with decreasing 

solar distance is indeed compatible with a decrease of the organics towards the Sun. Such results are in 

favor of the predominance of dust of cometary origin in the interplanetary dust cloud, at least below 1.5 

AU. The implication of these results on the delivery of complex organic molecules on Earth during the 

LHB epoch, when the spatial density of the interplanetary dust cloud was orders of magnitude greater 

than today, is discussed. 

Keywords interplanetary dust · light scattering properties · thermal properties · atmospheric entry ·

comets · asteroids · meteoroids

1 Introduction 

The question of the origin of the dust particles that are permanently replenishing the interplanetary dust 

cloud, thus allowing the appearance of the zodiacal light, has been extensively discussed all over the 

past years. Before the 1980s, the main source was assumed to be the dust released by active cometary 

nuclei in the interplanetary dust cloud (Whipple, 1955). In 1983, the detection of asteroidal bands and 

cometary trails by the Infrared Astronomical Satellite (IRAS) has allowed some authors to estimate that 

the main source was dust released by asteroidal collisions or disruptions (see e.g. Sykes and Greenberg, 

1986). While minor sources of dust, such as dust from Jupiter and Saturn systems and dust of interstellar 

origin, have also been detected by Ulysses, Galileo and Cassini spacecraft (see e.g. Grün et al., 2001 and 

references therein; Taylor et al., 1996), the main source of interplanetary dust in the Earth environment 

has remained an open question. 

It is most likely that the sources of most meteor streams are comet nuclei and that those of most 

meteorites are asteroidal fragments. Nevertheless, it is difficult to estimate whether comets or asteroids 

predominantly contribute to the zodiacal cloud, even in the vicinity of the Earth, and finally to know 

 

A. CLevasseur-Regourd ( • J. Lasue 

UPMC (Univ. Paris 6), UMR 8190, BC 102, 46-45, 4ème, 4 place Jussieu, 75252 Paris Cedex 05, France. Phone: +33 1 4427 4875; Fax: 

+33 1 4427 3776; E-mail: aclr@aerov.jussieu.fr 

Lunar and Planetary Institute, 3600 Bay Area Blvd., Houston, TX 77058, USA 

LANL, Space Science and Applications, ISR-1, Mail Stop D-466, Los Alamos, NM 87545 USA 


what are the sources of sporadic meteors and of micrometeorites. These questions are all the more 

important that the interplanetary dust cloud, even if assumed to be stationary, is likely to undergo 

numerous evolution processes, e.g. with fragmentation, weathering and partial sublimation of its dust 

particles. We will propose some answers through an approach that relies upon inversion of observations 

of the near-Earth zodiacal light and zodiacal thermal emission, and upon interpretations through 

numerical simulations. Finally, we will compare our results with those obtained for cometary dust and 

for the interplanetary dust through other approaches, and assess their implication for the delivery of 

carbonaceous compounds to the early Earth. 

2 Results Derived From Observations 

Observations from Earth’s orbit in the visual and near infrared domains allow for the detection of the socalled zodiacal light and zodiacal thermal emission (see e.g. Levasseur-Regourd et al., 2001 and 

references therein). The zodiacal light is a faint veil of solar light, brighter towards the Sun and the nearecliptic invariant plane of the solar system. The zodiacal thermal emission is the most prominent 

component of the light of the night sky in the 5 to 100 !m region, at least away from the galactic plane. 

2.1. Near-Earth Zodiacal Light and Zodiacal Thermal Emission 

The zodiacal light actually originates in the scattering of solar light by dust particles. The sharp increase 

of its brightness Z, towards the Sun and the invariant plane, indicates an increase in the space density of 

the interplanetary dust cloud, which forms a thick disk around the Sun. A slight enhancement in 

brightness, the gegenschein, also takes place in the anti-solar region; it corresponds to a backscattering 

effect. As expected from the scattering of randomly polarized solar light in an optically thin medium, the 

zodiacal light is partially linearly polarized. The polarization P is defined as the ratio of the difference to 

the sum of the brightness components respectively perpendicular and parallel to the scattering plane; it is 

slightly negative in the gegenschein region. 

The brightness Z (in W m-2 sr-1

!m-1) and the polarization P (in percent), as determined as 

functions of the helio-ecliptic latitude and ecliptic longitude, after correction for the invariant plane 

inclination (e.g. Leinert et al., 1998; Levasseur-Regourd et al., 2001), provide an estimation of the 

foreground noise induced by the zodiacal light, together with an optimization of the epochs of 

observations of faint extended astronomical objects. The zodiacal thermal emission, whose maximum is 

slightly above 10 !m, as observed from the Earth environment, corresponds to a temperature of about 

250 K along the line-of-of sight. In the very near infrared domain, by 0.8 to 1.2 !m, the thermal 

emission is still negligible and the scattered light prevails. For larger wavelengths, observation of the 

thermal emission (which is isotropic) provides an easier detection of local heterogeneities than 

brightness emission, as recently illustrated by the detection from Spitzer spacecraft of the dust trail of 

comet 67P/Churyumov-Gerasimenko, the target of the Rosetta mission (Kelley et al., 2008). 

2.2. Data Inversion and Local Results 

Since the concentration and the temperature of the dust are changing significantly with the solar distance 

R, the local brightness and thermal emission are expected to vary along the line-of-sight for Earth or 

near-Earth based observations. Besides, it cannot be assumed that the interplanetary dust cloud is 

homogeneous and that the properties of the dust (e.g. albedo, size distribution) are the same everywhere 


in the cloud. The brightness, as well as its perpendicular and parallel components, and the thermal 

emission are thus integrals that need to be, at least partially, inverted. A rigorous inversion is feasible, 

for a line-of-sight tangent to the direction of motion of the observer and for the section of the line-ofsight where the observer is located. This approach has, up to now, provided bulk values of some local 

properties in the vicinity of the Earth (Table 1). To retrieve local information in regions that are not 

located on the orbit of the Earth, inversion mathematical methods, leading to comparable results, have 

been independently initiated by Dumont and Levasseur-Regourd (1988) and by Lumme (2000). 

Table 1. Parameters relevant to the local properties of the interplanetary dust particles and their dependence with 

distance to the Sun R (0.3 to 1.5 AU range) in the near-ecliptic invariant plane (adapted from Levasseur-Regourd et 

al., 2001): Linear polarization P at 90° phase angle, temperature T, geometric albedo A and space density. 

Parameter Heliocentic gradient Comment 

P90°(R) 

T(R) 

A(R) 

Space density(R) 

30 R+0.5 ± 0.1 (%) 

250 R-0.36 ± 0.03 (K) 

A0 R-0.34 ± 0.05 

10-17R-0.93± 0.07 (kg m-3)

Evolution of local polarization 

Not a perfect black-body 

Evolution of geometric albedo 

Most likely 1/R

One result is related to the shape of the local polarimetric phase curve (see Fig. 11 in LevasseurRegourd et al., 2001). At 1.5 AU from the Sun in the invariant plane, it is smooth, with a slight negative 

branch, an inversion angle in the 15° to 20° range and a positive branch with a maximum of about 30 

percent. This trend indicates that the scattering particles are irregular with a size greater than the 

wavelength of the observations, i.e. about 1 !m; it also suggests, assuming that the Umov empirical law 

is valid, that the particles have quite low an albedo. Another key result is related to the variations with 

the solar distance R (between 0.3 and 1.5 AU) of some local properties, which approximately follow 

power laws. The trend obtained for the local polarization at 90° phase angle, a ratio independent upon 

the concentration (see Fig. 5 in Levasseur-Regourd et al., 1991), establishes that the interplanetary dust 

cloud is heterogeneous, i.e. that the intrinsic properties of the dust vary with R. Since the dust particles 

spiral towards the Sun under Poynting-Robertson drag (or are blown away by solar radiation pressure), it 

can be assumed that the intrinsic properties vary with time and that the dust particles suffer a significant 

temporal evolution. 

3 Interpretation Through Numerical Simulations 

3.1 Zodiacal Light Results 

Results need to be interpreted through appropriate simulations, with tentatively realistic assumptions 

about the size distribution, the composition and the structure of the particles (Levasseur-Regourd et al., 

2007; Lasue et al., 2007). The size distribution may be assumed to be similar to that derived from in-situ 

measurements by Grün et al. (2001), showing a size distribution with a few branches following powerlaws. We have approximated this size distribution with power-laws of index about -3 for sizes below 20 

!m and about -4.4 for larger sizes. A predominance of silicates, with an average complex refractive 

index of about (1.62 + 0.03i) at 550 nm, and absorbing organic molecules or carbon, with an average 

complex refractive index of about (1.88 + 0.1i) at 550 nm, has been suggested from an analysis of 

previous studies of IDPs and micrometeorites by Lasue et al. (2007). The particles may either be 


compact, as expected for fragments resulting from asteroidal collisions and for some cometary dust, or 

constituted of aggregates, as expected for other cometary dust particles (as confirmed by Stardust 

mission, see also paragraph 4.1). 

Figure 1. Best fit for the local polarimetric observations at 1.5 AU near the ecliptic. The dashed curve corresponds 

to non-absorbing silicates, the dotted curve to absorbing organic material. The solid curve is the best fit obtained by 

mixing 40% of organics and 60% of silicates in mass. (adapted from Lasue et al. 2007) 

A combination of T-matrix calculations for small particles and ray-tracing simulations for larger 

particles is used to compute the light scattering from a cloud of dust particles built up of prolate 

spheroids and fractal aggregates of them. The best fit to the observational results constraints, at 1 AU in 

the invariant plane, the particles composition to 25-50% of organics in mass, and conversely to 75-50% 

of silicates in mass. The best estimate of the contribution of aggregated dust particles, simulated by 

irregular aggregates of spheroids randomly oriented, correspond to -at least- 20% of aggregates in mass 

(Lasue et al., 2007). This in turn, as extrapolated from the bulbous to single track ratio from the Stardust 

aerogel analyses (35% of bulbous tracks; Hörz et al., 2006; Burchell et al., 2008), would correspond to 

at least 50% in mass for the contribution of dust particles from comets. 

 

Figure 2. Interpretation of the decrease in polarization observed for the near-ecliptic zodiacal dust between 1.5 and 

0.5 AU through an evolution of organics contribution. The results suggest the sublimation of the organics present in 

the particles. 


3.2 Thermal Emission Results 

The temperature variations with R, as deduced from the observations, do not follow a black-body 

relationship. This certainly indicates particular properties of the zodiacal dust cloud. The thermal 

equilibrium temperature of dust particles can be computed by equating the incident and emitted light 

integrated over a large range of wavelengths, , (typically from 0.1 to 1000 !m). At a distance R (in 

AU) from the Sun, this is obtained by solving the expression: 

r

R

 

 



2

B  ,TS Qabs  a,

0



" d 
 # B  ,T Qabs  a,

0



" d (1) 

where r is the radius of the Sun, B(,T) the Planck function, TS the solar surface temperature, $, the ratio 

of the emitting surface over a

2

/4, with a the diameter of the emitting particle and Qabs(a, ) the 

absorption efficiency of a particle with a given optical index (see, e.g. Kolokolova et al., 2004). 

The temperature variation with R (for R varying between 0.5 AU and 1.5 AU) of the dust 

particles is calculated by taking the absorption and emission properties of compact (spheroids) and 

irregular aggregates (aggregates of spheroids) dust particles with optical indices ranging from low 

absorbing silicates to highly absorbing carbonaceous compounds. The optical indices are taken to be 

those of astronomical silicates (Draine & Lee 1984) and refractive organic material (Li & Greenberg 

1997). The behavior of the temperature for large particles (size > 100 !m) is always close to the blackbody approximation. Only highly absorbing and small particles show a significantly different behavior. 

The variation with the solar distance is very dependent on the optical properties and size of the particles 

and less on the actual shape of the particles. The best estimate for the observed variation of temperature 

(Table 1) corresponds to small particles (effective radius < 2 !m) constituted of highly absorbing 

carbonaceous compounds such as organics or carbon as shown in Figure 3. Figure 3 also shows the 

thermal gradient with the solar distance for spheres and spheroids, indicating that the actual shape of the 

particle does not significantly modify the thermal behavior of the particles between non-absorbing 

silicates and absorbing organic compounds. 

-0.60

-0.55

-0.50

-0.45

-0.40

-0.35

-0.30

0.01 0.10 1.00 10.00 100.00

effective radius (microns)

zodiacal cloud

astronomical silicates spheres

organics spheres

astronomical silicates spheroids

organics spheroids

Figure 3. Calculations of the temperature gradient between 0.5 AU and 1.5 AU for two shapes of grains (spheres in black

and spheroids in blue) as a function of the equivalent volume size of the grains and for the two different compositions 

relevant to the interplanetary dust cloud. (adapted from Lasue et al. 2007) 


3.3 Significance of the Previous Results 

To summarize, the local values derived from observational results, i.e. polarization, geometric albedo, 

temperature, indicate that, in the near-ecliptic invariant plane and in the 0.5-1.5 AU solar distance range, 

the dust cloud is heterogeneous and that the dust particles do not behave as black-bodies; they suggest 

that the dust properties change with time, as most of the particles spiral towards the Sun under PoyntingRobertson drag. Interpretation of the results obtained for the zodiacal light and the zodiacal thermal 

emission through robust numerical simulations favours the presence of both silicates and organics, with 

a steady decrease of the organics contribution. While the simulations require a significant amount of 

aggregates (most likely of cometary origin), it may be added that the 1/R law derived for the increase of 

space density with decreasing solar distance is precisely what would be expected for dust particles under 

Poynting-Robertson drag in their formation region; in the above-mentioned region, significant amounts 

of cometary dust are actually ejected from active cometary nuclei, while it is unlikely that significant 

amounts of dust are released by asteroidal collisions. 

4 Discussion and Conclusion 

4.1 Comparison with Cometary Dust Properties 

In-situ Vega and Giotto missions to comet Halley have revealed previously unsuspected properties of 

the dust ejected by the nucleus of this famous comet. From the dust mass spectrometer on-board Vega, 

the major constituents have been found to be silicate minerals and organic refractory materials (so-called 

CHON from their constitutive elements), both in comparable proportions (Kissel et al., 1986). From the 

optical probe and the dust impact detector on-board Giotto, the dust density has been estimated to be of 

about 100 kg m-3 (Levasseur-Regourd et al., 1999; Fulle et al., 2000). More recently, Stardust mission 

has provided some ground truth about the structure of the dust collected in comet Wild 2 coma, though 

the presence of both compact particles and fragile aggregates (Hörz et al., 2006). 

As far as remote polarimetric observations are concerned, numerical simulations of the numerous 

observations of comets Halley and Hale-Bopp, through an approach similar to that described in 3.1, have 

allowed us to suggest that the dust particles present in the coma of these two comets consist of 

aggregates and some compact particles, with a percentage in mass of 40-65% of silicates and, 

conversely, of 60-35% of organics (Lasue et al., 2006; Lasue et al., 2009). In that work, the amount of 

aggregates present in the comae of comets Hale-Bopp and Halley was estimated to be at least 

respectively 18% and 10% in mass. We have mentioned in section 2.1 that 35% of the particles collected 

by Stardust were aggregates. Assuming that aggregate particles originate only from comets, such values 

would imply that from 50% up to 100% of the particles -both aggregates and compact- present in the 

zodiacal cloud would be of cometary origin. Experimental simulations have been also attempted to fit 

the polarimetric observations of comets. They also favour the presence, in addition to some compact 

silicates, of fluffy aggregates of silicates and carbonaceous compounds (Hadamcik et al., 2007). Finally, 

the presence of fragile low-density aggregates in the comae of various comets demonstrates that the 

aggregates noticed in the IDPs collected in the Earth stratosphere are of cometary origin. 


4.2 Comparison with Recent Dynamical Studies 

Nesvorny et al. (2010) have recently presented a new zodiacal cloud model based on the orbital 

properties and lifetimes of comets and asteroids, and on the dynamical evolution of dust after ejection, in 

order of determining the relative contributions of asteroidal and cometary material to the zodiacal cloud. 

The authors conclude that about 90% of the observed mid-infrared zodiacal thermal emission is 

produced by particles ejected from Jupiter family comets and that about 10% is produced by Oort cloud 

comets and/or asteroidal collisions. 

While their approach is completely different from ours, and is only constrained by IRAS 

observations, it is certainly interesting to point out that both approaches establish that particles of 

asteroidal origin cannot be claimed to be the major source of interplanetary dust. Besides, it may be 

noticed that the value of about 50% in mass that we obtain for the contribution of dust particles from 

comets to the zodiacal cloud is likely to be underestimated. Dust particles of cometary origin are indeed, 

while their spiral towards the Sun under Poynting-Roberstson drag, most likely to suffer some 

evaporation of dark carbonaceous compounds, as well as some collisions, and thus to get more compact 

and comparable to particles of asteroidal origin. Finally, Nesvorny et al. (2010) estimate that the inner 

zodiacal cloud was at least 104

 times brighter during the Late Heavy Bombardment epoch and derive the 

amount of primitive dark dust material that could have accreted on terrestrial planets. Taking into 

account the characteristic structure (with irregular grains and fluffy aggregates) of the particles of 

cometary origin, as already pointed out in Levasseur-Regourd et al. (2006), we will now carefully 

investigate this critical topic. 

4.3 Implication for Earth Delivery of Carbonaceous Compounds 

The theory of meteoritic ablation during atmospheric entry, including the effects of thermal radiation, 

heat capacity and deceleration for solid particles, has been described in a number of publications (e.g. 

Jones and Kaiser, 1966). In general, the thermal equilibrium of the particle is given by: 

1

2

%av

3

Aproj 
 Atot&' S Ts

4 Te4

 

4

3

r

3

 mcs

dTm

dt (2) 

where % is the heat transfer coefficient, a the density of the atmosphere, v the entry velocity of the 

particle, Aproj the projected surface of the particle, Atot the total surface of the particle, & the emissivity of 

the particle, 'S the Stefan constant, Ts the surface temperature of the particle, Te the environment 

temperature (atmosphere), r the equivalent radius of the particle (quantity for which 4r 3 /3 equals the 

volume of the particle), m the density of the particle, cs the specific heat of the meteoric substance, Tm

the mean temperature of the particle, and t the time. This expression determines the relationship between 

the heat transfer from the atmospheric molecules to the particle and the light emission and heating of the 

particle. 

As a first approximation, the transfer heat coefficient and the emissivity can be assumed to be 

equal to unity (Jones and Kaiser, 1966). Moreover, if the particle is small enough, typically with r less 

than tens of microns, then its temperature is always uniform (Murad, 2001) and the rightmost term of the 

equation (2) can be ignored. The equation (2) simplifies to: 

a1 ( ) 

' STb

4

v

3 (3) 


where ) = Atot /Aproj. In the case of spherical particles, ) = 4, and assuming the evaporation temperature 

is about 2.1×103

 K (Öpik, 1958), then evaporation of a particle that enters the atmosphere at 30 km s-1

starts at 101 km of altitude. Knowing that the ratio ) can be 1.7 times higher for the case of typical 

spheroidal particles (oblate with a ratio of semi major axes of 2) and up to ~ for the case of aggregated 

fractal particles (Meakin and Donn 1988), this equation gives values for the altitude of evaporation of 

about 97 km and 93 km respectively for the same entry velocity. 

However, the deceleration of the particle due to the collisions with the atmosphere molecules 

should also be taken into account. Assuming that the molecules stick to the particle and thus transmit all 

their momentum to the particle, the conservation of momentum implies: 

v 
 v exp 3Ha

4R m cos  *

+

,-

.

/0 (4) 

where H is the typical height of the atmosphere and * the angle of the entry trajectory with respect to the 

zenith. Substituting this expression in equation (2) gives the expression for which the temperature 

obtained is maximal to be: 

Tmax

4 
 1

)



4%R mv

3 cos  *

18e' S&H (5) 

with e the natural base of logarithms. From this equation, the critical radius of the particles that can enter 

the atmosphere of Earth without being completely ablated can be determined. We have already seen that 

the shape parameter ) can range from 4 for spherical particles to 4 for aggregated particles. The effect 

of the shape of the particles on the equilibrium temperature reached during atmospheric entry can be 

seen in Figure 4, assuming an entry velocity of 30 km s-1. While the radius for which spherical particles 

reach the ground without being ablated is about 4.7 !m (Jones and Kaiser, 1966), the largest equivalent 

volume radius of irregularly shaped particles can reach up to 15 !m. 

Figure 4. Maximum equilibrium temperatures for particles entering the Earth atmosphere at 30 km s-1. The 

horizontal line corresponds to the temperature of sublimation of meteoritic materials suggested by Öpik (1958) of 

2.1×103

 K. The increase in size for the more efficiently decelerated particles (spheroids and aggregates) is obvious. 


All parameters staying the same, irregularly shaped particles and fluffy aggregates can bring up to ~

3

more material in volume without being ablated to the Earth’s surface than compact spherical particles. 

Cometary dust particles are therefore ideal candidates to bring carbonaceous compounds for seeding life 

on early Earth. 

5 Conclusions 

The long-standing controversy debated in the interplanetary dust community, around the relative 

contributions to the interplanetary dust cloud of dust resulting from asteroidal collisions and dust ejected 

by comet nuclei seems now about to be closed, with evidence for a major contribution of particles of 

cometary origin in the inner solar system and in the vicinity of the Earth, as established from their 

morphology (significant amount of aggregates), their composition (significant amount of organics) and 

their region of formation (inner solar system). It may thus be suggested that, not only meteor streams, 

but also sporadic meteors and micrometeorites, have mostly a cometary origin. 

While more precise zodiacal observations are expected in a near future from Akatsuki spacecraft 

during its cruise between the Earth and Venus, a key implication of these conclusions is related to the 

early evolution of the solar system. During the LHB epoch, while the spatial density of dust in the 

interplanetary dust clouds was orders of magnitude greater than nowadays, the structure of dust particles 

originating from comets has quite likely favoured the survival of organics during their atmospheric 

entry. 

Acknowledgments 

We acknowledge partial funding from CNES. This is J. Lasue LPI contribution number ####. 

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Origin of Short-Perihelion Comets 

A. S. Guliyev1

Abstract New regularities for short-perihelion comets are found. Distant nodes of cometary orbits of 

Kreutz family are concentrated in a plane with ascending node 76° and inclination 267° at the distance 

from 2 up to 3 a.u. and in a very narrow interval of longitudes. There is a correlation dependence 

between q and cos I concerning the found plane (coefficient of correlation 0.41). Similar results are 

received regarding to cometary families of Meyer, Kracht and Marsden. Distant nodes of these comets 

are concentrated close three planes (their parameters are discussed in the article) and at distances 1.4; 

0.5; 6 a.u. accordingly. It is concluded that these comet groups were formed as a result of collision of 

parent bodies with meteoric streams. One more group, consisting of 7 comets is identified. 5 comet pairs 

are selected among sungrazers. 

Keywords short-perihelion comets · meteor streams · split comets 

1 Kreutz Cometary Family 

The Kreutz cometary family is quite a mysterious phenomenon in the solar system. The strength of this 

family, by rate of comets discovered during last years, might be estimated as tens of thousands. Hence, 

Kreutz comets form a singular belt around the Sun. Meanwhile, research on Kreutz comets, essentially, 

covers observation of individual objects of this class. This system is studied in insufficient detail. The 

reason for this is that the system is quite young and quickly replenishes. 

There are some explanations concerning an origin of short-perihelion comets of the Kreutz 

family. However it is impossible to consider any of them as comprehensive one. It might be possible to 

consider conventionally that these comets are fragments one or several large proto-comet nucleus. The 

version about disintegration proves to be true even when some Kreutz comets sometimes break up to 

separate parts during astronomical observations. 

We present and comment some new regularities of considered system in the present book. They 

were not known earlier. These regularities, in our opinion, might give a sufficient basis for revision of 

the discussed origin’s mechanism concerning to Kreutz comets or bring essential updates in this 

mechanism, at least. 

According of the catalogue by Marsden and Williams (2008) and Minor Planet Electronic 

Circulars for 2008-2009, the number of long-period comets with parameters close to values 

 q = 0.006..; e =1;  = 80°; 
 = 0°; i = 144°

is equal to 1502 (as of early 2010). 

 

A. S. Guliyev ( ) 

 Shamakhy Astrophysical Observatory, Academy of Sciences of Azerbaijan. Phone: +9940503325958; Fax. +99412 4975268; E-mail: 

ayyub54@yahoo.com 


Primary viewing of Kreutz comets shows that their perihelions are not concentrated chaotically 

around a certain center. There is absolutely other way for the better description of perihelion 

distribution. Perihelion of comets are located along some arch of the celestial sphere. Before making 

comments on this feature of Kreutz comets, we have to make a substantiation of this assumption. If 

each point of perihelion with parameters (Li, Bi) is present as a material point on a surface of a certain 

sphere, then coordinates (L, B) of the of inertia center of this sphere will be determined from 

expressions: 

 Nk cos L cos B = cos Li cos Bi

 Nk sin L cos B = sin Li cos Bi

 Nk sin b = sin Bi , 

where N and k are number of perihelion and level of inferred concentration, accordingly. Calculations 

for 1502 points give following values: 

 L= 282°.82; B = 35°.06; R = 0.992 

As a residual dispersion it is possible to consider value Ésin2

i , where i are angular distances of 

perihelion from point (L, B). 

 Sp = sin2

i = 12.33 (1) 

Now let us consider a working hypothesis about perihelion location along the big circle of 

celestial sphere with parameters 
' (ascending node) and ' (inclination). Calculations made by us give 

following values 

 ' = 37°.48 
' = 171°.32 (2)

A residual dispersion in this case will be Sres = 5.24. This is almost twice less, than (1). 

It was found other plane with parameters 

 I'= 76°.34; 
'= 267°.15 (3) 

concerning which distant nodes of Kreutz comets orbits have maximum in the interval 2 – 3 a.u. (Figure 

1). It is close to the normal distribution with the maximum near 2.5 Ü.u in the interval of 0-5 a.u. 

(Hereinafter in the analysis are used overlapping on an axis abscissa each other intervals). 

 In addition angular sizes of distant nodes (DN) concerning a plane (3) have a sharp maximum in 

a narrow interval of longitude (Figure 2). These features of the distant nodes theoretically can be 

explained by two reasons: 1. Comets are generated by a planet body moving in the plane (3) and on 

distance nearby 2.5 a.u.; 2. There is an unknown meteoric stream in this plane and in the distance near 

2.5 a.u., which is the reason of smashing Kreutz comets. 

The first explanation seems to be extremely improbable as there is no similar body among known 

asteroids. If even it existed in the solar system, the mechanism of generation cometary nucleys by them 

would be not clear. Therefore it is evident to decide in favor of the second mechanism. It seems quite 

logical and explains almost all features of considered Kreutz comets. 


0

20

40

60

80

100

120

140

160

180

200

0123456

N

R

Figure 1. Distribution of distant nodes of Kreutz comets regarding to the plane (3) in the interval up to 5.3 a.u. 

0

400

800

1200

1600

30 80 130 180 230 280 330

DN

N

Figure 2. Distribution of distant nodes (DN) longitudes of Kreutz comets relative (3). 

It is reasonable to make the following hypothesis on the origin of studied comets. Huge protocomet nuclei, appearing in the inner part of the solar system at first, have fallen into unknown meteoric 

stream. It has got a lot of cracks. These cracks in a combination with tidal influence of the Sun have led 

to disintegration of proto-comet nuclei on to finer fragments. Fragments have fallen in the same 

meteoric stream at their next returning to perihelion and have got sets of impacts and cracks which lead 

to their secondary splitting, etc. 


2 Meyer Group of Short – perihelion Comets 

 

Under Meyer group of comets we will mean comets with parameters, varying around values: 

 q = 0.036..; e =1;  = 57°; 
 = 73°; i = 73°

The number of such long-period comets, as of early 2010, was 100. 

Results of our calculations and analyses show that the assumption of concentration along the 

plane 

 I' = 53°.69; 
' = 11°.07 (4) 

describes real distribution of perihelion better, than the similar assumption regarding to some point (Sp = 

Ésin2 Bi

Ý

 = 0.265). Ninety percent of points are concentrated in the field of ±4° regarding the plane (4) 

Calculations show, that there is one more plane with parameters 

 I '= 84°.68; 
' = 270°.87 (5) 

near which distant nodes of cometary orbits have significant concentration in the interval 1.1 – 1.4 a.u. 

(Figure 3). 

0

10

20

30

40

50

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5

R

N

Figure 3. Distribution of distant nodes of Meyer comets regarding to the plane (5) 

These features in combination with correlation between q and cos I (coefficient of correlation is 

equally to -0.3) give a basis to put forward the following hypothesis. One of the long-period comets 

having parameters 

 I = 72°.8; 
 = 72°.6; q = 0.036


and appearing in the inner part of solar system for the first time at passage of the zone with parameters R

~1.4 Ü.ß.; I' = 84°.68; 
' = 270°.87 has got powerful jets of a meteoric stream. The orbit of comet had an 

inclination to this plane about 150°. Therefore a head-on collision occurred, i.e. impacts of meteoric 

particles on comet nuclei were powerful. As a result, comet nucleus has collapsed on to many fragments. 

3 Kracht and Marsden Cometary Groups 

Analogical results have been obtained concerning the cometary groups of Kracht and Marsden. First of 

them has following characteristics 

 q = 0.045..; e =0.98;  = 59°; 
 = 44°; i = 13°

and contains 35 comets (2010). It is established at first that distant nodes of these comets are 

concentrated near the plane 

 I'= 24°.08; 
' = 104°.51 

and in the interval of the distance 0.4 – 0.6 a.u. There is a sharp concentration of distant nodes on 

longitude in this case too. 

Group of Marsden has following characteristics 

 q = 0.050..; e =0.98;  = 24°; 
 = 79°; i = 27°, 

and contains 32 comets (2010). Calculations show that perihelion of these comets are concentrated near 

the plane 

 I' = 10°.21; 
' = 359°.60 

At the same time we have found that distant nodes of these comets are concentrated near the plane 

 I'= 89°.50; 
' = 101°.22 

and in the distances from 3 up to 8.7 a.u. 

In the opinion of the author, these two groups have been formed as a result of comet-meteor 

stream collisions, too. 

4 New Group of Sungrazers and Other Splitted Comets 

The author has analyzed features of 63 sporadic short-perihelion comets by own methods described in 

the book. A new group was identified among them. It contains 7 comets (C/2007 K19, C/2006 L7, 

C/2007 L12, C/2005 L10, C/2006 M6, C/2007 M6, C/1997 M5). Perihelion of these comets are 

concentrated near the plane with parameters: 

 

 I'= 53°.9; 
' = 222°.1. 


Five pairs among short-perihelion comets are selected except this group: C/2002 V5 and C/1996 

V2; C/2004 U2 and C/2005 M3; C/2005 D1 and C/2007 C12; C/2000 V4 and C/2001 T5; C/2008 S2 

and C/2004 X7. Probably they are fragments of splitted comets. 

References 

B.G.Marsden and G.V.Williams, 2008. Catalogue of Cometary Orbits, 17th ed. 195p. 


Identification of Optical Component of North Toroidal Source of Sporadic Meteors 

and its Origin 

T. Hashimoto1• J. Watanabe2• M. Sato2• M. Ishiguro3

Abstract We succeeded to identify the North Toroidal source by optical observations performed by the 

SonotaCo Network, which is a TV observation network coordinated by Japanese amateurs. This source 

has been known only for radar observations until now. The orbits of the optical meteors in the North 

Toroidal source are relatively large eccentricity and semi-major axis, compared with those of the radar 

meteors. In this paper, we report the characteristics of this North Toroidal source detected by optical 

observations, and discuss the possible origin and evolution of this source. 

Keywords sporadic source · North Toroidal · optical method 

1 Introduction 

The major six sources of sporadic meteors were discovered mainly by radar observations: Helio (H) and 

Antihelio (HA), South and North Apex components (SA/NA), and South and North Toroidal (ST/NT). 

Due to the high efficiencies realized in modern radar technologies, high resolution and sensitive 

observations have been carried out on these sporadic sources (Campbell-Brown 2008). On the other 

hand, optical data has not been enough to study these sources until now. Especially, Toroidal sources 

have never been identified by optical method. In this paper, we report the first identification of the North 

Toroidal sources among the data obtained by the TV observation network coordinated by Japanese 

amateurs. We also report the characteristics of the orbits of meteors belonging to the NT source, and 

discuss the possible origin and evolution of this source. 

2 Observational Material 

We analyzed data collected by SonotaCo network, which is the coordinated monitoring observation 

network of automated detection for bright meteors or fireballs among amateur astronomers (SonotaCo 

2009). We selected the meteors by using analysis software, UFOOrbit ver. 2.11 for securing welldetermined orbits with the following conditions: length of the trail ¿ 1.5 degrees, the angle of the 

intersection of two apparent passes of trails’ extension ¿ 10 degrees. The total number of the selected 

samples is 13,275. Among them, 5,341 meteors are judged to belong to 20 major meteor showers using 



T. Hashimoto ( ) 

The Nippon Meteor Society 1-28-1, Kinugaoka, Hachioji, Tokyo, 192-0912, Japan , E-mail: thashi@din.or.jp 

J. Watanabe • M. Sato 

National Astonomical Observatory of Japan 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan 

M. Ishiguro 

Department of Physics and Astronomy, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea 


the analysis software UFOAnalyzer Ver. 2. The rest of 7,934 meteors are thought to be sporadic 

meteors. The radiants of these 7,934 meteors are plotted in Figure 1. 

Figure 1. Distribution of radiant points of 7,934 sporadic meteors. 

 While it is clear that there are concentrations corresponding to HA, and SA/NA, there is also a 

weak concentration at around  Â sun = 230 ~ 290 degrees, and  = +50 ~ +80 degrees. This area 

corresponds to the NT source determined by radar observations. There are 410 meteors with radiants are 

located in this area. 

3 Characteristics of Optical NT Meteors 

Assuming these meteors belong to the NT source, we analyzed the characteristics of these meteors in 

order to compare to radar NT meteors. Due to the optical monitor, these meteors are relatively bright, 

including the fireball-class. Figure 2 shows the absolute magnitudes of detected optical NT meteors. 

This means that the original size of the optical NT meteoroids is larger than that of radar NT meteoroids. 



Figure 2. Absolute magnitude of optical NT meteors.


 The orbital elements of the optical NT meteors are also different from radar NT meteors. Figures 

3 and 4 indicate the distribution of their eccentricities and semi-major axes, respectively. Each figure 

contains the value of the radar NT meteors studied by Jones and Brown (1993) for comparison. 

Figure 3. Distribution of eccentricity of optical NT meteors. 

Figure 4. Distribution of semi-major axis of optical NT meteors.


 The optical NT meteors have a more eccentric orbit with larger semi-major axis than the radar 

NT meteors. On the other hand, the inclination is not so dierent from radar NT meteors, as shown in 

Figure 5. 

Figure 5. Distribution of inclination of optical NT meteors. 

4 Origin of the NT 

It is clear that the orbits of the NT meteors depend on their size such that larger eccentricity and semimajor axis with larger meteoroids, while the inclination is similar. This situation gives us a strong 

implication regarding the orbital evolution of the NT meteoroids. Because of the P.R. effect, the smaller 

meteoroids change their orbits faster than the larger ones. Even if the orbits of all the meteoroids of 

different size are the same initially as large eccentricity and semi-major axis, the orbits of smaller 

meteoroids shrink into smaller and circular orbits more rapidly than larger meteoroids. The NT 

meteoroids are thought to be a stage on the way of such orbital evolution. If so, we speculate that the 

parent object or objects should have been close to the orbit of larger-size meteoroids, namely large 

eccentricity and relatively large semi-major axis of more than a few A.U. 

 The theoretical evolutional tracks of the orbits of the NT meteoroids can be plotted in the a-e

diagram. Within this diagram, the evolutional track depends strongly on the initial orbit, and not on the 

size of meteoroids. Smaller meteoroids evolve along the track into the smaller and circular orbits faster 

than larger meteoroids. Therefore, the observed distribution of the orbits of optical and radar NT 

meteoroids should be located in the one evolutional track if the origin is the same. It is important to find 

out any appropriate evolutional track which passes through the both observed components of the NT. 

Our preliminary trials show that two possible groups of evolutional tracks are plausible. One is a group 

of large-e & small-a orbits, and the other is that of large-e & large-a orbits. Figures 6 and 7 show the a-e

diagrams with evolutional tracks of the two groups, respectively. 


Figure 6. a-e diagram of the possible evolutional track of the meteoroids from large-e and large-a orbits. 

Figure 7. Same as Figure 6, but from large-e and small-a orbits. 


The former group is suggesting high-inclined short-period comets, which was already suggested 

by Wiegert (2008). Although Wiegert et al. (2009) also tried to simulate the NT from the near-Earth 

asteroids, it seems to be impossible to explain the origin of the large-a meteoroids detected in optical 

NT, if we assume the origin of the NT is only one object. 

 However, it should be noted that there is an annual variation of the NT source. In our sample, the 

number of the optical NT increased in autumn and winter. Recent detailed study of the radar NT meteors 

by Campbell-Brown & Wiegert (2009) clearly shows that the NT has several components of dierent 

orbital characteristics. This suggests that the NT source has been originated from several dierent parent 

objects. Anyway, no definite candidate has been identified yet. Further studies should be needed to 

clarify the origin of the NT source. 

5 Conclusion 

We identified the optical component of the North Toroidal source that the size of the meteoroids is 

larger than that detected by the radar method. These larger NT meteoroids have different orbital 

characteristics; larger eccentricity and semi-major axis than those of the radar NT meteoroids. This 

strongly suggests the orbital evolution of the meteoroids in the NT source by the P.R. effect. One of the 

possible parent(s) of the NT source should have larger eccentricity and semi-major axis of a few or 

much larger values. 

References 

Campbell-Brown, M.D., Wiegert, P., Seasonal Variations in the north toroidal sporadic meteor source, Meteoritics & Planet. 

Sci., 44, 1837-1848 (2009) 

Campbell-Brown, M.D., High resolution radiant distribution and orbits of sporadic radar meteoroids, Icarus, 196, 144-163 

(2008) 

Jones, J., and Brown, P., Sporadic meteor radiant distributions: orbital survey results, Mon. Not. Roy. Astron. Soc., 265, 524-

532 (1993) 

SonotaCo, A meteor shower catalog based on video observations in 2007-2008, WGN, Journal International Meteor 

Organization, 37, 55-62 (2009) 

Wiegert, P., The dynamics of low-perihelion meteoroid streams, Earth, Moon and Planets, 102, 15-26(2008) 

Wiegert, P., Vaubaillon, J., and Campbell-Brown, M., A dynamical model of the sporadic meteoroid complex, Icarus, 201, 

295-310 (2009) 


Distributions of Orbital Elements for Meteoroids on Near-Parabolic Orbits 

According to Radar Observational Data 

S. V. Kolomiyets1

Abstract Some results of the International Heliophysical Year (IHY) Coordinated Investigation 

Program (CIP) number 65 “Meteors in the Earth Atmosphere and Meteoroids in the Solar System” are 

presented. The problem of hyperbolic and near-parabolic orbits is discussed. Some possibilities for the 

solution of this problem can be obtained from the radar observation of faint meteors. The limiting 

magnitude of the Kharkov, Ukraine, radar observation program in the 1970’s was +12, resulting in a 

very large number of meteors being detected. 250,000 orbits down to even fainter limiting magnitude 

were determined in the 1972-78 period in Kharkov (out of them 7,000 are hyperbolic). The hypothesis 

of hyperbolic meteors was confirmed. In some radar meteor observations 1 Â 10% of meteors are hyperbolic meteors. Though the Advanced Meteor Orbit Radar (AMOR, New Zealand) and Canadian 

Meteor Orbit Radar (CMOR, Canada) have accumulated millions of meteor orbits, there are difficulties 

in comparing the radar observational data obtained from these three sites (New Zealand, Canada, 

Kharkov). A new global program International Space Weather Initiative (ISWI) has begun in 2010 

(http://www.iswi-secretariat.org). Today it is necessary to create the unified radar catalogue of nearparabolic and hyperbolic meteor orbits in the framework of the ISWI, or any other different way, in 

collaboration of Ukraine, Canada, New Zealand, the USA and, possibly, Japan. Involvement of the 

Virtual Meteor Observatory (Netherlands) and Meteor Data Centre (Slovakia) is desirable too. 

International unified radar catalogue of near-parabolic and hyperbolic meteor orbits will aid to a major 

advance in our understanding of the ecology of meteoroids within the Solar System and beyond. 

Keywords meteors · meteoroids · meteor orbits · meteor radar · hyperbolic meteors 

1 Introduction 

In a series of publications (Kolomiyets and Kashcheyev 2005, Kolomiyets 2002, Andreyev et al. 1993) 

the authors have identified a set of meteor orbits, with e ¿ 1, of meteor sporadic background based on 

the Kharkov radar observations, which they named “hyperbolic meteors” similar to previous 

publications (Vsekhsvyatskiy 1978; Shtol 1970) based on analogous data. The Kharkov radar orbital 

data from the 1970s has proven to be extremely promising for nding the real hyperbolic orbits, as they 

were statistically many in terms of volume and uniformity, there have been twenty-four-hour and round 

off the annual cycles of observations were weaker meteors between masses 106 Â 109 kg, which are 

important for the building of the Meteor engineering distribution models (Dikarev et al. 2001). In 

addition, these data were obtained as a result of carefully designed and carefully executed multi-year 

monitoring experiment (Kashcheyev and Tkachuk 1980), using the Meteor automated radar system 

(MARS) of the Kharkov National University of radio electronics (KhNURE), which was recognized at 

that time to be the best in the world (Fedynskiy et. al. 1976, Kashcheyev 1977, Kashcheyev et al. 1977, 



S. V. Kolomiyets ( ) 

Kharkiv National University of Radioelectronics, Lenin ave., 14, Kharkiv, 61166, Ukraine. E-mail: s.kolomiyets@gmail.com 


Voloshchuk et. al. 1984). Hyperbolic meteors were recorded and continue to be recorded by other 

meteor radar and optical observations (Kramer et. al. 1986), and in “in situ” experiments 

(Weidensehilling 1978, Grün et al. 2001). The information on hyperbolic orbits is currently available as 

the new 2003 version at the International Astronomical Union Meteor Data Center IAU (MDC), provided by scientists from Slovakia (Hajdukova 2008; Hajdukova and Paulech 2006). Nevertheless, data 

on hyperbolic orbits that are available to scientists in print is very heterogeneous and not always 

meaningful for the categorical conclusions. Part of it are the consequence of errors (Hajduk 2001). In 

addition to that the real hyperbolic meteor complex has a naturally compound structure. The theories of 

the origin of hyperbolic meteor orbits near the Earth orbit and in the Solar System are still ambiguous 

and contradictory (Meisel et al. 2002a,b; Janches et al. 2001; Grun and Landgraf 2000; Kramer et al. 

1998; Belkovich and Potapov 1985; Kazantsev 1998; Vsekhsvyatskiy 1978). The majority of scientists 

do not contradict the reality of hyperbolic meteor orbits altogether, but at the same time it is becoming 

increasingly attractive to research the emergence of new information and new submissions on this issue. 

As a rule the number of meteor orbits with the eccentricities much greater than 1 is very small, both 

theoretically and experimentally ( 1%). Thanks to scanty statistics the problem of hyperbolic identities 

meteors (e ¿ 1)is actually a problem near-parabolic orbits meteoroids (e ~ 1). The set of near-parabolic 

orbits of meteoroids is the most dynamic part of meteor substance of the Solar System. This orbital 

series is statistically far richer than the set of hyperbolic meteor orbits only and its properties and 

characteristics are the keys to solving both problems of hyperbolic meteor orbits, and other problems of 

cosmology and cosmogony of the Solar System. (Lebedinets 1980, 1990; Rietmeijer 2008, Drolshagen 

et. al. 2008, Suggs et. al. 2008, Chapman 2008). 

2 The Kharkov (Ukraine) Meteor Radar Data 

The final test of the validity of a theory has always been an experiment. The 1972-1978 Kharkov meteor 

radar data mentioned above was the result of a carefully designed and performed at the highest level 

experiment. During the radar observations of faint meteors in Kharkov, special attention was paid to the 

regularity, continuity and stability of the sensitivity of the surveillance equipment. The scheduling of 

observations was designed such that the observing cycles were distributed more or less evenly 

throughout the year. For example, during 1975, 29 observing cycles, ranging five to eight days, took

place and, as a result, over 54,000 orbits of meteoroids were determined. The monitoring, carried out in 

times when main meteor showers were absent, with few exceptions (for ex., Geminids and Quadrantids), 

allows observation of prevalently the sporadic meteor background. Therefore the derived distribution of 

meteors was hardly influenced by meteoroids of main showers and characterized mainly sporadic 

meteor complex. In the 1972-1978 MARS of the KHNURE (Kharkov) registered about 250 thousand 

radiants, velocities and orbits of small meteoroids. The limiting magnitude of the Kharkov radar 

observation program in the 1970s was +12m (faint meteors). Parameter distributions of small meteoroid 

orbits registered in Kharkov were constructed. Variations of those distributions with time, seasons, and 

factors of selectivity were taking into account. Thus, the empirical model of the meteor substances from 

radar data in Kharkov between masses 106 Â 109 kg with mass parameter s = 2 was formed. Some of the 

properties and characteristics of this model were published (Kashcheyev and Tkachuk 1979, Tkachuk

1979). As a guide to the Kharkov meteor orbital empirical model, based on monitoring data of the 1972-

1978, the selective catalogue of 5,317 meteors of up to +12 magnitude (Kashcheyev and Tkachuk, 1980) 

can be used. It demonstrates in brief all the characteristics of the model, the parameters, the 

methodology and peculiarities of radar observations (Kashcheyev et al. 1967, Tkachuk 1974). It contains 


5,317 orbits, registered in Kharkov during the 1975, out of total record of 54,000 orbits. 

 Some characteristics of the Kharkov empirical model of orbital distributions of meteoroids using 

radar observations from 1975 in Kharkov are shown in Figure 1, where the dashed lines represent the set 

of elliptical orbits, available in the catalogue of Kashcheev and Tkachuk (1980), and the solid lines 

represent the set of hyperbolic orbits, selected by Kolomiyets (Kashcheyev et al. 1982). Meteoroid 

number distributions are plotted versus three orbit elements: perihelion distance, inclination and 

perihelion argument. The author listed nearly 1,000 meteor hyperbolic orbits with eccentricities close to 

1, based on the 1975 data obtained in Kharkov. Their orbital distributions and some other facts support 

the existence of “hyperbolic meteors” (Kolomiyets 2001). 

Figure 1. Left: Histograms of the number of orbits N (in %) depending on the perihelion distance q (in AU). 

Middle: inclination (in degrees) and right: argument of perihelion  (in degrees) for two types of orbits with 

dierent values of the eccentricity: elliptical (dashed lines) and hyperbolic( solid lines). 

 In Table 1 we show an example of the data on hyperbolic and near-parabolic orbits of meteoroids 

registered on July 12-13, 1975 by radar method in Kharkov. During the 1990s, registered meteor data 

from 1972-1978, including the velocities, radiant coordinates and orbits, have been recalculated and put 

into electronic format. On the basis of this electronic database, the more sophisticated model of the 

meteor complex near the Earth’s orbit for elliptical orbits of meteoroids (for stream and sporadic 

components) of faint meteors was constructed. A detailed description of the specified database and its 

thorough analysis for elliptic orbits is presented by Voloshchuk et al. (1995, 1996, 1997). In this analysis 

we did not include the hyperbolic orbits of meteoroids. Now the KhNURE scientists have the possibility 

to use the re-calculated meteor orbit database of the 1972-1978 dataset when they perform meteor 

research in the KhNURE. For the analysis of distributions of hyperbolic and near-parabolic orbits of 

meteoroids according to radar observations during the period 1972-1978, the author also used the 

recalculated KHNURE electronic database. 


Table 1. Example of data on the hyperbolic and near-parabolic orbits of meteoroids from Kharkov (36.90E, 49.40 

N) radar observations program 1975 (July 12-13). The columns are: (H:M) – hour and minute; Vg – geocentric 

velocity; Vh –heliocentric velocity; (à, à) – radiant heliocentric coordinates; Esà – radiant elongation from the Sun; e

– eccentricity and e – the standard deviation of eccentricity; q – perihelion distance; p – orbit parameter; i – 

inclination;  – perihelion argument; 
 – longitude of ascending node; 	 =  + 
 – longitude of perihelion; (R
1, 

R
2 ) – nodes radius vectors. 

H:M Vg Vh ' ' Es’ e ± e q p i  
 	 R
1 R
2

July, 12 

02:09 41±2.2 50±1.9 40 240 120 1.78±0.19 0.81 2.3 48 226 109 336 – 1.02 

04:45 54±2.8 56±2.6 70 215 95 2.63±0.34 1.01 3.7 71 188 109 297 – 1.02 

04:53 40±2.1 44±1.9 52 239 112 1.25±0.18 0.88 1.9 59 220 109 330 – 1.02 

05:03 46±2.4 59±2.6 46 174 73 2.91±0.34 0.96 3.7 49 157 109 267 – 1.02 

05:06 67±3.4 43±3.4 28 342 121 1.15±0.26 0.76 1.6 145 238 109 348 4.07 1.02 

05:08 65±3.3 49±3.2 36 313 136 1.45±0.23 0.55 1.4 118 257 109 6 1.99 1.02 

05:40 44±2.3 42±2.0 68 232 101 1.12±0.19 0.98 2.1 71 201 109 311 – 1.02 

06:10 59±3.0 41±3.0 21 313 148 0.99±0.08 0.28 0.5 136 296 109 46 0.38 1.02 

06:46 59±3.0 56±3.2 55 272 122 2.35±0.37 0.80 2.7 78 226 109 336 – 1.02 

07:43 55±2.8 51±3.1 60 272 118 1.83±0.32 0.84 2.4 80 223 109 333 – 1.02 

07:49 67±3.4 43±3.3 43 38 76 1.20±0.32 0.97 2.1 134 155 109 265 – 1.02 

08:02 39±2.1 48±3.0 46 232 111 1.62±0.30 0.90 2.4 51 215 109 325 – 1.02 

09:10 58±3.0 52±4.3 37 281 122 1.94±0.46 0.80 2.3 84 227 109 337 – 1.02 

11:54 39±2.1 44±1.6 -0 138 28 1.06±0.05 0.26 0.5 0 243 289 173 1.02 0.35 

July, 13 

02:05 42±2.1 44±1.0 21 264 113 1.09±0.07 0.33 0.7 42 287 110 37 0.53 1.02 

03:40 41±2.2 41±1.7 63 236 111 0.97±0.15 0.95 1.9 68 210 110 321 11.93 1.02 

05:26 59±3.1 67±3.2 57 229 105 4.15±0.49 0.97 5.0 60 199 110 310 – 1.02 

05:31 62±3.2 43±3.1 16 318 147 1.04±0.10 0.31 0.6 147 290 110 41 0.46 1.02 

08:37 67±3.4 49±3.6 43 328 125 1.57±0.32 0.74 1.9 123 236 110 347 14.32 1.02 

15:29 35±1.9 46±1.6 9 152 42 1.25±0.10 0.52 1.2 14 96 110 207 1.33 1.02 

15:57 31±1.7 41±1.4 28 158 53 0.98±0.09 0.65 1.3 36 106 110 217 1.78 1.02 

16:08 50±2.6 71±2.5 15 168 59 4.22±0.35 0.8 4.4 17 142 110 253 – 1.02 

16:23 34±1.9 54±1.7 18 170 61 2.14±0.18 0.84 2.6 21 138 110 249 – 1.02 


2.1 Empirical Model of Orbital Distributions of Meteoroids with Near-parabolic Orbits According to 

the Kharkov Radar Data 

Celestial bodies are moving around the Sun in curves of the second order, which are the conic sections 

with the Sun in one of the foci. The orbital elements are p, e, , 
, i, , where p is the orbital parameter, 

e is the eccentricity,  is the argument of perihelion, 
 is the longitude of ascending node, i is the 

inclination and  is the time registration. These elements are called Kepler’s elements and they 

determine the orbit of any type, elliptical e < 1, parabolic e = 1 or hyperbolic e > 1. 

The author presents here the empirical model of orbital meteoroids complex for near parabolic 

orbits of faint meteors. This model is based on the observational data obtained by the MARS radar 

system in 1972-1978 in Kharkov. The model is presented in the form of distributions of numbers of 

orbits versus the orbital elements, perihelion distance q, inclination i and argument of the perihelion , 

for different types of orbits and different eccentricity values. As an important informative source, the 

distributions of the number of orbits versus geocentric and heliocentric velocities were also constructed. 

The model is constructed in such a way that one can compare a specific orbit-registered-size meteoroid 

samples that represent sets of orbits, which are close to the exact parabolic orbit, for both elliptical and 

hyperbolic orbits. That is, the selection of orbit was based on the approximation to the exact parabola in 

varying degrees. Depending on the degree of approximation the selections were called classic, close or 

average. These approximations had the following criteria. Classic selection for elliptical site of orbits 

(approaching the parabola from one side) was performed according to 0.9 < e < 1.0, and hyperbolic test 

for site of orbits (approaching the parabola from the other side) by criterion 1.0 < e < 1.1. Close 

approximation had 0.99 < e < 1.0 for elliptical orbits, and 1.0 < e < 1.01 for hyperbolic orbits. Average 

approximation criterion was 0.95 < e < 0.98 for elliptical orbits, and 1.1 < e < 2.35 for hyperbolic orbits. 

The set of the distributions (the empirical model) gives a clear representation of behavior of a meteoric 

orbital complex near a parabolic limit e = 1 (Figures 2-6). 

Figure 2. Histograms of the number of orbits N with different values of eccentricity e vs. perihelion distance q (in 

AU) for two types of near-parabolic orbits, elliptical (left column) and hyperbolic (right column). 


Figure 3. Number of orbits N with different values of eccentricity e vs. inclination i (in degrees) for elliptical (left 

column) and hyperbolic (right column) orbits. 

Figure 4. Number of orbits N with different values of eccentricity e vs. perihelion argument  (in degrees) for 

elliptical (left column) and hyperbolic (right column) orbits. 


Figure 5. Histograms of the number of orbits N with different values of eccentricity e vs. geocentric velocity Vg for 

elliptical (left column) and hyperbolic (right column) orbits. 

Figure 6. Histograms of the number of orbits N with different values of eccentricity e vs. heliocentric velocity Vh

for elliptical (left column) and hyperbolic (right column) orbits. 


3 Small-size Orbits of Meteoroids Near the Earth’s Orbit 

In the studies of hyperbolic meteors, the meteoroids on hyperbolic and near-parabolic orbits are mostly 

regarded as newcomers from distant regions of the Solar System and even from interstellar space 

(Baggaley 2005, Weryk and Brown 2005, Meisel et al. 2002a, b; Hawkes et. al. 1998). The fact that part 

of the hyperbolic and parabolic orbits complex can be formed and replenished by the component with 

small-size orbits in the nearby space between the Sun and the Earth’s orbit is largely ignored. The recent 

sharp increase in interest in small bodies in the Solar System is undoubtedly due to the immediate 

opportunity to observe the Sun-grazing comets thanks to SOHO/LASCO and STEREO/SECCHI programs carried out over the past thirteen years. Spectacular images of comets, recorded on the disk of the 

Sun special satellites are available online (http://sungrazer.nrl.navy.mil/index.php) and are exciting to 

everyone. Comets grazing the Sun have been known for a very long time as the Kreutz comets. The 

working hypothesis of the origin of the Kreutz comets is the ongoing disintegration of one giant comet 

(Marsden 1967), and today there is some additional data to it (Guliyev 2010). These sungrazing comets 

are one of the specific parent sources of meteoroids with small-size orbits. The second specific parent 

source of meteoroids with small-size orbits is the Aten, Apollos and Amor streams that cross the Earth’s 

orbit (AAA-asteroids). 

 An asteroid is considered a Near Earth Asteroid (NEA) when it comes to within 1.3 AU of Earth. 

A NEA is called a Potentially Hazardous Asteroid (PHA) when its orbit comes within 0.05 AU of the 

Earth’s orbit and its absolute magnitude becomes H < 22 mag (i.e., its diameter is D > 140 m). The 

estimated total population of PHAs is  25, 000 (http://neo.jpl.nasa.gov/ca). At the same time it is 

estimated that 32% of the total number of NEAs are Amors, 62% are Apollos and 0.6% are Atens. 

The meteoroids-asteroids population discovered by A.K. Terent’yeva (Galibina and Terent’yeva 

1981) is known as the Eccentrides. A table presenting the sample of orbital elements of some of the 

Eccentrides (Simonenko et al.1986) is shown in Table 2. 

Table 2. Orbital elements of some of the Eccentrides. Columns N2, N3 are as in Simonenko et al. (1986). Other 

column names are as in Table 1. 

N N2 N3/name e a q Q 
  i 

1 4 6096 0.62 0.61 0.23 1.0 113 176 139 

2 15 10573 0.87 0.54 0.07 1.0 191 177 135 

3 19 11855 0.77 0.61 0.14 1.1 42 349 10 

4 20 11941 0.79 0.62 0.13 1.1 44 13 47 

5 38 231 0.75 0.57 0.14 1.0 260 354 34 

6 39 11041 0.85 0.56 0.09 1.0 210 353 9 

7 43 4473 0.94 0.53 0.03 1.0 177 3 17 

8 51 1954XA 0.35 0.78 0.51 1.1 190 57 4 

9 52 Hathor 0.45 0.84 0.46 1.2 211 40 6 

10 53 Ra-Shalom 0.44 0.83 0.47 1.2 170 356 16 

Eccentrides were defined as groups of small bodies in the Solar System with the smallest orbits 

(a < 1 AU) of medium or large eccentricity whose aphelion is near the Earth’s orbit (Q < 1.15 AU). 

From existing meteors’ and bolides’ photographic data, Simonenko et al. (1986) has selected fifty 

Eccentrides. Three asteroids of the Atens team were also selected as Eccentrides (2340 Hathor, 2100 

RA-Shalom and 1954 HA), although Hathor and RA-Shalom have an aphelion distance of Q +1.2 AU. 


Out of these objects, seven deserve special attention as a specific group having the most eccentric orbits 

(Simonenko et al. 1986). These orbits, projected on the ecliptic plane, are shown in Figure 7 (the orbital 

elements are presented in Table 2). 

Figure 7. Seven Eccentrides with most eccentric orbits, projected on the ecliptic plane (orbital elements presented 

in Table 2). The numbers next to the aphelions are object numbers and their orbital inclinations, respectively 

(Simonenko et al. 1986). 

 According to Levin et al. (1981), at least 10% of the meteorites on Earth come from the 

population that has very small-size orbits, located entirely within the orbit of the Earth (such as, for 

example, Mauch, Murray, Old Peschanoe, Gorlovka and Vashugal). This class of meteorites has 

attracted the special attention of researchers, since they belong to the source of potentially dangerous 

objects for the Earth. 

As the most dynamic component of the Solar System, meteoroids on near-parabolic orbits and 

orbits with very high eccentricities are a valuable source of information either about their progenitors, or 

about the place and mechanism of their formation. For example, from the Kharkov database of nearparabolic orbits it is possible to select a set of orbits with the aphelions that are characteristic for the 

Eccentrides. Figure 8 shows the distribution of near-parabolic orbits of sporadic meteoroids with the 

same aphelion distances Q as for Eccentrides. Using the streaming component (5160 orbits) of the 

Kharkov meteor electronic database (Voloshchuk et al. 1996, 1997, 1998), Voloshchuk et al. (2002), 

while calculating the probability of collision between the Earth and the parent bodies of meteor streams, 

has found that the most dangerous are the parent bodies whose corresponding meteor orbits have an 

aphelion distance of 1 AU. The authors selected 100 of the most potentially dangerous meteor streams, 

whose parent bodies may fall on Earth. Almost all of their orbits are the Eccentridestype. A table with 

examples from this list of the Eccentrides with 0.9 < e < 1 (i.e. near-parabolic) is given in Table 3, 

where N2 is a number in the list of meteoroids of the Kharkov Meteor database (ordered according to the 

likelihood of the stream falling on the Earth). This factor, identified above for the sporadic meteors of 

the Eccentrides-type, of the very low values of the perihelion distance q (“the Sungrazing orbits”), has 

also been identified in 12 meteor streams selected as the Eccentrides. 


Figure 8. Distribution of the number of near-parabolic orbits of sporadic meteoroids with aphelion distance Q. The 

labeling of x and y-axes is the same as in Figs. 2-6 for Eccentrides. Vh is heliocentric velocity, Vg is geocentric 

velocity, (, ) are radiant latitude and longitude in ecliptic system, q and Q are perihelion and aphelion distance, 

is the argument of the perihelion, and i is the orbital inclination. 


Table 3. Parameters of some streams according the KhNURE data (Eccentrides-type with e > 0.9) that have the 

highest probability of colliding with the Earth. N2 is the number from the list of 100 dangerous streams, N3 is the 

number in the KhNURE catalogue, Members - quantity, e is the eccentricity, i is the inclination, q is the perihelion 

distance and Q is the aphelion distance (Voloshchuk et al. 2002). 

N N2 N3 Members e i q Q 

1 11 855 7 0.983 32.5 0.008 0.99 

2 15 1167 10 0.98 172.9 0.001 1.02 

3 16 3621 10 0.914 148.2 0.045 1.00 

4 24 2807 13 0.958 163.3 0.022 1.02 

5 31 313 13 0.943 41.4 0.029 1.00 

6 36 4333 21 0.906 137.7 0.049 0.99 

7 42 3175 18 0.923 160.2 0.041 1.03 

8 45 3155 13 0.966 110.2 0.018 1.01 

9 51 4123 8 0.943 159.1 0.030 1.03 

10 62 3981 13 0.935 77.1 0.034 1.00 

11 65 2596 7 0.996 155.2 0.002 1.04 

12 98 3530 9 0.910 27.4 0.049 1.04 

4 World Radar Data Resources of Hyperbolic Orbits 

Main modern holders of world radar data resources of orbits of meteoroids are specified in Table 4. 

From Table 4 it can be seen that the r`esource-monitoring data on near-parabolic and hyperbolic orbits 

of meteoroids is quite impressive. 

Table 4. World data resources of hyperbolic orbits: data, the methodology and the nominal parameters of meteoric 

automatic radar systems MARS, CMOR, and AMOR. 

Country Ukraine Ukraine Canada New Zealand Puerto Rico 

Radar name MARS MARS CMOR AMOR Arecibo meteor radar 

Radar type VHF VHF HF/VHF SKiYMET HF/VHF SKiYMET UHF, HPLA 

Method Impulse-diffraction, Impulse-diffraction, Impulse-diffraction, Impulse-diffraction, Not mirror 

 mirror reflect mirror reflect mirror reflect mirror reflect reflection 

Frequency 22.38 MHz 31.1 MHz 29.85 MHz 26.2 MHz 430 MHz 

City Kharkov Kharkov Tavistock, ON Banks Peninsula Arecibo 

LAT 49.4 N 49.4 N 43.3 N 43.2 S 18.3 N 

LON 36.9 E 36.9 E 80.8 W 172.5 E 66.8 W 

Period 1967-1971 1972-1978 2002-2004 1995-1999 1997-1999, 2002 

Enter data ATC ATC ATC ATC Head echo 

Record / 

Holding

Oscillograph / 

photofilm 

Computer/paper tape/ 

Electronic (with 1996)

Computer / 

Electronic

Computer / 

Electronic

Computer / Electronic 

Orbits ~90,000 ~250,000 >1,000,000 ~500,000 ~50,000 

Magnitude or 

size 

+8m / +12m +12m +8m +8m / +13m < 20 – 100 ãm 

Hyperbola 

content 

Didn’t search 1-3% 1-10% 1-3% ~2% 

There are radars in New Zealand and Canada providing extensive observation results (reported by 

Baggaley et al. 2001, Weryk and Brown 2005). The Advanced Meteor Orbit Radar (AMOR) is located 

near Banks Peninsula on the South Island in New Zealand (172.6E, 43.6S). The Canadian Meteor Orbit 

Radar (CMOR) is located near Tavistock, Canada (80.8W, 43.3N). The CMOR has accumulated over 

one million meteor orbits. These meteor radars (AMOR and CMOR) are based on the commercially 

available SKiYMET system. The Kharkov meteor radar of 1970s (MARS) had some distinctions. 


Difficulties exist in comparing the radar observation data obtained from these three sites (Banks 

Peninsula, New Zealand; Tavistock, Canada; Kharkov, Ukraine). Moreover, comparison of data 

collected by the above mentioned three stations with the classical meteor radar and the Arecibo radar 

data requires an even more complex approach (Pellinen-Wannberg 2001). This data is not published in 

full and is not accessible for the general use, neither it is transferred to the IAU MCD. 

 A new global program “International Space Weather Initiative” (ISWI) started in 2010 

(http://www.iswisecretariat.org). Today it is necessary to create the general unified meteor radar orbit 

catalogue (with hyperbolic and near-parabolic orbits) in the framework of this new international 

program ISWI (or in any other way) with the collaboration of Ukraine, the USA, Canada, New Zealand, 

possibly Japan, and other countries. Both the IAU MDC (Slovakia) and the Virtual Meteor Observatory 

(the Netherlands) shall be used for creating this International Radar Catalogue. 

5 Links to International Projects 

5.1 International Heliophysical Year 

This work was undertaken in the framework of the international project 2007-2009 International 

Heliophysical Year (Harrison et. al.2007, Davila et. al.2004). Meteor research was officially included as 

an IHY program under the title “Meteors, Meteoroids and Interplanetary Dust” only in 2007 

(Kolomiyets and Slipchenko 2008). The principal mechanism for coordinating scientific activities for 

the IHY was the Coordinated Investigation Programs (CIPs). Information on research works in the 

scientific discipline “Meteors, Meteoroids, Dust” (Coordinator Svitlana Kolomiyets, Ukraine) of the 

IHY project is shown in Table 5. 

Table 5. The meteor IHY 2007/9 Activities of the NIS (the Discipline: Meteor/Meteoroids/Dust). It has 7 

Coordinated Investigation Programs: CIP 60, CIP 65, CIPs 72-76. 

CIP Program Title Lead Proposer Affiliation, city, country 

CIP 60 Influence of Space Weather on 

Micrometeoroid Flux 

Dr. Thomas Djamaluddin, 

Senior Researcher, 

Head of Center for Application of 

Atmospheric Science and Climate 

National Institute of 

Aeronautics and Space (LAPAN), 

Bandung, Indonesia 

CIP 65 Meteors in the Earth Atmosphere 

and Meteoroids in the Solar System 

Dr. Svitlana Kolomiyets, 

Researcher, 

Meteor Radar Centre 

Kharkov National University of 

Radioelectronics (KhNURE), 

Kharkov, Ukraine 

CIP 

72/65 

Meteors in the Earth Atmosphere 

and Meteoroids in the Solar System Prof. Oleg Belkovich Kazan State University, Zelenodolsk branch, 

Kazan, Tatarstan, Russia 

CIP 

73/65 Meteors in the Earth Atmosphere Prof. Nelly Kulikova Obninsk State Technical University, 

Obninsk, Russia 

CIP 74 Meteoroid-Atmosphere Interactions Dr. Olga Popova, 

Senior Researcher (SR) 

Institute for Dynamics of Geospheres of the 

Russian Academy of Sciences, 

Moscow, Russia 

CIP 75 Meteoroid Streams: Origin, 

Formation, Observations Prof. Galina Ryabova Tomsk State University, Tomsk, Russia 

CIP 76 

Physical Properties of Meteoroids 

and Bolide-Meteorite-Asteroid 

Associations 

Dr. Natalia Konovalova, 

Senior Researcher 

Institute of Astrophysics, 

Tajik Academy of Sciences, 

Dushanbe, Tajikistan 


The IHY, an international program of scientific collaboration in order to understand the external 

drivers of planetary environments, has come to the end. Many aspects of the IHY are continuing through 

the program International Cosmic Weather Initiative. As it was presented and discussed on February 18, 

2009 at the meeting of the UN’s COPUOS (United Nation Committee on the Peaceful Uses of Outer 

Space) Science and Technical Subcommittee (STSC), the ISWI is a 3-year plan (2010-2013). The study 

of the energetic events in the Solar System will pave the way for safe human space travel to the Moon 

and planets in the future, and may serve as an inspiration for the next generation of space physicists. To 

complement the ground-based data, a huge amount of data from space-based missions on the Earth and 

heliospheric phenomena is available. Support of local governments and institutions is needed for local 

scientists to participate in the analysis and interpretation of this data. 

5.2 The Meteor Heritage of the Twentieth Century 

One of the objectives of the IHY project and the coordinated research IHY CIP65 Meteors in Earth’s 

atmosphere and meteoroids in the Solar System is to reflect the important role in the development of 

meteor studies during the previous similar worldwide program The International Geophysical Year 

1957 (IGY). At the same time the CIP 65 draws the attention of the scientific community in a large 

reserve not only unpublished observation data and knowledge gained during the Soviet period in the 

meteor centers of the USSR, but also to the significant scientific publications of the meteor heritage of 

the former USSR, which continue to be available only in Russian. The huge amount of data and 

knowledge about meteors of scientific value was accumulated in the former USSR thanks to the rapid 

development of meteor science during the second half of the twentieth century, from realization of the 

IGY project in 1957-1959 (Lebedev and Sologub 1960). The linguistic barrier, along with other 

reasons, limits access of world meteor science to the sources of meteor information of the former Soviet 

Union. The meteor heritage of the NIS is also not available to every modern researcher of meteors. 

Without the knowledge and the experience of meteor centers of the former USSR, the modern researchers of meteors sometimes have to ‘invent a bicycle all over again’. This, of course, impoverishes 

modern meteor science and, perhaps, slows the pace of its development. In Fig. 12 the table displays the 

main supervision centers of meteor studies in the former USSR that participated in the international IGY 

program, and where the powerful meteor scientific schools were subsequently developed. These centers 

keep the meteor heritage of the twentieth century of the former Soviet Union. 

5.2.1 Historical Note 

The IGY program played an important role in the development of science, and the meteor science, inter 

alia. The IGY was the largest and most extensive international scientific program of the 20th century on 

the world-scale with 69 countries participanting, whose most significant result was the launch of the first 

artificial satellite of the Earth (Sputnik). The IGY has established the institutions for international 

scientific collaboration, which continues to play an important role in modern scientific cooperation. One 

such structure is the International Data Centers (IDC) that were created to store the obtained 

information. The first data centers were established in the USA (Boulder, IDC A), the Soviet Union 

(Moscow, IDCB), the UK (Slough) and Japan. The IDCs collected the observational reports from participants in all sections of geophysics, including meteor data (activity numbers, etc.). The preparations 

for the IGY started in 1950, but the meteor program was introduced only after 1954. The founders of 

the IGY Meteor Program were Prof. D. Link, Prof. V. Guth and Prof. B. Lovell. The IGY meteor studies 

were supervised by the 22 Commission of thr International Astronomical Union (IAU) with Prof. Guth 


in charge. At the same time, the Special Committee for the IGY was established in the USSR and Prof. 

V. V. Fedynskiy was appointed as the head of the Soviet meteor program adapted to local conditions. 

 The main objective of the IGY was the research of solar-terrestrial connections, with the 

emphasis on understanding the ionosphere and near-Earth space. Rocket technology and radar 

techniques were the cornerstones of the IGY. These areas are directly connected to the studies of 

meteors in the Earth’s atmosphere and of meteoroids in the Solar System. Meteors as a research area 

were included in section V “Ionosphere” of the IGY program under the title “Ionosphere. Meteors”. The 

main reason for the progress in IGY meteor studies was the implementation of the radar method. This is 

reflected in the table in Table 6. 

Table 6. Participants of the IGY-1957 meteor program (section V Ionosphere. Meteors) in the USSR. Meteor 

observations: R radar, Ph photographic, V visual (Fedynskiy 1962). 

No City, 

number   H m Scientific institute/Republic of the USSR/Head 

Program 

IGY 

number 

1 Ashkhabad 

(C126) 

37° 

56’ 

58° 

24’ 200 Astrophysical Laboratory of the Institute of Physics and Geophysics 

AS / Turkmen SSR / Sadykov, Ya.F., Astapovich, S.I. 

R, Ph, V 

N696 

2 Kazan 55° 

47’ 

49° 

07’ 80 Astronomical observatory named Engelgart of the Kazan University / 

Tatarstan / Russian SFSR / Kostylyov, K.V. 

R 

N233 

3 Kiev 50° 

27’ 

30° 

30’ 185 Astronomical observatory of the Kiev University named Shevchenko / Ukrain. SSR / Bogorodskikh, A.F. 

R, Ph 

N320 

4 Odessa 46° 

29’ 

30° 

46’ 50 Astronomical observatory of the Odessa University / Ukrain. SSR / 

Tsesevich, V.P. 

R, Ph, V 

N680 

5 

Stalinabad 

(Dushanbe) 

(C115) 

38° 

34’ 

68° 

46’ 820 Institute of Astrophysics AS Tajik SSR / Tajik SSR / Babadzhanov, P.B. 

R, Ph, V 

N680 

6 Tomsk 56° 

29’ 

84° 

59’ 120 Tomsk Polytechnical Institute / Russian SFSR / Fialko, Ye.F. 

R 

N224 

7 Kharkov 

(B141) 

50° 

90’ 

36° 

14’ 140 Kharkov Polytechnical Institute / Faculty of Radioengineering / Ukrain. SSR / Kashcheyev, B.L. 

R 

N358 

All meteor centers of the Soviet Union that performed the IGY observation program had to carry out 

radar observations. In the former USSR a great importance has been given to the fulfillment of the IGY 

meteor program with allocation of public funds (the main initiative and the general management was 

performed by Prof. V.V. Fedynskiy). During the existence of the USSR, the research on meteors, both in 

specified centers (see Table 6) and some other establishments, has been actively sponsored at the highest 

level (as is a rule for large international projects). In the second half of the twentieth century, the 

experimental meteor radar-tracking supervisions, lead by Kharkov, were considered as one of the best in 

the world. 

 With the purpose of preservation and the development of meteoric knowledge in view of a 

meteor heritage of the former Soviet Union, it is necessary to establish a sponsored program for the 

accumulation of Soviet meteor study results of the NIS. The first implementation of such a program can 

be the establishment in Kharkov, Ukraine, of the first piloted center of preservation and development of 

meteor knowledge of the former Soviet Union on the basis of the KhNURE. KhNURE possesses access 

to the basic part of the meteor scientific heritage of the former USSR due to the fact that it is one of the 

oldest meteor radar centers of the former USSR. 

 Other countries also face problems in the preservation of the meteor scientific potential of the 

20th century, especially for NIS. In the 20th century, the amount of data was so great that the 


researchers were unable to cope with its handling, especially since the existing computer facilities were 

inadequate. In the 21st century, new levels of information processing may allow processing of data 

from previous years with modern methods. This also applies to the meteor data that were preserved in 

WDCs (Boulder, USA; Moscow, Russia; Slow, UK, and Japan). Finding, extracting and translating 

meteor observation data of the past to modern media could fill up the Slovakia international meteor data 

centre. This also applies to the meteor data recorded in the sixties on 35-mm film everywhere in the 

world. 

6 Conclusions 

This work was undertaken in the framework of international projects 2007-2009 International 

Heliophysical Year. 

Received in the KhNURE, distributions of parameters of a class of near-parabolic and hyperbolic 

meteoric orbits on the Kharkov data of radar-tracking supervision of 1972-1978 represent an 

empirical model of an observable sporadic complex of meteor orbits of this class. 

Separate attention is deserved with an observable complex of meteoric orbits of the small sizes 

(e.g. the Eccentrides, the Sungrazing group). 

The problem of near parabolic/hyperbolic orbits is not solved yet. 

There are facts supporting the reality of “hyperbolic meteors”. Scientists haven’t enough 

published uniform hyperbolic orbital data. 

There are difficulties in comparing the radar observation data obtained from 4 sites (Banks 

Peninsula, New Zealand; Tavistock, Canada; Kharkov, Ukraine; Arecibo, Puerto Rico). 

Today it is necessary to create the common unified radar catalogue, maybe, in the frame of the 

international program ISWI, maybe other ways, with collaboration of the Ukraine, the USA, 

New Zealand, Canada, Slovakia (IAU MDC), the Netherlands (Virtual meteor radar 

observatory), Japan, etc. in addition to the major advances in our understanding of the ecology of 

meteoroids within the Solar System and beyond it. 

There is dormant meteor data in the Meteor Centers of the IGY and WDCs. 

It is necessary to create international meteor centers of the NIS for preserving meteor heritage, 

outreach and to promote meteor research, for example, with a pilot center located in Kharkov. 

Acknowledgements 

This work was undertaken in the framework of international projects of the 2007-2009 International 

Heliophysical Year, discipline “Meteors meteoroids, dust”, CIP 65. Svitlana V. Kolomiyets is grateful 

for the support from the Meteoroids 2010 LOC, the Kharkov National University of Radioelectronics, 

the Ukrainian Astronomical Association, the International Charitable Fund of Olekcandr Feldman, The 

Fund of Oleksandr Feldman for her participation in the Meteoroids 2010 Conference. The author would 

like to express her gratitude to Dr. M. Safonova for considerable help with English editing. 


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2005), pp. 221-227 


Preliminary Results on the Gravitational Slingshot Effect and the Population of 

Hyperbolic Meteoroids at Earth 

P. A. Wiegert1

Abstract Interstellar meteoroids, solid particles arriving from outside our Solar System, are not easily 

distinguished from local meteoroids. A velocity above the escape velocity of the Sun is often used as an 

indicator of a possible interstellar origin. We demonstrate that the gravitational slingshot effect, resulting 

from the passage of local meteoroid near a planet, can produce hyperbolic meteoroids at the Earth’s 

orbit with excess velocities comparable to those expected of interstellar meteoroids. 

Keywords meteors · meteoroids · interstellar material · orbital dynamics 

1 Introduction 

The search for interstellar meteoroids is complicated by contamination of the sample by the abundant 

meteoroids originating within our own Solar System. Meteoroid velocity is frequently used as a filter to 

distinguish between these two samples, with velocities above the hyperbolic limit at the Earth’s orbit 

taken as being interstellar in origin. This criterion is based on the assumption that meteoroids on 

hyperbolic orbits do not originate within our Solar System. 

 However, there are processes at work in our Solar System that certainly produce unbound 

meteoroids. One of these is the so-called gravitational slingshot, whereby a meteoroid or other particle 

passing near a planet can exchange energy and momentum with it. Such interactions should produce 

hyperbolic meteoroids at the Earth’s orbit that are of a purely local origin. In order to distinguish these 

from true interstellar meteoroids, an understanding of the properties and fluxes of such meteoroids is 

needed. 

 Meteoroids ejected from other solar systems are expected to enter the Solar System with excess 

velocities typical of the velocity dispersion of stars in the solar neighborhood, about 20 km/s. Since 

energy and not velocity is conserved, they would arrive at Earth with a velocity near (202 +422

)

1/2 ä 46.5 

km/s where 42 km/s is the escape velocity from the Sun calculated at the Earth’s orbit. The presence of 

this excess velocity has been the traditional hallmark searched for when one looks for extra-solar 

meteors. 

2 Review 

Whether of an interstellar nature or not, hyperbolic meteors have been reported in the past, having been 

observed both in space and at the Earth. Spacecraft dust detectors aboard the Ulysses, Galileo and Helios 



P. Wiegert ( ) 

Dept. of Physics and Astronomy, The University of Western Ontario, London Ontario CANADA. Phone.: +1-519-661-2111 ext. 81327; 

Fax: +1-519-661-3283; E-mail: pwiegert@uwo.ca 


spacecraft (Grün et al 1993; Krüger et al 2007) have detected very small (10-18 - 10-13 kg) grains moving 

at speed above the local solar system escape velocity and parallel to the local flow of interstellar gas. 

These particles are too small to be detected as meteors at the Earth, sizes > 10-10 kg may be required for 

this. These larger particles have also been reported to have a significant hyperbolic component. 

Between 0.2% and 22% of meteors observed at the Earth by various surveys, optical and radar-based, 

have shown a hyperbolic component according to a recent review by Baggaley et al (2007). Conversely, 

other work (Hajduková and Paulech 2007; Hajduková 2008) has shown that many hyperbolic meteors 

may only appear so as the result of measurement errors. For example, many of the hyperbolic meteors 

are associated with shower radiants or the ecliptic plane, unlikely associations for interstellar meteors. 

As a result observations of hyperbolic meteors in the Earth’s atmosphere remain somewhat 

controversial. The problem rests on the velocity, the key signature of an interstellar origin, but which 

often has an uncertainty (~10%) which is of the same order as the effect one is trying to detect. 

 The question of the nature of hyperbolic meteors and the possible presence of interstellar 

meteoroids within our Solar System is an interesting one, but here we address the question of whether or 

not hyperbolic meteors could be produced within our own Solar System, in particular by the 

gravitational slingshot effect. 

3 Model 

In this preliminary work, we simply consider the well-known problem of two-dimensional gravitational 

scattering of meteoroids off a moving planet. The planets are all considered to be on circular coplanar 

orbits, with the meteoroids moving within this same plane. A proper treatment relevant to our Solar 

System will require considering the full three-dimensional scattering problem, but the simple two 

dimensional problem provides us with initial insight into the broad strokes of the result. 

 We consider the scenario depicted in Figure 1 below. The planet is moving to the left with a 

velocity V. The meteoroid arrives with speed v, direction  and impact parameter y, all measured in the 

heliocentric frame. The arrival velocity is assumed to be less than the local solar escape velocity at the 

scattering planet. After scattering off the planet, the meteoroid departs with a new velocity vf and 

direction f. If this final velocity places the meteoroid on an unbound orbit but one which will cross that 

of the Earth before leaving the Solar System, we conclude that it constitute an observable hyperbolic 

meteoroid of local origin. 

Figure 1. The angle  and the impact parameter y are defined as shown, in the heliocentric frame. 


For the purposes of this study, we assume that all the planet are bombarded by meteoroids 

arriving from all directions, with all possible impact parameters and (bound) velocities, and ask what 

fraction of these would become observable hyperbolic meteors at the Earth. 

 The results for meteoroids arriving at a particular planet with a particular speed can be 

summarized in a single figure displaying the scattering results for a range of arrival direction and impact 

parameter, here taken on a 100x100 grid. Figure 2, for example, shows the result of meteoroids arriving 

at Jupiter with a heliocentric velocity of 1.4 times the local circular velocity. A substantial fraction of 

these objects, indicated by the black area in the figure, leave Jupiter on hyperbolic Earth-crossing orbits. 

Of course, having arrived at Jupiter on nearly-unbound orbits (the local escape speed is 21/2 ä 1.414 

times the circular velocity), many of these meteoroids are close to the parabolic limit and thus are 

relatively easy to scatter onto hyperbolic orbits. Lower arrival velocities (Figures 3 to 5) produce fewer 

hyperbolic meteoroids, as would be expected. 

Figure 2. Scattering results for meteoroids arriving at Jupiter with 1.4 times the local circular velocity. Phi is the 

arrival direction  and y is the impact parameter, as a fraction of the size of the Hill sphere. Grey indicates particles 

which leave on hyperbolic heliocentric orbits but do not cross the Earth’s orbit, black indicates particles scattered 

onto hyperbolic Earth-crossing orbits. 


Figure 3. Scattering results for meteoroids arriving at Jupiter with 1.3 times the local circular velocity. 

Figure 4. Scattering results for meteoroids arriving at Jupiter with 1.2 times the local circular velocity. 

 


Figure 5. Scattering results for meteoroids arriving at Jupiter with 1.1 times the local circular velocity. 

The distribution of velocities that these meteoroids would have measured should they happen to 

impact the Earth is displayed in Figure 6. This figure collects all the hyperbolic meteoroids produced 

during the simulations used in the production of Figures 2 to 5, and displays the excess velocity that 

would be observed at Earth. Most of the hyperbolic meteoroids are just above the hyperbolic limit, but 

there are some which can reach excess velocities of a few km/s, just what is expected of interstellar 

meteoroids. Thus we cannot conclude that hyperbolic meteoroids are necessarily of interstellar origin. 

Figure 6. Distribution of excess velocities measured at the Earth for hyperbolic meteoroids of Figures 2 to 5. 

Fraction is relative to the total number of meteoroids simulated. 


 The other planets are also capable of producing hyperbolic meteoroids. Mercury and Mars are 

the least efficient due to their low masses, and are not plotted amongst the following figures, which 

illustrate the velocity distribution produced from a similar consideration of Saturn (Figure 7), Uranus 

(Figure 8), Neptune (Figure 9) and Venus (Figure 10). These planets are all much less efficient than 

Jupiter and produce hyperbolic meteoroids that almost exclusively arrive at Earth with excess velocities 

below 1 km/s. 

Figure 7. Distribution of excess velocities measured at the Earth for the hyperbolic meteoroids scattered by Saturn. 

Missing points indicate those arrival velocities which are not produced by any of the initial conditions considered. 

Figure 8. Distribution of excess velocities measured at the Earth for the hyperbolic meteoroids scattered by Uranus. 


Figure 9. Distribution of excess velocities measured at the Earth for the hyperbolic meteoroids scattered by 

Neptune. 

Figure 10. Distribution of excess velocities measured at the Earth for the hyperbolic meteoroids scattered by 

Venus. 

4 Conclusions 

The gravitational slingshot effect can produce meteors with hyperbolic heliocentric velocities measured 

at Earth that originate wholly within our Solar System. Though our study here is far from exhaustive, we 

have found that hyperbolic are most easily produced by Jupiter from meteoroids with near-parabolic 


orbits. The majority have small (< 1 km/s) excess velocities but some can exceed 5 km/s. Thus we 

conclude that hyperbolic excess velocities, even of a few km/s, are not unequivocal signatures of an 

interstellar nature. 

 Future work would involve extending these results to full three-dimensional scattering, which we 

are currently undertaking. In addition, estimates of the flux of gravitationally scattered meteoroids at the 

Earth would be of great value. However, this calculation will require the determination of the meteoroid 

environments of the planets first, as the production of hyperbolic meteoroids depends sensitively on both 

the speed and direction with which the meteoroids approach the scattering planet, and the relative 

populations of such meteoroids is not yet known. 

Acknowledgements 

This work was performed in part with support from the Natural Sciences and Engineering Research 

Council of Canada. 

References 

Baggaley WJ, Marsh SH, Close S (2007) Interstellar Meteors. Dust in Planetary Systems 643:27–32 

Grün E, Zook HA, Baguhl M, Balogh A, Bame SJ, Fechtig H, Forsyth R, Hanner MS, Ho-ranyi M, Kissel J, Lindblad B, 

Linkert D, Linkert G, Mann I, McDonnell JAM, Morll GE, Phillips JL, Polanskey C, Schwehm G, Siddique N, 

Staubach P, Svestka J, Taylor A (1993) Discovery of Jovian dust streams and interstellar grains by the ULYSSES 

spacecraft. Nature 362:428–430, DOI 10.1038/362428a0 

Hajduková M (2008) Meteors in the IAU Meteor Data Center on Hyperbolic Orbits. Earth Moon and Planets 102:67–71, DOI 

10.1007/s11038-007-9171-5 

Hajduková M Jr, Paulech T(2007) Hyperbolic and interstellar meteors in the IAU MDC radar data. Contributions of the 

Astronomical Observatory Skalnate Pleso 37:18–30 

Krüger H, Landgraf M, Altobelli N, Grün E (2007) Interstellar Dust in the Solar System. Space Science Reviews 130:401–

408, DOI 10.1007/s11214-007-9181-7, 0706.3110 



CHAPTER 4: 

METEOROID IMPACTS ON THE MOON 


Lunar Meteoroid Impact Observations and the Flux of Kilogram-sized Meteoroids 

R. M. Suggs1• W. J. Cooke2• H. M. Koehler • R. J. Suggs • D. E. Moser3• W. R. Swift4

Abstract Lunar impact monitoring provides useful information about the flux of meteoroids in the 

hundreds of grams to kilograms size range. The large collecting area of the night side of the lunar disk, 

approximately 3.8×106 km2

 in our camera field-of-view, provides statistically significant counts of the 

meteoroids striking the lunar surface. Over 200 lunar impacts have been observed by our program in 

roughly 4 years. Photometric calibration of the flashes observed in the first 3 years along with the 

luminous efficiency determined using meteor showers and hypervelocity impact tests (Bellot Rubio et 

al. 2000; Ortiz et al. 2006; Moser et al. 2010; Swift et al. 2010) provide their impact kinetic energies. 

The asymmetry in the flux on the evening and morning hemispheres of the Moon is compared with 

sporadic and shower sources to determine their most likely origin. These measurements are consistent 

with other observations of large meteoroid fluxes. 

Keywords impact flash · lunar impact · meteoroid flux 

1 Introduction 

Video observations of the Moon during the Leonid storms in 1999 and 2001 (Dunham et al. 2000; Ortiz 

et al. 2000, 2002) confirmed that lunar meteoroid impacts are observable from the Earth. One probable 

Geminid impact was observed from lunar orbit by Apollo 17 astronaut Dr. Harrison Schmitt (NASA 

1972). NASA’s Marshall Space Flight Center (MSFC) began routine monitoring of the Moon in June 

2006 with multiple telescopes following our first detection in November 2005 (Cooke et al. 2006 and 

2007). Of the more than 175 impacts observed in the first 3 years, 115 of them have been used to 

determine the flux of impactors in the 0.1 to 10s of kilogram size range. This flux is compared with 

other measurements in section 5 and the correlation of the observations with meteor showers and 

sporadic is examined in section 4. 

2 Observation and Analysis Process 

The observations are carried out at the Automated Lunar and Meteor Observatory located on-site at the 

 

R. M. Suggs ( ) 

NASA, Space Environments Team, EV44, Marshall Space Flight Center, Huntsville, AL 35812, USA. E-mail: rob.suggs@nasa.gov 

W. J. Cooke • H. M. Koehler • R. J. Suggs 

NASA, Space Environments Team and Meteoroid Environment Office, EV44, Marshall Space Flight Center, Huntsville, AL 35812, USA 

D. E. Moser 

MITS Dynetics, Space Environments Team, EV44, Marshall Space Flight Center, Huntsville, AL 35812, USA 

W. R. Swift 

Raytheon/MSFC Group, Space Environments Team, EV44, Marshall Space Flight Center, Huntsville, AL 35812, USA 


MSFC near Huntsville, Alabama (latitude 34.66 north, longitude 86.66 west) and at a remotely 

controlled observatory near Chickamauga, Georgia (34.85 north, 85.31 west). The instrument 

complement has changed somewhat over time beginning with a 10 inch (254 mm) diameter Newtonian 

reflector for the initial observations then two Meade RCX400 14 inch (355mm) diameter telescopes with 

Optec 0.33x focal reducers and StellaCam EX or Watec 902H2 Ultimate monochrome video cameras. 

Both cameras use the same Sony HAD EX 1⁄2 inch format CCD. The effective focal length is 

approximately 923mm giving a horizontal field of view of 20 arc minutes covering approximately 4x106

square km or 12% of the lunar surface (see Figure 1). In 2008, one of the 14 inch telescopes was 

replaced with a Ritchey Chretien Optical Systems 20 inch (0.5 m) telescope with the focal reducer 

adjusted to give approximately the same field of view as the 14 inch instruments. The limiting stellar 

magnitude at the 1/30 second frame rate is approximately 12. The video from the cameras is digitized 

using a Sony GV-D800 digital tape deck and sent by Firewire to a personal computer where it is 

recorded on the hard drive for subsequent analysis. 

Figure 1. Camera field of view and orientation. 

The observations of the night portion of the Moon are made when the sunlit portion is between 

10% and 50% illuminated. This occurs on about five nights and five mornings per month. No 

observations are attempted during phases less than 10% since the time between twilight and moon rise 

or set is too short. Observations are not made during phases greater than 45 - 50% because the scattered 

light from the sunlit portion of the Moon is too great and masks the fainter flashes. Large lunar albedo 

features are easily visible in the earthshine and are used to determine the approximate location of the 

impacts on the lunar surface. 

The recorded video is analyzed using two custom programs. LunarScan (available at 

http://www.gvarros.com) was developed by Peter Gural (Gural 2007). The software finds flashes in the 

video which are statistically significant (as described in Suggs et al. 2008) and presents them to a user 

who determines if they are cosmic ray impacts in the detector, sun glints from satellites between the 

Earth and the Moon, or actual meteoroid impacts. By requiring that a flash be simultaneously detected 

in two telescopes, cosmic rays and electronic noise can be ruled out. Five of the detected impacts were 

observed with only one telescope early in the program but only flashes which spanned more than two 

video frames and showed a proper light curve (abrupt brightness increase followed by gradual decay) 

were counted. There have also been a few impacts independently observed by amateur astronomers 

using 8 inch (200 mm) telescopes (Varros 2007; Clark 2007). For short flashes where satellite motion 

might not have been detectable, custom software was used to check for conjunctions with Earth orbiting 


satellites whose orbital elements are available in the unclassified satellite catalog (www.spacetrack.org). Since there is some probability that orbital debris or a classified satellite not listed in this 

catalog could cause such a short flash, a remotely controlled observing station was constructed in 

northern Georgia about 125 km from MSFC. This allows parallax discrimination between impact 

flashes and sun glints from manmade objects, even at geosynchronous altitude. After 3 years of 

operation of the remote observatory only one candidate flash due to orbital debris has been seen that 

could have been mistaken for an impact and that one showed orbital motion upon closer inspection. 

Whenever the weather doesn’t allow operation of the remote observatory, temporally short flash images 

are enhanced and closely examined for any sign of motion with respect to the lunar surface. 

After detection and confirmation, another computer program, LunaCon, is used to perform 

photometric analysis (Swift et al. 2007). Background stars are used as photometric references to 

determine the observed luminous energy of the flashes. Since a reference star is unlikely to be in the 

frame during a flash, the earthshine on the Moon is used as a transfer standard thereby correcting for 

first order extinction. LunaCon also displays graphics showing the lunar surface brightness, contrast 

between the lunar surface and space next to the limb, lunar elevation angle, lunar surface area in the 

field of view, and other data quality diagnostics as a function of time during the night. These displays 

make it obvious when clouds pass, twilight is contaminating the observations, the Moon drifts in the 

field of view, and atmospheric extinction is extreme. Using this information, time spans of clear 

weather and good data quality were determined for use in the calculations of observation time necessary 

for flux calculations. Flashes outside of these time spans were not used in the analysis reported here. 

Photometric accuracy is estimated to be approximately ± 0.5 magnitudes. 

3 Observational Results 

Using the photometric quality criteria described above, 115 impacts were observed during periods of 

consistent photometric quality. By plotting the histogram of number of flashes per magnitude bin 

(Figure 2), we determined that our completeness limit was approximately 10th magnitude (JohnsonCousins R band) and there were 108 flashes brighter than that. These were included in the dataset for 

further analysis. 

Magnitude Distribution

Magnitude

12 11 10 9 8 7 6 5 4

Number

0

10

20

30

40

50

60

1

6

17

34

50

7

Figure 2. Histogram of flash magnitudes showing completeness to approximately magnitude 10 


Calculating the flux to this completeness limit: 

Flux = 108 impacts / (212.4 hours * 3.8×106 km2

) = 1.34×10-7 km-2 hr-1 

 To compare with other estimates of meteoroid fluxes, the limiting kinetic energy corresponding 

to the limiting magnitude of our observations must be determined. We observe the intensity of the 

impact flash in our camera passband. The ratio of the optical energy and the impact kinetic energy is the 

luminous efficiency 12

\ 

]^_&=`+abc+&a+^ddae

	

 +f+g

\
"h  	i  	
/C+/jkC

l

where m is the mass of the impactor and v is its velocity. The luminous efficiency is a function of 

velocity and has been determined using laboratory measurements at low velocities (Swift et al. 2010) 

and using several meteor showers (Bellot Rubio et al. 2000 for Leonids and Moser et al. 2010 for 

Geminids, Lyrids and Taurids). The luminous efficiencies determined from laboratory and shower 

observations have been assimilated into a single expression by Swift et al. (2010) for the passband of the 

cameras used in our observations 

m

1

Using this expression and the velocities of the various showers associated with the observations 

we estimated the mass at our completeness limit to be approximately 100 grams. 

The impact asymmetry between the western (left, leading) and eastern (right, trailing) 

hemispheres evident in Figure 3 is real and when corrected for hours of observation amounts to a ratio of 

1.45:1. The explanation for this asymmetry is addressed in the next section. 

Figure 3. Impact flashes observed between June 2006 and June 2009 and culled for use in this 

analysis. Continuous monitoring was from April 2006 to the present. 


4 Modeling 

Our initial explanation for the asymmetry was this: observations of the western hemisphere occur 

leading up to first quarter phase when the observed portion of the Moon is exposed to both the Apex and 

Anthelion sporadic meteoroid sources. The eastern hemisphere is observed following last quarter phase 

when the Apex source is only visible from the farside of the Moon thus no Apex meteoroids can impact 

the portion of the Moon we are observing. The Apex source’s flux is lower than the Antihelion’s but the 

velocities are higher so the impact kinetic energy at a given mass would be higher. Thus the limiting 

mass would be lower and more meteoroid impacts would be visible. This seemed like a reasonable 

explanation but modeling of the asymmetry using the Meteoroid Engineering Model (McNamara et al. 

2004) showed that the ratio would be 1.02:1 rather than the observed 1.45:1 so sporadics could not be 

the dominant source of the impacts. This result was confirmed by similar calculations by Wiegert 

(private communication). 

Shower meteoroids then were a more likely explanation for the observed impacts and the 

expected rates and hemispheric asymmetry were calculated to test this hypothesis. Figure 4 shows the 

temporal variation of impacts compared with shower peaks. 

Figure 4. Impact flash distribution versus time compared with meteor showers. The red points are the observed 

rates with error bars representing the square root of the number of impacts per bin. The black curve is the impact 

rate calculated from observed values of zenithal hourly rate at the Earth. See text for discussion of this calculation. 

 The predicted flash rate was calculated using the reported shower zenithal hourly rates (ZHR), 

speed, and population/mass index. Knowledge of the camera energy threshold, combined with the 

shower speed and the luminous efficiency (Swift et al. 2010), enables the computation of the limiting 

mass for each shower. This may then be used with the ZHR (corrected for the lunar location) and the 

population and mass indices to obtain a flux. The predicted rate is obtained by multiplying this flux by 

the fraction of the observed lunar surface visible from the shower radiant. There are obviously 


uncertainties in the photometry and other quantities, so these were used to constrain the adjustment of 

the energy threshold, which was varied until a best fit with the observed Geminid rate was achieved. The 

Geminids were chosen because 1) they are the strongest annual shower in terms of rates, and thus 2) 

they have the best determined mass and population indices. The resulting impact rate was plotted for 

comparison with the observed rates (Figure 4). 

 There is a clear correlation between the observed and predicted rates. Some of the weaker 

showers, such as the June Bootids, JBO, do not correlate as well due to their small zenithal hourly rate 

and poorly determined mass index. The shallow mass indices for showers relative to the steeper one for 

sporadics means that there are relatively more large particles in the showers. This fact alone argues that 

observed lunar impacts are dominated by shower meteoroids. Sporadic source populations are less 

likely to contain larger particles but they do contribute to the overall observed rate. Since we are 

observing impacts from meteoroids larger than 10-1 kg and visual and video observers (from which the

population indices and ZHRs are derived) have limiting masses around 10-7 to 10-5 kg, we are 

extrapolating over several decades in mass to estimate the impact rate we observe. It is remarkable that 

the rates match as closely as seen in Figure 4. The mass indices for two showers had to be adjusted to 

get a better match. Figure 5 shows that the calculated impact rate for the Quandrantids (QUA) was too 

high and for the Lyrids (LYR) was too low. A better fit was obtained for the 2007 Lyrids when its 

population index was changed from 2.9 to values of 2.5, 2.3, and 2.6 for the dates of April 21, 22, and 

23, respectively. This shallower distribution increased the number of larger meteoroids to better match 

those impacts we observed. The 2008 Quadrantids had a reported population index of 2.1 which 

overestimated the number of large meteoroids by a factor of 10. When the population index was 

adjusted to 2.6, a better match with our observations was obtained. Figure 4 has these adjustments 

included while Figure 5 does not. 

Figure 5. Impact flash distribution versus time compared with meteor showers using observed ZHRs and 

population indices from the International Meteor Organization (http://www.imo.net/data/visual). The symbols are 

similar to those in figure 4. Adjustment of the population indices for the Quadrantids (2.1 to 2.6) and Lyrids (2.9 to 

~2.5) yielded the better fit seen in Figure 4. 


 Using these adjusted rates for the meteor showers gives a predicted hemispheric asymmetry 

during our observation periods of 1.57 compared to the observed ratio of 1.45:1. This is compelling 

evidence that shower meteoroids, including those from minor showers, dominate the observed impacts. 

5 Flux Comparison 

The observed flux of meteoroids with impact energies greater than our completeness limit was compared 

with fluxes determined by other techniques for larger objects. Figure 6 plots the flux determined using 

impact observations with those determined by all-sky fireball cameras, infrasound of meteor entries, 

lunar craters, satellite observations of fireballs, and telescopic observations of near-earth asteroids 

(Silber et al. 2009). The comparison is very favorable including the slight downturn from the power-law 

fit observed by the fireball network. 

Figure 6. Number of meteoroids striking the Earth each year versus the impact energy in kilotons of TNT. Our 

measurement is to the extreme upper left. The cyan curve closest to our measurement is determined from all-sky 

camera observations of fireball meteors in the Earth’s atmosphere. 

6 Conclusions 

MSFC’s 4 years of routine lunar impact monitoring has captured over 200 impacts. Data from the first 3 

years of operation were analyzed to investigate the source of the meteoroids, their flux, and the observed 

hemispheric asymmetry. It was found that shower meteoroids dominate the environment in this size 

range and explain the evening/morning flux asymmetry of 1.45:1. The observed flux of meteoroids 


larger than 100 g impacting the Moon is consistent with fluxes determined by all-sky fireball meteor 

cameras. With sufficient numbers of impacts, this technique can potentially help determine the 

population index for some showers in a size range not normally measured. 

Future plans include performing detailed calculations to investigate the observed concentration 

of impa

cknowledgements 

he authors wish to acknowledge the meticulous and dedicated support of the following observers who 

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supporting robotic lunar seismic and dust investigation missions are also planned. 

A

T

helped record the video: Leigh Smith, Victoria Coffey, and Richard Altstatt. Thanks also to Anne 

Diekmann who performed some observations and a portion of the analysis. This work was partially 

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MSFC Engineering Directorate. 

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gert, P.: 2008, private communication. 


An Exponential Luminous Efficiency Model for Hypervelocity Impact into Regolith 

W. R. Swift1• D. E. Moser2• R. M. Suggs3• W. J. Cooke

Abstract The flash of thermal radiation produced as part of the impact-crater forming process can be 

used to determine the energy of the impact if the luminous efficiency is known. From this energy the 

mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, , is 

a unique function of velocity with an extremely large variation in the laboratory range of under 6 km/s 

but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into 

granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that 

the energy is deposited via a serial impact process which affects the rate of deposition of internal 

(thermal) energy. An exponential model of the process is developed which differs from the usual 

polynomial models of crater formation. The model is valid for the early time portion of the process and 

focuses on the deposition of internal energy into the regolith. The model is successfully compared with 

experimental luminous efficiency data from both laboratory impacts and from lunar impact 

observations. Further work is proposed to clarify the effects of mass and density upon the luminous 

efficiency scaling factors. 

Keywords hypervelocity impact · impact flash · luminous efficiency · lunar impact · meteoroid 

1 Introduction 

The impact of meteoroids on the lunar surface is accompanied by a brief flash of light, detectable with 

small telescopes from the ground, Figure 1. These impact flashes have been successfully observed on 

the Moon by Earth-based telescopes during several showers (e.g. Dunham et al., 2000; Ortiz et al., 2000; 

Cudnick et al., 2002; Ortiz et al., 2002; Yanagisawa & Kisaichi, 2002; Cooke et al., 2006; Yanagisawa 

et al., 2006, Cooke et al., 2007; Suggs et al., 2008a,b; Yanagisawa et al., 2008) and for sporadic 

meteoroids by a campaign conducted by the NASA Marshall Space Flight Center (MSFC) since early 

2006. Although the initial shock wave from a hypervelocity impact produces a significant high 

temperature plasma and blackbody flash lasting on the order of microseconds as the shock wave passes 

through the material this is generally buried below the regolith surface and not readily observable, 

Figure 2 lower (Ernst and Schultz, 2007). Also obscured and/or quenched by the regolith is the plasma 

and vapor plume observed from impacts into solid surfaces, Figure 2 upper, as modeled in early lunar 

impact models (Melosh et al., 1993; Nemtchinov et al., 1998). What is observed at video rates by 

terrestrial telescopes is the secondary blackbody radiation from the cooling hot debris thrown upwards in 

 

W. R. Swift ( ) 

Jacobs ESTS Group/Raytheon, NASA/Marshall Space Flight Center, Huntsville, AL, 35812 USA. E-mail: wesley.r.swift@nasa.gov 

D. E. Moser

MITS/Dynetics, NASA/Marshall Space Flight Center, Huntsville, AL, 35812 USA 

R. M. Suggs • W. J. Cooke

Meteoroid Environment Office, NASA/Marshall Space Flight Center, Huntsville, AL, 35812 USA 


the initial moments of crater formation. Since the optical energy of such flashes can be readily 

measured telescopically, it is highly desirable to be able to estimate the energy of the meteoroid impact 

given the luminous efficiency  of the event. The concern then is how the luminous efficiency scales 

with the velocity, mass, and density of the impactor. 

Figure 1. Lunar impact as seen on May 2, 2006 with a 254mm aperture telescope at 30 frames/second. The lower 

sequence shows a magnified view of the flash decay versus frame. This impact is one of the brighter impacts 

observed to date. 

 Similarly, in light gas gun experiments into pumice and lunar simulant, Figure 2, there is often a 

very brief (microsecond) high temperature spike recordable by high speed photodiodes (Ernst and 

Schultz, 2004, 2007). This early-time spike is followed over the next tenth(s) of a second by a slowly 

decaying secondary production of light from the hot ejecta. Moderately fast ejecta particle trails are 

quite evident in video rate (1/30 second) images of gas gun tests as is the cooling of the ejecta from 

frame to frame. Although the first video field after impact is usually the brightest, localized initial shock

heating is not readily apparent in the hot ejecta dominated image. High speed camera images of lab tests 

(not shown) also show the primary source of illumination to be hot ejecta moving up, away from the 

impact rather than primary emissions from the shock wave propagating down into the target. Due to the 

much longer time period of these secondary emissions, their total output is significantly larger than the 


brief but intense shock and plasma emissions. This is especially true since most of the prompt emissions 

are hidden beneath the impactor and the particulate target surface. 

Figure 2. Traditional hypervelocity impact observations compared with impact into regolith. The emissions are 

thermal in nature and much longer lasting.

 A series of light gas gun experiments were conducted at the Ames Vertical Gun Range (AVGR) 

in which a Pyrex® glass bead was shot into JSC-1a lunar regolith simulant (McKay et al., 1997; Zeng et 

al., 2010) at various angles and velocities. It was a relatively simple matter to calculate the luminous 

efficiency of light gas gun experiments since the mass, material properties, and velocity of the impactor 

were precisely known and the flash intensity readily measured. A problem arose when one attempted to 

correlate this luminous efficiency with velocity over the small range of velocities (< 7 km/s) available to 

the technique. The increase of luminous efficiency with velocity between 2 km/s and 6 km/s was so 

steep that polynomial fits extrapolate to unrealistic ( > 1) values well before the usual meteoroid 

velocities, Vm, of some tens of km/s. Furthermore, if curves analogous to conventional impact crater 

dimension scaling with exponents of V 1

 to V 2 (Holsapple, 1993) are plotted through the luminous 

efficiency versus velocity data (almost vertical) they appear orthogonal (almost horizontal) to the data 

from these experiments. This implies the existence of additional phenomena that scales quite differently 

from conventional impact crater dimension scaling. 

In order to determine an appropriate model of impact luminous efficiency versus impact velocity, 

it is useful to briefly examine the internal energy produced by the initial impact shock wave itself and 

early post shock conditions. One can then relate these conditions to the special case of the luminous 

efficiency of an impact into lunar regolith to obtain evidence leading to an appropriate model. Finally, 

this model will be compared to knowledge of the luminous efficiency from both light gas gun 

experiments and the growing database of lunar impact measurements. 


2 Lunar Impact Luminous Efficiency 

It is useful to estimate the kinetic energy of an impactor on the moon’s surface from the total optical 

energy detected by a camera, E, using a ratio known as the luminous efficiency,  defined as: 

E KEimpactor / 1  3  (1) 

where E is defined as that energy at the source which is radiated into all space (4	 steradians) as 

measured by that proportion received in the camera aperture and KEimpactor is the kinetic energy of the 

impactor. Previous work has assumed surface radiation into 2	 steradians (Swift et al. 2008) or 

radiation into 3	 steradians (Belio Rubio et al. 2000). The geometric projection removes the effect of 

telescope aperture from the measurements leaving bandpass considerations unresolved. Initial 

assumptions that the radiation was from the early crater surface and thus into 2	 steradians were 

abandoned when it was realized that the primary radiation was from free particles above the surface. E

is instrument specific, leading to the camera optical ratio, Oc  E / Et, with an alternate definition of 

luminous efficiency, t or total luminous efficiency, based on total radiant energy, Et 

i impactor

i

1t 3 Et / KEimpactor 
 5miE4 / KE (2) 

where the summation is over i particles of mass mi and specific energy E’

i. Note that Oc is less than 

unity and is a function of the camera spectral response convolved with the declining blackbody 

emissions over the time of the observation. Improvements in the determination of Oc and the variation 

from camera to camera are underway but the distinctions between E and Et, are poorly defined. Note 

that, unlike the rate of thermal emissions, which is fourth power in temperature, Et, is the integral over 

time and is almost linear in temperature since the thermal specific energy for each particle is the specific 

heat capacity, Cp, times the temperature change, T, during emission, E’

i = ,CpTi. Unless otherwise 

defined, whenever  is mentioned it is usually safe to assume that  is implied for the purpose of this 

paper. 

 NASA’s Marshall Space Flight Center has been consistently monitoring the Moon for impact 

flashes produced by meteoroids striking the lunar surface since early 2006 (Cooke et al 2006). The 2006 

Geminids, 2007 Lyrids, and 2008 Taurids, Table 1 below, produced a small but sufficient, sample of 

lunar impact flashes with which to perform a luminous efficiency analysis like that outlined in Bellot 

Rubio et al. (2000b). The analysis technique, discussed in detail by Moser et al. (2010), involves 

‘backing out’ the luminous efficiency by relating the number of impacts expected on the Moon as a 

function of energy to the time integral of the flux of meteors of known size and the lunar area 

perpendicular to the shower radiant of known mass index, S. The resulting luminous efficiencies for the 

cameras used for the observations are shown in Table 1 with the published results of Bellot Rubio et al. 

(2000b) for the 1999 Leonids. Although their results are for a less sensitive camera and are based on the 

assumption of radiation into 3	 steradians rather than 4	 as assumed here, the results are consistent with 

the current determinations. Also shown are the results of hydrocode modeling of the 1999 Leonids by 

Artemieva et al. (2000, 2001). Although the agreement of this hydrocode model to the other results is 

entirely fortuitous, it is shown here for reference purposes. Expected errors are less than ± 20% for the 

camera dependant luminous efficiency. Note the almost constant luminous efficiency, , over these 

velocities. 


Table 1. Luminous Efficiency from Lunar Impact Observations (Moser et al., 2010). 

Shower # Flashes Obs. Time (hr) V (km/s) S (mass index) 

2008 Taurids 12 7.93 27 1.8 1.6×10-3

2006 Geminids 12 2.18 35 1.9 1.2×10-3

2007 Lyrids 12 10.22 49 1.7 1.4×10-3

1999 Leonids* 5 1.5 71 2 2×10-3*

1999 Leonids** N/A (model) 71 N/A 1×10-3/2×10-3

*

 Bellot Rubio et al. (2000) results for a different camera and slightly different geometry. 

** Artemieva et al. (2000, 2001) hydrocode model results for densities 0.1 / 1.0 g/cm3. 

3 Light Gas Gun Camera Angle, Impact Angle and Velocity Experiments 

A series of hypervelocity impacts into JSC-1a lunar regolith simulant at various angles and velocities 

were observed with the same video cameras used for lunar impact monitoring (Suggs et al. 2008b). 

Multiple cameras at three view angles were used in staring mode at the video rate of 29.97 frames per 

second. Their field of view, Figure 3 left, comprised the complete impact zone and the lenses were 

fitted with calibrated neutral density filters to obtain correct exposures. This contrasts with traditional 

light gas gun observations as illustrated in Figure 2, particularly in the time scale here of hundreds of 

milliseconds as opposed to hundreds of microseconds or less. Due to the long exposure sequence and 

good near IR sensitivity of the cameras, the hot ejecta from these impacts forms a cooling curve lasting 

multiple frames very similar to the bulk of the signals observed in lunar meteoroid impacts. 

Figure 3. Software was written to semi-automatically determine the illuminated area and to compensate for 

background and video intensity scaling. The complete “encircled” image is in the false color image on the left while 

an enlarged view centered on the impact is to the right. 

For these experiments, Pyrex® spheres 6.35mm in diameter and of mass 0.29 g were fired in 

vacuum at velocities from 2.4 km/s to 5.75 km/s at elevations of 15 to 90 degrees into a deep horizontal 

pan of JSC-1a lunar simulant. The cameras were mounted to observe at three angles: A) camera 2 with 

a 25mm lens used at f/10.84 was aimed near normal at 65 degrees elevation, 2.13m from impact, B) 


camera 3 with a 25mm lens used at f/12.04 was aimed at 33 degrees elevation, 1.75m from the impact 

and C) camera 5 with a 17mm lens used at f/4.0 viewed horizontally 1.3m from the impact. Cameras 2 

and 3 were StellacamEX video cameras set at the gain used for lunar meteor impact observations. For 

these observations the cameras were fitted with Andover precision neutral density filters from optical 

density (OD) from OD 1.02 to OD 3.77. These dark filters were chosen to keep the extremely bright 

signals from saturating the images. Camera 5 was a Watec model 902-H2 Ultimate with the same 

charge coupled device (CCD), gain, and filters as the others. A parallel set of cameras fitted with 

photographic grade neutral density filters had radiation leaks in the IR so the data was discarded. 

Laboratory and stellar calibrations were used to determine the electron gain of these cameras and the 

published quantum efficiency curve, QE(), for the Sony ICX248AL CCD was used to evaluate spectral 

response. The QE was used to convert from photon counts, which these cameras measure, to detected 

energy in order to determine . Software was written in the Interactive Data Language (IDL) computer 

language, Figure 3, to isolate the flash area in each image, compensate for NTSC-J video scaling, 

measure the intensity, subtract backgrounds, and calibrate the results. The total emission meaning that 

from all illuminated pixels for all illuminated frames is used to calculate  as shown in Figure 4. 

Figure 4. Total luminous efficiency of impacts of Pyrex into JAS-1 versus velocity and impact elevation. On the 

left is the horizontal view and on the right is the view from above. Note the convergence in both elevation and view 

angle near 5.5 km/s. 

A brief examination of the variation of  with velocity and angle of impact in Figure 4, shows a 

convergence in both tangential (horizontal) and normal (overhead) views to very similar values at higher 

velocities for all angles of incidence. The low velocity enhancement of low angle impacts due to the 

“plowing up” of particles is evident as well as the negation of the effect at higher velocities. The low 

velocity, low angle of incidence  can be “compensated” to an equivalent  at normal incidence with a 

simple sine function of the impact angle that disappears above 4.4 km/s: , c = *Sin(i)^(4.4-

MIN(4.4,v)). One can see the effect of incidence compensation in Figure 5 where the normal data is 

shown as blue diamonds and the compensated normal data with yellow triangles. This compensation 

makes comparison with meteoroid impacts more realistic. The independence of luminous efficiency 

with angle of incidence at high velocities was also noted by Artemieva et al. (2000) and Nemtchinov et 


al. (1998). It is also a very convenient result for lunar impact observations since the impact angle is 

often unknown. 

 It is also desirable to correct for view angle, particularly since, due to gun emplacement, the 

normal view is not available. A useful viewing geometry, although inexact, is that of an oblate spheroid 

having a unit circle projection from above (normal) and an elliptical projection seen from any other 

angle. Development of this spheroid cross section model is straight forward. One lets the tangential 

view be approximated by a standard ellipse with unity half width a and half height b with area 	ab. The 

normal view is a circle with unit radius a and area 	a

2

 so that the tangential cross section ratio is b/a or 

just b. The height of the cross section of the spheroid viewed from angle  is given by the radius in 

polar form of the ellipse where r, is given by r

2

 = a

2

b2 / (a2 sin2 + b2 cos

2

). The area at view angle 

is 	ar so that the cross section ratio is simply r. Given experimental normal and tangential emission 

components at various velocities, their ratio can be used to determine the parameter, b = 0.8V -0.13, a 

function of velocity which becomes unity (spherical) above 10.9 km/s. This has been used to correct the 

camera 2 data to the normal in Figure 5 prior to impact angle compensation. The primary lesson learned 

from this is that the surface intensity ellipse converges to a sphere and view angle effects are minimal 

for the higher velocities found in lunar meteoroid impacts: a very convenient result. Furthermore, it is 

the normal result from impact experiments that is to be compared with meteoroid impacts. A likely 

explanation is that at high impact velocities, most of each particle’s emission is into free space 

significantly above the surface. This implies radiation into 4	 steradians rather than 2	 surface radiation 

or a compromise of 3	 steradians (Bellot Rubio et al. 2000b). 

Figure 5. A trial fit compensating the luminous efficiency data for impact elevation was made for the vertical 

(normal) view. The normal, incidence compensated view is the one to use when comparing to meteoroid velocity 

lunar impacts.. Also shown is a power law velocity fits to V 6

, light blue, and an exponential fit, dark line. The 

power law fit becomes absurd at meteoroid velocities giving ¬ > 1 above 28.7 km/s. 

Also shown in Figure 5 are trial fits to the incidence compensated  versus impact velocity data. 

As can be expected with a log-linear plot, a traditional power law fit appears curved while an 

exponential is a straight line fit to the data. The normal incidence data is approximated by a power law 


fit of V 6

 which, unfortunately, becomes improbable at meteoroid velocities giving  > 1 above 28.7 

km/s. It is also difficult to imagine a physical model with such an exponent of velocity covering three 

orders of magnitude change for a less than 3x change in velocity. Simple exponential functions, 

although a better fit over the range of the data, also become unlikely at meteoroid velocities implying an 

exponential form that is not simply direct with velocity as is the one shown here. These questions drive 

much of the discussions to follow. 

 A luminous efficiency error analysis was performed for the  determinations yielding an 

estimated one sigma precision of 21% in . The largest contributors to the error are the camera distance, 

the electron gain, the effective QE and the average energy per photon. The distance is problematic since 

the emission plume is a dynamic, three-dimensional object and each pixel views a part of the image at a 

different distance. Note that if one doubles this error the final uncertainty will increase by about 27% to 

30%. The electron gain uncertainty, e-/IU, is relatively small but can be reduced further with careful 

spectral calibration. The effective QE and energy per photon uncertainties are both due to incomplete 

understanding of how the CCD reacts to the color changes in images of rapidly cooling particles. 

Refinements for future experiments are possible which would significantly reduce the uncertainty 

although, due to the extremely large dynamic range of the  data (up to five orders of magnitude), the 

estimated precision is deemed sufficient for current purposes. 

4 Impact of Shock Waves in Materials 

A logical first step to determine the correct scaling of impact luminous efficiency versus impact velocity 

is to briefly examine the internal energy produced by the initial impact shock wave itself and early post 

shock conditions. Indeed, this is the approach used in hydrocode modeling of impacts (Nemtchinov, 

1998; Artemieva, 2000, 2001). One can then relate these conditions to the special case of the luminous 

efficiency of an impact into lunar regolith to deduce an appropriate model. One starts with a review of 

the basics (Melosh 1989; Lyzenga 1980). 

 Impact of a hypervelocity projectile with a solid target surface, such as that of a particle of 

regolith, produces shock waves which propagate from the point of impact through the target. The shock

wave speed in the target, Us can be represented by the linear Hugoniot shock velocity relation in the 

notation of Melosh (1989): 

Us = Cb + S up. (4) 

Here Cb is the bulk speed of sound in the target, up is the particle speed and S is an 

experimentally determined material property. Coupling at impact is determined by comparing the shock

impedance Zs of the target and the impactor: 

s Us Z pressure velocity 0 3 6 / 6 
  (5) 

 Then Ps 
 Zsu p 
  0Usu p (6) 

Here 0 is the initial target density and Ps is the pressure behind the shock wave. Note that, from 

Equation 6 above, the shock pressure is second order in up, which in direct impact experiments is the 

impact velocity. A few idealized special cases serve to introduce the role of shock impedance. Assume 

the target and impactor are the same size and Ztarget < Zimpactor then the impactor and target move together 


after impact at a reduced velocity. Similarly, if Ztarget > Zimpactor then the impactor bounces back from the 

target and target and impactor move in opposite directions. If both materials have the same shock

impedance then the impactor will stop and the target will move away at the contact speed up. The 

extreme pressures Ps of the shock wave which give rise to acceleration of the target to up also give rise 

to irreversible effects which can include heating, thermal radiation, phase change, and decomposition. 

Due to the energy lost from the shock wave, Us and thus up decline along the direction of propagation. 

This implies that, in a series of impacts, the energy transferred in each impact is some fraction of that of 

the preceding impact. 

Early high pressure research (Walsh and Christian, 1955; McQueen et al., 1967) showed that 

solid materials under extreme pressure followed a pressure-volume curve characteristic of the material 

called the Hugoniot, Figure 6 (Lyzenga, 1980). Indeed, the determination of the Hugoniot for 

geophysical materials, (McQueen et al., 1967; Ahrens et al.,1969) is of central importance in planetary 

mantle investigations and drives much of the impact work to date. In a material which is transparent in 

the un-shocked state, shock temperature and shock velocity, Vs, can be measured by optical pyrometry. 

The work by Lyzenga (1980) and Lyzenga and Ahrens (1982) in which the primary thermal emissions 

from shocked transparent minerals are examined provides a useful introduction to the techniques 

involved. Shock emission techniques are further developed theoretically and experimentally by 

Svendsen et al. (1987) with attention paid to emissions from the shock interface. Of particular interest is 

the sensible (thermal) internal specific energy of the shocked state, which can be determined from the 

product of the change in volume times the change in pressure, E

 = 1⁄2(V0-V1)P, as in Figure 6, since 

this energy gives rise to the observed primary and secondary thermal emissions. Although similar 

determinations for opaque materials such as lunar regolith are not as easily performed the same 

principles apply. Also note that the physical properties of the material, including shock impedance, 

melting point, heat of fusion, emissivity, etc. all tend to vary along the Hugoniot adding an interesting 

complexity to the problem. 

Figure 6. Simple Hugoniot compared with isotherm and isentrope of compression by Lyzenga (1980). Upon 

impact, a solid target is compressed along the Rayleigh line from Vo to V1. Decompression after shock wave 

passage is at V1 along P followed by isentropic relaxation The total energy is given by the shaded area while 

the irreversible internal specific energy, the red portion, is E

 = 1⁄2(V0-V1)P. 


The sensible portion of this internal energy is expressed immediately as a temperature change giving 

rise to the primary thermal radiation observed in transparent shocked materials. Although the shock

temperature with phase change is less than it would be without phase change, observed shock

temperature ranges from 4000 K to 8000 K as measured by multi channel optical pyrometry. A fast 

response (5 ns) is required since sample thicknesses of approximately 3 mm result in emissions lasting 

about a third of a microsecond while the shock wave traverses the material. Such direct emissions are 

consistent with the brief initial spike observed in impacts into pumice (Ernst and Schultz, 2007) and 

lunar simulant by a transparent projectile but not an opaque one. Investigations have been performed by 

Ahrens et al. (1973) and Ahrens and Cole (1974) using lunar regolith returned by the Apollo missions to 

determine their shock properties. Similar work (Anderson and Ahrens, 1998, Schmidt et al., 1994) has 

also been done for chondritic meteorites where the porosity was found to be of particular importance. 

After relaxation, the remaining sensible energy and much of the phase change internal energy will be 

found in thermal form providing the cooler but still hot particles observed in a laboratory or lunar impact 

into granular materials. 

 It is desirable to compare these investigations to the observations of higher velocity meteoroid 

impacts on the moon (Ahrens and O’Keef, 1972) and indeed the material properties determined in the 

laboratory are used in hydrocode simulations which attempt to answer similar questions. For current 

purposes, it is sufficient to note the following: 

 Passage of shock wave leaves energy in the target 

 This residual shock energy is expressed as heat in the target 

 Residual specific energy (heat) is traditionally expressed as V2

 Remainder of shock wave energy is passed on as kinetic energy 

 Target material becomes an impactor with reduced kinetic energy 

 Powder targets imply multiple serial impacts within the target 

5 Shock Waves in Porous Materials and Powders

The moon is covered with a thick layer of porous lunar regolith so lunar impact emissions are governed 

in a large part by the porosity of the target. In the usual model, porous materials are first compacted to a 

dense state prior to the initiation of the shock wave into the body of the material. Although this 

compaction occurs at pressures well below that of the shock wave, volume changes and PV work can 

be a significant contributor to the post shock temperature of the bulk material (Dijken and DeHosson, 

1994a). For experiments to determine the Hugoniot of some material this “interface” heating is an 

annoying artifact but for impact sintering to form exotic materials the effect does useful work (Dijken 

and DeHosson, 1994b). 

The approach taken by Dijken and De Hosson (1994a, 1994b) for powder sintering by impact is 

particularly instructive in that they couch the effects in term of impactor velocity up and the ratio of solid 

to powder specific volume V0/V0. In their approach, they follow a path in the P-V plane that 

compresses at zero pressure from initial powder specific volume V00 to solid density V0 then compress 

with V0 constant to the constant internal specific energy (E

-E0) curve giving the shock pressure Ps as 

the starting point for determining us. This implies an additional internal energy component of (V00-

V0)PS. In their development, the powder is viewed as initially separated planes of identical solid 

material which, by symmetry, leads to the equipartition of internal and kinetic energy. One can define a 


partition function B of energy in the target mass mt between internal (thermal) and kinetic energy as 

follows: 

1⁄2 (1 ) ( ) m u /2 (7) 2

0 t t

2 KEimpactor 
 mi

ui 7 B mt E4 E4  B

Equipartition 2

0 1⁄2 ut 8 B 
 1/ 2 8 (E4 E4) 


The simple equipartition approximation is shown to be particularly accurate (better than 5%) for 

loose powders with impactor velocities below 5 km/s when compared with data and more precise 

models (Dijken and DeHosson, 1994c). Lunar regolith (Ahrens and Cole 1974) with a bulk density of 

1500 to 1800 kg/m3

 and a solid density averaging 3100 kg/m3, has a relative powder density of 0.48 to 

0.58, for which the above approximations are reasonable. The JSC-1a lunar regolith simulant (McKay 

et al. 1997) used in the above luminous efficiency determinations is by design very similar to the Apollo 

samples in these respects. 

When one examines the internal energy effects of a sequence of impacts, Figure 7, each target 

particle becomes the impactor for the subsequent impact. From the equipartition assumption, B = 1/2 

and the energy is quickly expended in the powder as internal (thermal) energy within a short distance 

from the initial penetration track. One can imagine a similar result when the effect is generalized to a 

branched chain series of impacts. Radiation, conduction, and plasma quenching, all lead to a rapid 

statistical distribution of this energy within the initial zone. Although the primary impactor can have 

impedance significantly different from the solid particles of the powder giving an initial ratio, B0, 

different from the equipartition assumption, the serial impacts between like particles in the regolith 

predominate. In any case, it is clear that the impactor energy is thermalized very rapidly in the 

penetration phase of the impact into regolith. This view is confirmed by recent high speed camera results 

by Ernst et al. (2010) which show that in the first 50 μs the energy of the impactor is primarily confined 

to several impactor radii of the impact. This compact thermal reservoir leads to a useful macroscopic 

thermal approach to the problem of energy partitioning in the impact zone. 

Figure 7. Cartoon of the effect of serial impacts in a particulate target. In the usual case, B = 1⁄2 corresponding to 

equipartition of energy. Note that the specific kenetic energy expressed by velocity Un declines extremely rapidly. 


6 A Statistical Physics Approach 

The impact zone defines a thermal reservoir of many small but macroscopic particles thermally linked 

with one another. These are precisely the assumptions used in the development of the canonical 

probability distribution of the particle energy states, Figure 8. It is a small extension of the canonical 

representation of the energy of particle r, Er, in Joules to the representation of that energy as an energy 

density, E'r in J/Mol. Similarly, the temperature parameter,  = 1/kT, becomes 1/RT when expressed as 

an energy density. The ratio remains unchanged. Similarly, the specific energy of particle r can be 

expressed as E'r = V2

r in J/kg and the specific energy of the impact zone thermal system can be 

expressed as E'r = V2

m in J/kg where Vm is the impactor velocity and Vr is the specific energy equivalent 

velocity of state r. The resulting probability of a particle being in state r becomes 

2

2

m

r

V

V

Pr Ce




 (8)

where C is the normalization constant. The energy density E'

T of any particular set of states, those states 

emitting visible radiation in this case, then becomes 

4 
 5 9



visible

m

r

r

r

V

V

ET Ce V 2 2

2

 (9)

Figure 8. With hypervelocity impacts into particulate regolith, the impact specific energy is rapidly thermalised 

leading to a statistical physics approach. The specific energy of the impact is an exact analog of the canonical 

energy density of a thermal system leading to a canonical expression of the probability of a particle being in any 

particular energy state. 


 For the macro case of blackbody radiation the possible states, r, are numerous making Vr is 

essentially continuous allowing the summation in Equation 9 to be converted to an integral: 

"



4 


2

2

2

2

( )

2

m

T

m

V r

V

r

V

V

ET C e d V (10)

Where the energy densities are left as velocities squared for clarity. In Equation 10 the velocity 

of the lower limit, VT is that of the lowest detectable energy. If the problem were to determine the 

portion of the energy expended to melt the regolith, then this would be just the square root of the 

minimum energy density of the molten material. For the cameras it would be the velocity equivalent of 

the coolest visible blackbody radiator. In Figure 9 the fraction of photons collected from a blackbody 

emitter are plotted versus temperature for a typical camera used for lunar impact studies. From this it 

becomes evident that there is no defined threshold, VT ,for the lower limit which would enable the 

integral in Equation 10 to be evaluated directly. One can, however, somewhat arbitrarily put a lower 

bound on the visible blackbody temperature of 1000K for a T of about 900K for these silicon Vis/NIR 

cameras. From this one can set a lower bound on VT of about 1.2 km/s. 

Figure 9. Fraction of blackbody emissions detected by the typical camera used for lunar impact flash detection. 

From this it is evident that there is no particular minimum detectable blackbody temperature. If 1000K is taken as a 

lower bound then the equivalent specific energy velocity, VT would be about 1.2 km/s.

At this point we apply the Mean Value Theorem. When applied to Equation 10 the mean value 

theorem implies that: 

there exists  m such that VC : VT ,V 	   2

2

2 2 m

C

V

V

T m T E C V V e



4 
 (11)

IF then 2 2 Vm ;; VT

2

2

2 m

C

V

V

T m E CV e



4 < (12)


Where an integration with a difficult limit, VT , has been replaced with a characteristic velocity, 

Vc , and a simpler form in Equation 12. Note that for the usual case with an unresolved camera constant, 

Oc is lumped with the normalization constant, C. With ET normalized as energy density E'T and 

recognizing that E'

m = V2m the luminous efficiency of the impact assumes a particularly simple form: 

 since 2

m

T

m

T

V

E

E

E 4 1 
 
 then   2

2

m

C

V

V

Vm Ce



1 
 (13)

where one has two undetermined constants: a characteristic velocity VC and a scaling factor C. 

One can now use the luminous efficiencies determined from lunar impact observations in Table 1 

with the light gas gun luminous efficiencies using the same cameras in Figure 5 to estimate the 

characteristic velocity VC and scaling factor C. These results are shown in Figure 10, below. Also 

plotted for comparison are the historical luminous efficiency determinations of Bellot Rubio (2000) and 

Ernst and Schultz (2005). The data spans almost six orders of magnitude in  and ranges from just over 

2 km/s to 71 km/s in velocity. Due to the form of Equation 13, it is immediately evident that the scaling 

factor is almost completely determined by the lunar impact data while the light gas gun data affects the 

critical velocity to a great extent. The lunar impact data yields a scaling factor estimate of C = 1.5×10-3

± 10%. Due to the wide range and natural variability of the light gas gun data various fitting techniques 

gave slightly different results with characteristic velocity fit ranging from 9 km/s to almost 11 km/s. 

From this it is estimated that the critical velocity, Vc = 9.3 km/s ± 10%. 

Figure 10. Lunar impact data from Table 1 is shown with light gas gun data from Figure 5 and historical data. The 

constants in Equation 13 are fit to the combined Table 1 and Figure 5 data. Characteristic velocity Vc is estimated to 

be 9.3 km/s and the scaling factor C is estimated to be 1.5 × 10-3. 


7 Conclusions 

The luminous efficiency of hypervelocity impacts has been examined both in the laboratory and from 

observations of lunar meteoroid impacts. The luminous efficiency is a unique function of velocity with 

an extremely large variation with velocity in the laboratory range of 2 to 6 km/s, but a necessarily small 

variation with velocity in the meteoric range of 15 to 71 km/s. An exponential model of impact thermal 

emission efficiency is developed using fundamental principles of statistical physics which fits the 

combined laboratory and astronomical luminous efficiency data. This exponential model differs 

significantly from the polynomial models used to describe crater formation and dynamics. The model is 

valid for the early time portion of the process and focuses on the deposition of internal energy into the 

regolith which is subsequently observed as a bright blackbody flash. The model is compared with 

luminous efficiency data from laboratory impacts and from lunar impact observations. From these 

comparisons a critical velocity of 9.3 km/s and scaling factor of 1.5×10-3 are estimated. Further work to 

clarify the effects of mass and density of both the impactor and target upon the model is required. This 

model improves confidence in meteoroid mass estimates for lunar impacts and thus knowledge of the 

local space environment. 

The unique energy partitioning approach embodied by luminous efficiency and this model can 

perhaps be extended to impact melting, another early time energy concern. Note that, since the melting 

point can be precisely known, Equation 10 can be evaluated directly. Although some melting is evident 

in light gas gun impacts into regolith it is not measurable while the light flash is. This is a possible 

starting point for future investigations. 

Acknowledgements 

Special thanks are due to the NASA Ames Vertical Gun Range crew for their efforts and to Dr. Peter 

Schultz of Brown University for help in coordinating those efforts. Work for this paper was supported 

in part by NASA contracts NNM05AB50C (Swift), NNM10AA03C (Moser) and the NASA Meteoroid 

Environments Office. 

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Luminous Efficiency of Hypervelocity Meteoroid Impacts on the Moon Derived 

from the 2006 Geminids, 2007 Lyrids, and 2008 Taurids 

D. E. Moser1• R. M. Suggs2• W. R. Swift3• R. J. Suggs2• W. J. Cooke

2

• A. M. Diekmann4• H. M. 

Koehler2

Abstract Since early 2006, NASA’s Marshall Space Flight Center has been routinely monitoring the 

Moon for impact flashes produced by meteoroids striking the lunar surface. During this time, several 

meteor showers have produced multiple impact flashes on the Moon. The 2006 Geminids, 2007 Lyrids, 

and 2008 Taurids were observed with average rates of 5.5, 1.2, and 1.5 meteors/hr, respectively, for a 

total of 12 Geminid, 12 Lyrid, and 12 Taurid lunar impacts. These showers produced a sufficient, albeit 

small sample of impact flashes with which to perform a luminous efficiency analysis similar to that 

outlined in Bellot Rubio et al. (2000a, b) for the 1999 Leonids. An analysis of the Geminid, Lyrid, and 

Taurid lunar impacts is carried out herein in order to determine the luminous efficiency in the 400-800 

nm wavelength range for each shower. Using the luminous efficiency, the kinetic energies and masses 

of these lunar impactors can be calculated from the observed flash intensity. 

Keywords hypervelocity impact · impact flash · luminous efficiency · lunar impact · meteoroid 

1 Introduction 

When a meteoroid strikes the Moon, a large portion of the impact energy goes into heat and crater 

production. A small fraction goes into generating visible light, which results in a brilliant flash at the 

point of impact that can be seen from Earth. The luminous efficiency, , relates how much of the 

meteoroid’s kinetic energy, KE, is converted into luminous energy, LE, in wavelength range, . 

LE 
1KE (1)

The luminous efficiency plays a vital role in understanding observations and constraining models of the 

near-Earth meteoroid environment. Experiments into lunar regolith simulant at low velocities (2 to 6 

km/s) have been performed at hypervelocity gun test ranges in order to determine  (Swift et al., 2010), 

but high velocities – meteoroid speeds, 18 to 71 km/s – are impossible to replicate in the laboratory 

using particle sizes typical of meteoroids. Scaling these low velocity luminous efficiency results to the 

 

D. E. Moser ( ) 

MITS/Dynetics, NASA/Marshall Space Flight Center, Huntsville, AL, 35812 USA. E-mail: danielle.e.moser@nasa.gov 

R. M. Suggs • R. J. Suggs • W. J. Cooke • H. M. Koehler 

Meteoroid Environment Office & Space Environments Team, NASA/Marshall Space Flight Center, Huntsville, AL, 35812 USA 

W. R. Swift 

ESTS/Raytheon, NASA/Marshall Space Flight Center, Huntsville, AL, 35812 USA 

A. M. Diekmann 

ESTS/Jacobs Technology, NASA/Marshall Space Flight Center, Huntsville, AL, 35812 USA 


high velocity regime results in luminous efficiencies greater than 1 – a result that is completely 

unphysical. Numerical hydrocode simulations, like that of Nemtchinov et al. (1999), have mainly 

focused on particles of asteroidal composition moving at low speeds. There are limited simulations of 

high speed cometary particles impacting the Moon (e.g. Artem’eva et al., 2001). 

Impact flashes have been successfully observed on the Moon by Earth-based telescopes during 

several showers (e.g. Dunham et al., 2000; Ortiz et al., 2000; Cudnick et al., 2002; Ortiz et al., 2002; 

Yanagisawa & Kisaichi, 2002; Cooke et al., 2006; Yanagisawa et al., 2006, Cooke et al., 2007; Suggs et 

al., 2008a,b; Yanagisawa et al., 2008). Observations of lunar impact flashes associated with meteor 

showers offer an opportunity to measure  at high velocities, since some properties of the impactors, like 

direction and speed, are known. This was first accomplished by Ortiz et al. (2000) and later detailed in 

Bellot Rubio et al. (2000a, b) for the 1999 Leonid lunar impact flashes. 

The NASA Marshall Space Flight Center (MSFC) has routinely monitored the un-illuminated 

portion of the Moon for lunar impact flashes in the 400-800 nm range. As the Earth has witnessed 

several meteor showers in the past few years, so has the Moon. Since the beginning of our monitoring 

program in 2006, we have captured video of probable Leonid, Geminid, Lyrid, Quadrantid, Orionid, 

Bootid, Southern Delta-Aquariid, and Taurid meteoroid impacts on the Moon. Multiple lunar impact 

flashes were detected during the 2006 Geminids, 2007 Lyrids, and 2008 Taurids, allowing for a 

luminous efficiency analysis like that performed by Bellot Rubio et al. (2000b) for the 1999 Leonids. 

This paper is organized as follows: in Section 2, an overview of the lunar impact monitoring 

program is given, with specifics regarding the data collected during the showers of interest. In Section 

3, the luminous efficiency analysis is described, with the results for each shower presented and 

discussed in Section 4. 

2 Observations 

2.1 Lunar Impact Monitoring Program Overview 

MSFC conducts observations from the Automated Lunar and Meteor Observatory (ALaMO) located in 

Huntsville, Alabama, USA (34.°66 N, 86.°66 W) and the Walker County Observatory (WCO) near 

Chickamauga, Georgia, USA (34.°85 N, 85.°31 W). The un-illuminated (earthshine) portion of the 

Moon is simultaneously observed with two identical Meade RCX-400 0.35 m diameter Cassegrain 

telescopes, online in June 2006 and September 2007, and one RCOS 0.5 m diameter Ritchey-Chrétien 

telescope, online in January 2008; two telescopes reside at the ALaMO with the remainder at WCO. 

The ALaMO telescopes are outfitted with focal reducers resulting in nearly identical 20 arcmin fields of 

view covering approximately 4 × 106 km2

 or about 10% of the lunar surface. ASTROVID StellaCamEX 

and Watec 902-H2 Ultimate monochrome CCD cameras (400-800 nm bandwidth) are employed to 

monitor the Moon. The interleaved, 30 fps video is digitized and recorded straight to hard-drive. 

Impact flash detection and analysis is performed by two custom programs: LunarScan (Gural, 

2007) and LunaCon (Swift et al., 2008). LunarScan software is used to detect impact flashes in the 

video. LunaCon determines flash magnitudes, time on target, photometric quality (including sky 

condition), and lunar area within the field of view. Candidate flash detections are those multi-pixel 

flashes simultaneously detected in two or more telescopes at the same selenographic location or those 

that are more than 1 frame (1/30 s), or two video fields (1/60 s each) in duration. Candidate flashes do 

not exhibit any motion from video field to field but do demonstrate a suitable light curve: a sudden 

brightness increase followed by a gradual decrease. These criteria rule out cosmic rays, electronic noise, 


and most sun glints from orbiting satellites. The WCO telescope, located about 125 km from the 

ALaMO, functions only to eliminate any additional satellite sun glints via parallax. Short flashes 

observed before the second observatory came online, or flashes not detected by this third telescope due 

to weather, viewing geometry, or equipment problems, are checked against the unclassified satellite 

catalog. 

Observations of the un-illuminated portion of the Moon are typically conducted when sunlight 

illuminates between 10 and 50% of the Earth-facing surface. This yields a maximum of 10 observing 

nights per month. At illuminations greater than 50%, the scattered light overwhelms the video and faint 

flashes go undetected. Observing at illuminations less than 10% is considered an inefficient use of time 

and resources since the time between twilight and moon set or moon rise is very limited at these phases. 

Additional descriptions of the lunar impact monitoring program and analysis techniques are given in 

Suggs et al. (2008a,b) and Suggs et al. (2010). 

2.2 Shower Data 

The illumination criterion and weather conditions resulted in several nights of observations 

at/near the peak of the 2006 Geminids, 2007 Lyrids, and 2008 Taurids. Table 1 lists the observation 

dates coinciding with the showers, the telescopes employed, and the number of hours of data recorded 

that were of a consistent photometric quality. The 2006 Geminids, 2007 Lyrids, and 2008 Taurids were 

observed a total of 2.18 hrs, 10.22 hrs, and 7.93 hrs, respectively. Candidate flashes are associated with a 

shower if they occur within days of the shower peak and are located in an area on the Moon that is 

visible to the radiant. Visibility plots for each shower are shown in Figures 1. 

Table 1. List of observing times during the 2006 Geminids, 2007 Lyrids, and 2008 Taurids. All times UT. 

Date Shower Telescopes Obs Timespan Obs Time (hr) 

14 Dec 2006 Geminids two 0.35 m 08:30 – 09:29 0.98 

15 Dec 2006 Geminids two 0.35 m 09:12 – 10:24 1.20 

20 Apr 2007 Lyrids two 0.35 m 01:18 – 02:24 1.10 

21 Apr 2007 Lyrids two 0.35 m 01:16 – 03:18 2.03 

22 Apr 2007 Lyrids two 0.35 m 01:12 – 04:29 3.28 

23 Apr 2007 Lyrids two 0.35 m 01:11 – 05:00 3.81 

02 Nov 2008 Taurids 0.5 m, two 0.35 m 00:04 – 00:47, 23:46 – 24:00 0.95 

03 Nov 2008 Taurids 0.5 m, two 0.35 m 00:00 – 00:13, 00:30 – 01:33, 1.57 

 23:42 – 24:00 

04 Nov 2008 Taurids 0.5 m, two 0.35 m 00:00 – 02:09, 23:42 – 24:00 2.45 

05 Nov 2008 Taurids 0.5 m, two 0.35 m 00:00 – 02:58 2.96 

(a) (b) (c)

GEM LYR STA 

Figure 1. Shower visibility for the (a) 2006 Geminids, (b) 2007 Lyrids, and (c) 2008 Taurids. The colored portion 

indicates the area of the un-illuminated Moon visible to the radiant. 


In all, 12 Geminid, 12 Lyrid, and 12 Taurid impacts were detected during periods of consistent 

photometric quality. (The data for an additional 8 Geminids, 3 Lyrids, and 2 Taurids detected during the 

monitoring period was of poor quality and is not considered here.) The details for each flash are given 

in Table 2. 

 Table 2. Details of the lunar impact flashes detected during the 2006 Geminds, 2007 Lyrids, and 2008 Taurids. 

Shower 

[obs time]

ID Date Time (UT) 

± 0.02s 

Duration 

(ms) 

R Mag Lum. Energy, LEcam

(J) 

Geminids G01 14 Dec 2006 08:32:06.647 33 +9.2 5.6 × 104

[2.18 hrs] G02 14 Dec 2006 08:32:51.993 50 +8.9 7.1 × 104

 G03 14 Dec 2006 08:39:57.155 17 +9.8 3.1 × 104

 G04 14 Dec 2006 08:46:01.957 17 +9.6 3.7 × 104

 G05 14 Dec 2006 08:50:36.200 33 +8.4 1.2 × 105

 G06 14 Dec 2006 08:51:20.562 17 +9.1 6.2 × 104

 G07 14 Dec 2006 08:56:42.837 17 +8.7 8.5 × 104

 G08 14 Dec 2006 09:00:22.142 33 +8.4 1.2 × 105

 G09 14 Dec 2006 09:03:32.851 33 +9.8 3.1 × 104

 G10 15 Dec 2006 09:15:14.040 33 +8.4 1.1 × 105

 G11 15 Dec 2006 09:17:39.336 17 +7.6 2.3 × 105

 G12 15 Dec 2006 09:53:28.464 83 +6.4 7.0 × 105

Lyrids L01 20 Apr 2007 01:40:04.044 50 +7.8 2.1 × 105

[10.22 hrs] L02 22 Apr 2007 01:15:05.616 67 +8.8 7.9 × 104

L03 22 Apr 2007 01:15:43.956 33 +10.0 2.6 × 104

 L04a 22 Apr 2007 01:38:33.864 33 +8.0 1.6 × 105

 L05b 22 Apr 2007 03:12:24.372 67 +6.8 4.9 × 105

 L06 22 Apr 2007 03:52:37.182 17 +9.1 6.0 × 104

 L07 23 Apr 2007 01:15:54.547 17 +8.7 8.5 × 104

 L08 23 Apr 2007 02:23:21.361 50 +8.8 7.7 × 104

 L09 23 Apr 2007 04:08:48.755 50 +8.0 1.7 × 105

L10 23 Apr 2007 04:40:45.912 33 +9.2 5.6 × 104

L11 23 Apr 2007 04:42:34.781 83 +6.4 7.1 × 105

L12 23 Apr 2007 04:59:57.557 50 +7.3 3.3 × 105

Taurids T01 02 Nov 2008 23:48:39.996 50 +9.4 4.5 × 104

[7.93 hrs] T02 03 Nov 2008 00:11:06.144 50 +7.9 1.9 × 105

T03 03 Nov 2008 00:33:37.620 50 +9.1 6.0 × 104

T04 03 Nov 2008 23:59:24.504 50 +8.7 9.0 × 104

T05 04 Nov 2008 00:04:06.060 50 +8.9 7.2 × 104

T06 04 Nov 2008 01:10:01.272 67 +8.1 1.5 × 105

T07 04 Nov 2008 01:39:03.744 67 +6.3 7.8 × 105

T08 05 Nov 2008 00:38:37.860 117 +7.4 2.9 × 105

T09 05 Nov 2008 00:53:58.308 67 +8.5 1.1 × 105

T10 05 Nov 2008 02:05:07.908 100 +7.3 3.0 × 105

T11 05 Nov 2008 02:09:44.748 50 +9.3 4.9 × 104

T12 05 Nov 2008 02:32:47.184 67 +8.1 1.5 × 105

a

 Also detected by independent observer Dave Clark in Houston, Texas, USA using a 0.2 m Schmidt Cassegrain telescope. b

 Also detected by independent observer George Varros in Mt Air, Maryland, USA using a 0.2 m Newtonian telescope. 

All of the events had durations between 17 and 117 ms and magnitudes between +10.0 and +6.3. Impact 

flash locations are shown in Figure 2. Figures 3 and 4 give a sample of impact flashes detected during 

each shower, shown as video stills of the impact flash on the Moon, and as a sequence of 1/30 s image 

squares, respectively. 


Figure 2. Observed lunar impact locations. Numbering scheme refers to Table 2. 

G11 G12 

L04 L05 

T07 T10 

Figure 3. A sample of lunar impact flashes detected during the 2006 Geminids, 2007 Lyrids, and 2008 Taurids. 

Arrows indicate the direction of selenographic north. The numbering scheme refers to Table 2. 


G11 

G12 

L04 

L05 

T07 

T10 

Figure 4. A sample of lunar impact flashes detected during the 2006 Geminids, 2007 Lyrids, and 2008 Taurids. 

The dimensions of each square in the series are about 35 x 35 arcseconds and each covers 1/30 s. The numbering 

scheme refers to Table 2. 

The amount of sporadic contamination in this sample of meteoroids can be crudely calculated. 

Using the Grün sporadic flux model (Grün, 1985), and taking lunar shielding into account, it is 

estimated that roughly 3 of the 36 impact flashes may be caused by sporadic meteoroids as opposed to 

shower meteoroids. But there is no way to remove this contamination. 

3 Luminous Efficiency Analysis 

3.1 Theory 

The technique for determining luminous efficiency incorporates the method first referenced by Ortiz et 

al. (2000) and then detailed by Bellot Rubio et al. (2000a, b). Their method is restated in this section and 

referenced in the text hereafter as BR2000. In addition to this method, an iterative process is used to 

determine the final luminous efficiency , and is better suited to discussion alongside a description of 

the flux parameter inputs in Section 3.2.5. 

The number of meteoroids that impact the Moon in time span t1 to t2 is 

N F t A t dt t

"t 
 =

2

1

( ) ( ) (2)

where F(t) is the flux as a function of time, t, and An (t) is the observed lunar area that is perpendicular 

to the meteor shower radiant also as a function of time. 

The cumulative flux distribution of meteoroids of mass m is given by 

s

m

m F m F m

















 


1

0

0 ( ) ( ) (3)


where F(m) is the flux of particles having mass greater than m, F(m0) is the flux of particles of known 

mass greater than mass m0, and s is the mass index. 

The masses of the meteoroids impacting the Moon are unknown. For an impactor of mass m and 

velocity V, the kinetic energy is KE = 1⁄2 m V2

. Substituting this into Eq (3) gives a cumulative flux 

distribution as a function of kinetic energy. 

s

V m

KE F KE F m

















 


1

0

0 2

2 ( ) ( ) (4)

Solving Eq (1) for KE and substituting this into Eq (4) gives a cumulative flux distribution as a function 

of luminous energy, depending on the luminous efficiency  in a particular wavelength range. 

s

V m

LE F LE F m

















 


1

0

0 2

2 ( ) ( )







1

(5)

Using Eq (5), Eq (2) becomes the number of lunar meteoroid impacts producing luminous energies 

greater than LE in the time span t1 to t2. 

F m t A t dt

V m

LE N LE t

t

s

" =

















 
 2

1

( , ) ( ) 2 ( ) 0

1

0

2







1

(6)

This result is comparable to Eq (4) of BR2000. 

 In short, the analysis technique involves ‘backing out’ the luminous efficiency by matching the 

number of impacts expected on the Moon to that actually observed. One of the difficult problems in 

using this technique alone derives from uncertainties in the various inputs, namely the flux and mass 

index. This is discussed in the next section. 

3.2 Inputs 

The inputs for Eq (6) in the 400-800 nm range are summarized in Table 3 and outlined in the following 

sub-sections. 

Table 3. Input parameters for Eq (6) for the 2006 Geminids, 2007 Lyrids, and 2008 Taurids. The average area 

perpendicular to the radiant in the field of view is given, for illustration purposes. 

Shower V (m/s) s F(m0,t) (#/m2

/hr) m0 (kg) t1, t2 (hr) A⟘ave (km2

) LEcam (J) 

Geminids 35000 1.9 Suggs 4.7×10-2 from 3.2×106 from 

Lyrids 49000 1.7 et al. 8.4×10-2 Table 1.1×106 Table 

Taurids 27000 1.8 (2010) 2.4×10-2 1 3.6×106 2 

3.2.1 Luminous Energy, LE

The energy received at Earth [J/m2

] is calculated using 



 & > m Flux 0.4

0 10? 
 @ (7)

where  is the camera exposure time [s], Flux0 is the flux [J/m2/s] from a zero magnitude star in the 

camera’s wavelength range , and m is the measured magnitude of the impact flash. Stellacam and 


Watec cameras operate in the 400-800 nm range with a peak response approximated by the R passband. 

Flash photometry is performed utilizing local background stars in the video as reference and Vega is 

used as the calibration star with Flux0R = 3.39×10-9 J/m2

/s. The exposure time of the camera is 0.0167 s. 

The luminous energy at the Moon [J] is related to the energy received at Earth by 


 ?  & 

2 LE f d (8)

where f is a factor describing the distribution of the light (f = 4 for spherical emission into 4	 steradians, 

f = 2 for hemispherical emission into 2	 steradians, etc.) and d is the distance in meters between the 

impact flash on the Moon and the telescope on Earth. It is chosen that f = 4, since the radiating plume is 

most likely above the surface, created from hot meteoroid and regolith materials, and d is assumed a 

constant 3.84 × 108

 m. The resulting luminous energies for each flash, including a correction factor to 

produce energies in the camera’s passband, are seen in Table 2 as LEcam. For more photometry details, 

see Swift et al. (2008). 

This differs from the inputs in the BR2000 method in the choice of f (the compromise f = 3) and 

wavelength range (400-900 nm). In addition, the cameras used in their study peak in the visual range, 

whereas the cameras we use peak in the red-NIR. 

3.2.2 Time Span, t1 to t2

Observing sessions typically run from moonrise to twilight (waning phases) or twilight to moonset 

(waxing phases). Only those times that are of a consistent photometric quality are used in the analysis. 

For each video, plots of lunar disk brightness and contrast versus time are examined. Any video 

segments that exhibit obvious cloud attenuation, a loss of contrast due to cirrus haze or fogged optics, a 

rapid change in extinction during moonrise or moonset, twilight, or obvious obstructions from the 

observatory dome or trees, are excluded. The time spans t1 – t2 used in this analysis are listed in Table 1. 

3.2.3 Perpendicular Lunar Area, An (t) 

During each observing session the Moon drifts slightly within the telescope’s field of view, thereby 

changing the amount of lunar surface area detected. The LunaCon analysis software identifies and 

calculates the lunar area visible in the video. This is accomplished by first detecting the location of the 

limb within a video frame and solving for the center and radius of the lunar disc in image pixels. From 

the radius, the lunar area of the center pixel is calculated in square kilometers, and, knowing the radial 

distance of each pixel in the lunar image, a weight is applied for each pixel to compensate for spherical 

Moon effects (an image pixel near the limb contains more area than one near the center of the disc); 

pixels at the lunar limb with extreme weights are discarded. Summing over all the lunar pixels in the 

image with their appropriate weights yields the total lunar area. In this way, the lunar area within the 

field of view as a function of time is determined (Swift et al., 2008). 

 To determine the lunar area perpendicular to the shower direction within the field of view, An(t), 

the area as a function of time determined by LunaCon is modeled as 1 million equal area cells. The area 

in each cell is multiplied by the cosine of the zenith angle of the radiant. Summing yields the total 

perpendicular lunar area within the field of view as a fun n of time. For illustration purposes, the 

average perpendicular area, An+ave, for each shower is given able 3. 

ctio

 in T

 In comparison, the BR2000 method calculates An using Monte Carlo simulations and it is 

considered a constant during the 90 min of Leonid observations they performed in 1999. 


3.2.4 Shower Parameters, V and s 

The speeds, V, and mass indices, s, for each shower are taken from the annual meteor shower tables 

compiled by the International Meteor Organization (IMO, 2006, 2007, 2008). Gravitational effects from 

the Earth and Moon are not considered in the velocity parameter as they are too small to be considered 

significant. The mass index characterizing the mass distribution of (small) shower meteors in the visual 

range may not be applicable to large particles. As there are no measurements of the mass index for these 

shower meteoroids in the lunar impactor size range, it is only possible to estimate s from shower 

observations; this makes s a rather uncertain parameter input. The speeds and mass indices used are 

listed in Table 3. 

 In comparison, the BR2000 method explored the luminous efficiency results from two different 

mass indices. The first was an extrapolated mass index from the 1999 terrestrial Leonid fireballs of the 

IMO Visual Meteor Database and the second was a constant s = 2.0. 

Looking at the effects of varying s has not yet been done for the showers discussed here and is 

classified as future work. 

3.2.5 Flux Parameters, F(m0,t) and m0

To determine the flux parameters, the lunar impacts were first considered as an ensemble. The MSFC 

detected 115 lunar impact flashes in 212 hours of observing between 2006 and 2009, the majority of 

which are most probably produced by shower meteoroids (Suggs et al., 2010). We calculate an initial 

limiting magnitude and subsequently an initial limiting kinetic energy based on the ensemble lunar 

impact data, incorporating previously determined luminous efficiency values based on gun test work

(Suggs et al., 2008b) and the 1999 Leonid work by Bellot Rubio et al. (2000). This, in turn, is used to 

calculate the number of impacts we should have detected, based on observed and historical IMO ZHR 

data, and given the lunar collecting area in the field of view, observing time, and the shower geometry. 

Matching the observed and expected number values requires adjustment of the luminous efficiency or 

limiting magnitude. As there is more uncertainty in the limiting magnitude, this value was adjusted to 

best fit IMO observations, resulting in a final limiting kinetic energy corresponding to a mass of 100 g 

moving at a speed of 25 km/s. The final limiting mass, m0, for each shower yielding the equivalent final 

limiting kinetic energy is given in Table 3. The flux corresponding to this limiting mass is F(m0) and the 

data and time dependence is taken from the observed lunar impact flux, removing any impact flashes 

that have a magnitude fainter than the corresponding final limiting magnitude . For a more in depth 

discussion on the flux determination, see Suggs et al. (2010). 

 The procedure described above is just the first step in an iterative process. Using the ‘final’ 

limiting mass determined from the ensemble of lunar impacts, which incorporates an initial luminous 

efficiency estimate, a new luminous efficiency is calculated based on the energies of the individual lunar 

impact flashes using the technique outlined in Section 3.1. The new luminous efficiency is then used to 

compute a more accurate limiting energy, as in the above paragraph, and the process repeats until 

convergence. 

 The determination of the flux at the Moon in the original BR2000 method is quite different. The 

method scales the terrestrial flux for the 1966 Leonids by a factor of 4 and adopts the timing of the 

terrestrial 1999 Leonids, shifted to the Moon. Their fluxes are tied to the mass of a Leonid meteoroid 

producing a meteor of magnitude +6.5 on Earth. 

Looking at the ensemble of lunar impacts and comparing it to observations on Earth, we have 

instead determined a lunar flux for each shower, F(m0, t), of particles with mass greater than the limiting 


mass, m0. Fluxes are discussed in Suggs et al. (2010) and the limiting mass for each shower is listed in 

Table 3. 

4 Results and Discussion 

As stated previously, the analysis technique involves ‘backing out’ the luminous efficiency by matching 

the number of impacts expected on the Moon to that actually observed. The expected cumulative 

number of lunar meteoroid impacts, N(LEλ), producing luminous energies greater than LEλ (as discussed 

in Section 3) for the 2006 Geminids, 2007 Lyrids, and 2008 Taurids is plotted in Figures 5 alongside 

the observed cumulative lunar impacts using two different energy binning schemes. Fig 5(a) shows 

Figure 5. N(LEλ) vs LEλ, the comparison between expected number of cumulative impacts (colored solid lines) and 

observed data (black squares) for two different energy binning schemes for the 2006 Geminids, and 2007 Lyrids, 

and 2008 Taurids. (a) No binning of luminous energy observed during the impact flash, (b) observed luminous 

energies are binned with bin size = 65,000 J. Wavelength λ is 400-800 nm.

the comparison between expected cumulative number of impacts at various values of luminous 

efficiency and observed number using almost no binning, since number statistics are poor. Fig 5(b) 

shows this same comparison with luminous energy bins set at 65,000 J. Binning using the two different 

schemes yields similar results for luminous efficiency in the 400-800 nm range, ηcam, as listed in Table 4 

and illustrated in Figures 5. 

(a) 

(b) 


Table 4 Calculated luminous efficiencies ¬cam for the 2006 Geminids, 2007 Lyrids, and 2008 Taurids using two 

different binning schemes (a) and (b); listed in order of increasing velocity. An estimated impactor mass range 

corresponding to the flashes we detected for each shower is also calculated. 

Shower # 

Flashes 

Obs. Time 

(hrs) 

V

(km/s) 

s cam (a) cam (b) Mass Range 

(kg) 

2008 Taurids 12 7.93 27 1.8 1.6×10-3 1.5×10-3 0.09-1.4 

2006 Geminids 12 2.18 35 1.9 1.2×10-3 1.1×10-3 0.04-0.99 

2007 Lyrids 12 10.22 49 1.7 1.4×10-3 1.3×10-3 0.03-0.44 

1999 Leonids* 5 1.5 72 1.83 2×10-3 n/a 0.12-4.9 

* Bellot Rubio et al. (2000a, b), shown for reference. Results are from a different camera with a different  range. 

Errors in cam may be on the order of a few percent. The Bellot Rubio et al. (2000a, b) result for the 

1999 Leonids is reproduced in Figure 6. A better agreement between the observed number of impacts 

and the expected number of impacts was found in this work than in Bellot Rubio et al. (2000a, b), as 

seen by a comparison of Figures 5 and 6, indicating a perhaps more reliable value of luminous 

efficiency. 

¬=5e-4 

¬=1e-3 

¬=2e-3 

¬=5e-3 

Figure 6. Results of Bellot Rubio et al. (2000b). N(LE) versus LE adapted from Figure 2 of the same reference. 

Wavelength  in this case is 400-900 nm. Compared to Figure 5, the observed data points do not fit the curves as 

well. 

The luminous efficiency derived by Bellot Rubio et al. (2000a, b) for the 1999 Leonids is also 

listed in Table 4 for comparison purposes. It should be noted that this data was observed with cameras 

having a slightly different spectral response and sensitivity than the cameras in this study and a light 

distribution coefficient of f = 3 instead of 4; other differences in technique are outlined in Section 3.2. 

Despite these differences, the 1999 Leonid luminous efficiency is consistent with those of the 2006 

Geminids, 2007 Lyrids, and 2008. 

Luminous efficiency determinations at low speeds into lunar simulant JSC-1a have been made at 

the NASA Ames Vertical Gun Range employing the same cameras used to monitor the Moon (Swift et 

al., 2010). These values appear in Figure 7, along with the luminous efficiencies calculated in this 

paper. Also plotted for reference are previous results found in the literature. A fit to the lunar impact 

derived data from this paper and the hypervelocity gun test data from Swift et al. (2010) yields the 

following equation for luminous efficiency in the 400-800 nm wavelength range of our cameras 


2

2 (9.3)

3 1.5 10 V cam e

1 
  (9)

where V is the speed of the impactor in km/s. The lunar impact data mainly controls the constant scaling 

factor in Eq (9) while the hypervelocity gun test data largely controls the number in the exponential. 

Findings from other data sources shown in Figure 7 – Bellot Rubio et al. (2000b) for the 1999 Leonids at 

400-900 nm, Ernst & Schultz (2005) considering gun tests into powdered pumice at 340-1000 nm, and 

numerical hydrocode simulations by Artem’eva et al. (2001) for two different densities, 0.1 g/cm3

 and 1 

g/cm3

 – are not considered in the fit, but the results seem to be quite consistent. 

The range of estimated impactor masses is computed and given in Table 4, using the luminous 

efficiencies in binning scheme (a). Simulations by Artem’eva et al. (2001) indicate that luminous 

efficiency weakly depends (10-20%) on size of the impactor, while luminous efficiencies are twice as 

high as for low-density impactors. The dependence of luminous efficiency on impactor mass and/or 

density is left for future work. 

2

2 (9.3)

3 1.5 10 V cam e

1 
 

Figure 7. Plot of luminous efficiency versus velocity using several different methods. The data from gun tests into 

lunar regolith simulant from Swift et al. (2010) populates the low velocity end of the graph. At high meteoroid 

velocities (this work), the curve is relatively constant. The Bellot Rubio et al. (2000b) point from the 1999 Leonids 

and Ernst & Schultz (2005) point from gun tests into powdered pumice do not represent the spectral response of the 

cameras used in this study and were not used in the fit (solid black line); they are shown for comparison purposes 

only. The results of hydrocode simulations by Artem’eva et al. (2001) are also shown only for comparison 

purposes. The Bellot Rubio number has a correction applied to convert from the originally assumed f = 3 to f = 4. 

5 Summary 

Utilizing the technique of Bellot Rubio et al. (2000a,b), the best estimate for the luminous efficiency of 

lunar impacts involving the 2006 Geminid, 2007 Lyrid, and 2008 Taurid meteoroids is cam = 1.2 × 10-3, 

1.4 × 10-3, and 1.6 × 10-3, respectively, in the 400-800 nm wavelength range of our cameras. These 
values are consistent with that found by Bellot Rubio et al. (2000) for the Leonid lunar impacts of 1999 

and numerical simulations performed by Artem’eva et al. (2001). Number statistics are poor in all 

cases, however, and more observations are needed. It must be noted that  is highly dependent on the 

mass index though how much the determination of  varies with s is left to future work. Mass indices 

found in the literature and used in this analysis may not apply to the size range considered for lunar 

impacts. More work to determine mass indices for meteoroids larger than 100 g is needed. 

 Luminous efficiencies determined from lunar impact flash analyses are fairly constant at 

meteoroid speeds. Luminous efficiencies calculated as the result of hypervelocity gun tests into lunar 

simulant has revealed a large variation in  at low velocities. Luminous efficiency values imply impactor 

masses of roughly 30 to 1400 g. The dependence of luminous efficiency on impactor mass/density is 

also a topic of future work. 

Acknowledgements 

This work was partially supported by the NASA Meteoroid Environment Office, the Constellation 

Program Office, the MSFC Engineering Directorate, and NASA contracts NNM10AA03C and 

NNM05AB50C. 

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CHAPTER 5: 

METEOR LIGHT CURVES AND LUMINOSITY RELATIONS 


Constraining the Physical Properties of Meteor Stream Particles by Light Curve 

Shapes Using the Virtual Meteor Observatory 

D. Koschny1• M. Gritsevich2• G. Barentsen3

Abstract Different authors have produced models for the physical properties of meteoroids based on 

the shape of a meteor’s light curve, typically from short observing campaigns. We here analyze the 

height profiles and light curves of ~200 double-station meteors from the Leonids and Perseids using data 

from the Virtual Meteor Observatory, to demonstrate that with this web-based meteor database it is 

possible to analyze very large datasets from different authors in a consistent way. We compute the 

average heights for begin point, maximum luminosity, and end heights for Perseids and Leonids. We 

also compute the skew of the light curve, usually called the F-parameter. The results compare well with 

other author’s data. We display the average light curve in a novel way to assess the light curve shape in 

addition to using the F-parameter. While the Perseids show a peaked light curve, the average Leonid 

light curve has a more flat peak. This indicates that the particle distribution of Leonid meteors can be 

described by a Gaussian distribution; the Perseids can be described with a power law. The skew for 

Leonids is smaller than for Perseids, indicating that the Leonids are more fragile than the Perseids. 

Keywords meteor light curves · physical properties · meteoroids · double-station observations 

1 Introduction 

The shape of the light curve of meteors can be used as an indicator for the physical properties of the 

underlying meteoroid particle. In general, a single solid grain would be expected to increase in 

brightness and stop emitting light at the end of its flight path at the point of maximum brightness. 

Fragile particles will start to disintegrate high up in the atmosphere, and the luminosity will be the sum 

of the light emitted around the individual particles. In the extreme case, a meteoroid will fragment very 

quickly and reach its highest magnitude early on in its light curve. As the individual particles ablate and 

slow down, the magnitude of the complete meteor will decrease slowly over its path. 

Several authors have analyzed larger numbers of observational data, typically from observing 

campaigns of meteor streams (e.g. Fleming et al. 1993, Murray et al. 2000, Koten et al. 2004). Data 

from very few meteors was analyzed in very high detail e.g. by Jiang and Hu (2001) or Campbell-Brown 

and Koschny (2004). All of these analyses derive meteoroid physical properties from the shape of the 

 

D. Koschny ( ) 

European Space Agency, ESA/ESTEC, SRE-SM, Keplerlaan 1, Postbus 299, 2200 AG Noordwijk, The Netherlands. E-mail: 

Detlef.Koschny@esa.int 

M. Gritsevich 

Institute of Mechanics, Lomonosov Moscow State University, Michurinskii Ave. 1, 119192 Moscow, Russia; Faculty of Mechanics and 

Mathematics of the Lomonosov Moscow State University, Leniskie Gory, 119899 Moscow, Russia 

G. Barentsen 

Armagh Observatory, College Hill, Armagh BT61 9DG,United Kingdom


light curves. The underlying model is based on an idea by Öpik (1958) and was worked out in detail by 

Hawkes and Jones (1975) into the so-called dustball model. It assumes that meteoroids are composed of 

small grains held together by a low boiling point ‘glue’. By heating up the meteoroid this glue is 

evaporated and the particles disintegrate. This model was detailed e.g. by Beech and Hargrove (2004). 

Koschny et al. (2002) have modeled the light curve of meteors based on assuming mechanical 

fragmentation; Campbell-Brown and Koschny (2004) use a detailed aerodynamical model adding a 

thermal fragmentation mechanism. In this paper we analyze data obtained in several meteor campaigns, 

but also one data set (from the Perseids 2009) found only by data mining within the Virtual Meteor 

Observatory (VMO). In addition to the light curve evaluation, one goal of this work was to assess the 

useability of the VMO for this task. 

2 Input Data and Observational Setup 

We have been using data stored in the openly available Virtual Meteor Observatory. The Virtual Meteor 

Observatory (VMO) is a data storage facility for a wide range of meteor data; see Koschny et al. (2008) 

and Barentsen et al. (2008a, 2008b). In the currently available beta version single station video meteor 

data of the International Meteor Organization until ~2007 has been ingested. In addition, double-station 

data of selected campaigns in the time span from 1997 to 2009 is available. The database can be queried 

remotely using SQL syntax (SQL = Structured Query Language). All queries used for the paper here are 

available and can be reused in exactly the same way once more data is available. 

In this work we use so-called orbit data sets of the VMO. Most of them are derived from 

dedicated double-station observing campaigns, using image-intensified camera systems. One of the 

datasets was extracted by using the VMO functionality of finding potential double-station meteors. This 

query will go through the existing single-station data for a given time range, and read out the location 

and pointing direction of all cameras in the database. From the derived geometry, it will identify camera 

systems which look into the same volume in the atmosphere. Given a maximum delta time, the VMO 

will identify all observations which could possibly be the same meteor. A list of potential double-station 

meteors is then presented to the user. The user can select which one (or all) of the meteors should be 

used for computing orbits. The orbit computation is also done within the VMO using the software 

MOTS (Meteor Orbit and Trajectory Software, Koschny and Diaz del Rio, 2002). 

The contents of such a data set is a list of orbits computed from the observations from two 

different stations, giving time and initial shower association of a meteor together with all the orbital 

elements and their associated error bars. Additionally computed information is the peak magnitude of 

the meteor, a derived photometric mass, velocities, height for the begin, peak brightness and end points, 

the apparent and geocentric radiant of the meteor, the zenith angle and convergence angle, and a flag 

whether the meteor started and ended in- our outside the field of view. 

The cameras used to produce the data sets were either image-intensified cameras as described in 

Koschny et al. (2002) with field of views between 20A and 60A or, in the case of the Perseids 2009, a 

non-intensified Mintron camera with a 6 mm f/0.8 wide-angle lens yielding a field of view of 60A. The 

typical stellar limiting magnitude of the intensified cameras was between 5 and 6 mag; for the nonintensified camera of the Perseids 2009 data the limiting stellar magnitude was around 3 mag. 

The following datasets were used: 

(a) Perseids 1997 (data set name ORB-KOSDE-PER1997), using two intensified video cameras with 

30 deg circular field of view, a faintest star of 6.5 mag, and using a total of 74 meteors; 


(b) Perseids 2007 (data set name ORB-KOSDE-PER2007), again using intensified video cameras 

with 30 deg circular field of view, a faintest stellar magnitude of 6.5 mag, using a total 28 

meteors; 

(c) Perseids 2009 (ORB-KOSDE-PER2009), using one intensified video camera, one un-intensified 

camera, with only 13 orbits available. 

(d) Leonids 2001 (ORB-BARGE-LEO2001), using two intensified video cameras with 15 x 12 and 

33 deg field of view, with 64 available orbits. 

From these datasets, we selected only meteors containing 8 or more magnitude datapoints. 

3 Results 

3.1 Height Distribution 

For each dataset, we determined the average beginning height, height of peak light intensity, and 

average end height. The errors were computed by simply taking the standard deviation of the individual 

data points. To interpret these errors, one should keep in mind that the input data is quantized. Assume 

one meteor has precisely 8 data points, and it starts at 110 km and ends at 95 km (for a typical Perseid, 

see Figure 1). Then the ‘quantization noise’ already is about 15/8 km ~ 2 km. So each individual meteor 

height can not be determined more accurate than this simply due to the fact that we look at discrete 

video images. Table 1 shows the results. 

Figure 1. Average light curves from two different meteor showers. For a detailed explanation, see the text. No 

error bars are shown at the data points; the typical deviation between the mean value and the actual magnitude of a 

meteor in the given height bin is about 0.3 mag (indicated in the upper left area). 


Table 1. Average heights for the beginning point, the point of peak brightness, and the end point for the different 

datasets. For comparison, the values from a very similar paper as this one (Koten 2004) are given in the same table. 

The last column lists the F-parameter which indicates the skew of the light curve. 

Dataset hbegin in km hpeak in km hend in km F 

This work: 

PER1997 107.7 +/- 3.1 100.6 +/- 3.2 96.0 +/- 3.5 0.61 +/- 0.19 

PER2007 113.8 +/- 3.7 102.4 +/- 3.7 97.5 +/- 2.9 0.68 +/- 0.21 

PER2009 115.1 +/- 12.1 97.8 +/- 7.2 93.1 +/- 8.1 0.75 +/- 0.20 

LEO2001 117.0 +/- 10.9 110.1 +/- 10.3 103.0 +/- 10.7 0.47 +/- 0.26 

Koten 2004: 

PER1998-2001 113.9 +/- 2.4 104.4 +/- 2.9 96.0 +/- 4.1 0.535 +/- 0.010 

LEO2000 120.0 +/- 3.5 106.9 +/- 3.8 96.5 +/- 3.7 0.498 +/- 0.014 

3.2 Light Curves and F-parameter 

We present a novel way to show the typical light curves of a meteor stream. For each individual meteor, 

we compute the average brightness in magnitudes. Each individual brightness measurement is converted 

to a relative brightness by subtracting the average value. We then take height bins of one kilometer and 

average all values in this bin. This results in a smooth curve which is an indication for the typical light 

curve behavior of a meteor stream, independent of the magnitude. 

All Perseid years showed meteors starting between 108 and 113 km, ending between 94 and 

97 km. The peak seems to shift slightly from ~102 km in 1997 to 97-99 km in 2007/2009. However, due 

to the small number of meteors analyzed one should be careful in giving this result too much 

significance. The important result is that all three years the light curve is clearly peaked, with the peak

slightly behind the half length of the profile. 

The Leonids begin much higher, the end height is close to the Perseid end height. The main 

difference to the Perseids is that the curve shows a flat-topped shape, i.e. between 115 km and 105 km 

the brightness as about constant. This can mean that either all meteors are really flat-topped, or that the 

peak height of the Leonids varies in this range in such a way that the average curve looks flat. Looking 

at several individual light curves the former seems to be the case. This is also consistent with Murray 

(2000) for their Leonids 1998 data but not for their 1999 data. 

Note that by displaying the curve like this, any relation between e.g. end height and brightness 

will be hidden. The apparent increase in magnitude at the begin and end point are assumed to be 

artifacts, possibly by contamination due to sporadic meteors. 

The F-parameter (Hawkes and Jones, 1975, Fleming 1993) is defined as 

begin end

begin

H H

H H

F 


 max

where Hbegin is the beginning height, Hmax the height of peak brightness, and Hend the end height. The Fparameter was computed for each meteor individually. The result is shown in Figure 2 as a function of 

absolute magnitude (the peak magnitude normalized to a distance of 100 km) and shower. Obviously, 

the F-parameter is ill-defined for a flat-topped meteor light curve. Thus, interpreting of the Leonid 

results has to be done with care. Still, it can be seen that the values for the Leonids are in a different 

regime than those for the Perseids. For a given absolute magnitude, the Leonids show lower F-


parameters, i.e. the peak occurs earlier. In the average light curves shown in Figure 1 this is evident by 

the bump in the light curve for high altitudes; Table 1 shows the average F-parameter which is 0.47 for 

the Leonids but between 0.6 and 0.75 for the Perseids. 

Figure 2. The F-parameter as a function of absolute magnitude for the different data sets. A value of 1 means that 

the meteor has its peak brightness at the end; 0.5 indicates that the light curve is symmetric. Average values are 

shown in Table 1, this Figure shows the trend between different meteor streams and the relation to the magnitude. 

Both Leonids and Perseids show an ‘empty region’ in the lower left part of the diagram with 

	same tendency – there are no low F-values for brighter meteor, i.e. the brighter the meteor, the later 


reaches its maximum. 

3.3 Discussion 

Beginning, peak, and end heights as reported here are in good agreement with other papers; for 

comparison we give the height data and the F-parameter as determined by Koten et al. (2004) in Table 

1. The beginning height is an indication for the fragility of the meteoroids. More fragile meteoroids will 

disintegrate at larger heights, increasing in brightness above the detection level (Koten et al. 2004). We 

can thus confirm that the Leonids are more fragile than the Perseids. This is confirmed by comparing the 

F-parameter: The Leonids on average peak earlier than the Perseids (Note, however, that the flat-topped 

shape of the average light curve of the Leonids makes it more difficult to define the F-parameter). 

Plotting the F-parameter as a function of magnitude shows that brighter meteors normally peak

later. This has been shown for the Leonid 2001 dataset before by a different data interpretation method 

(Koschny et al. 2002) and can be explained by assuming that a single large grain which is not 

disintegrating is part of the meteoroid. The observed ‘empty’ region in the lower left area of Figure 2 

can be interpreted such that brighter meteors always must contain one or several large grains, which do 

not disintegrate easily. This shifts the peak of the light cuve to the back. 

Current meteoroid ablation models typically assume that meteoroids disintegrate when entering 

the Earth’s atmosphere. The individual fragments ablate and generate light. The shape of the light curve 


depends on the size distribution of these fragments. Campbell-Brown and Koschny (2004) use e.g.

Gaussian and power-law distributions to fit different light curves. Typically the Gaussian distribution 

will better fit the flat-topped light curve; power laws will better fit peaked light curves. Alternatively one 

can use a Poisson distribution derived from fracture mechanics to describe both shapes (Koschny et al.

2002) which is proposed here as it would allow to use only one number (the Poisson coefficient) to 

describe all light curve shapes. 

Flat-topped light curves have been observed before for the Leonids, see Murray et al. (2000). 

They only see the flat-topped light curves for their 1998 data; the 1999 data is more consistent with a 

peaked light curve. They argue that the 1998 has been ejected from the comet several revolutions before 

the material encountered in 1999. The longer flight time could imply that the meteoroids had been more 

fragmented over time. Our observation of flat-topped light curves for the 2001 Leonids is consistent 

with that proposal - most of the particles recorded by us in Australia are expected to be from the 1699 

perihelion (Asher 2000). 

4 Conclusion 

We have used the Virtual Meteor Observatory (VMO) to retrieve data of double-station observations of 

the Leonids 2001 and the Perseids 1997, 2007, and 2009. The 2009 data camera from cameras initially 

operated as single stations; the VMO functionality was used to identify the used camera systems as 

providing data of the same meteors. 

We analyzed the height profiles and light curves of all meteors having more than 8 data points 

(typically this means having more than 8 video frames). Our height data is consistent with other author’s 

results. The peak of the light curves of our Perseid meteors is somewhat later than in other publications, 

but showing the same trend. 

From the shape of the average light curves we can confirm that the Leonids are more fragile than 

the Perseid meteors. The Leonids show a more flat-topped light curve. Murray et al. (2000) explain flattopped versus peaked light curves by assuming a much higher meteor stream age. Our measurements 

confirm this proposal. 

In addition to the scientific results, we conclude that the concept of the VMO is good and the 

VMO can be used for doing extensive data mining once it has been moved from its current beta-version 

state to the final version. Additional data on meteors which would go beyond the scope of this paper is 

easily available and can be retrieved with a simple SQL query, e.g. plotting the end height versus 

photometric mass can be done in one line. However, the current data quality for orbital data still has to 

be improved. It is recommended that the VMO implement clearly defined data quality criteria. An 

important additional routine which would be needed in the VMO to allow further studies in the direction 

shown here would be to add an automated stream association mechanism. Currently, the meteor streams 

are simply assigned the shower code given by MetRec to the single-station data, which turned out to be 

not always correct after manually checking the orbital elements. 

The VMO will contain single-station data from the IMO video camera network and dedicated 

double-station data. Discussions are ongoing to include the SonotaCo network (SonotaCo et al. 2010) 

data. This will make the VMO the largest database for meteor data so far. While the data used here is not 

yet more numerous than previous studies, all these large datasets will be accessible using exactly the 

same scripts once the archive is fully operational. 


Acknowledgements 

The VMO is hosted by the European Space Agency’s Research and Scientific Support Department. 

Thanks to Günter Thörner and his team for providing the necessary support. All data providers of the 

IMO video network are acknowledged for making their data available through the VMO. 

References 

D. Asher, Proc. International Meteor Conference, Frasso Sabino 1999, ed. R. Arlt, International Meteor Organization, 5-21 

(2000) 

G. Barentsen, D. Koschny, J. Mc Auliffe, S. Molau, R. Arlt, EPSC Abstracts, Vol. 3, EPSC2008-A-00293 (2008a) 

G. Barentsen, R. Arlt, D. Koschny, P. Artreya, J. Flohrer, T. Jopek, A. Knöfel, P. Koten, J. Mc Auliffe, J. Oberst, J. Toth, J. 

Vaubaillon, R. Weryk, M. Wisniewski, P. Zoladek, WGN, the Journal of the IMO, 38:1, 10-24 (2008b) 

M. Campbell-Brown, D. Koschny, Astronomy & Astrophysics 418, 751-758. 

D. Fleming, R. Hawkes, J. Jones, Meteoroids and their parent bodies, Proc. Int. Ast. Symp., Smolenice, Slovakia, 6-12 July 

1992, Bratislava: Astronomical Institute, Slovak Academy of Sciences, 1993, edited by J. Stohl and I.P. Williams, 261-

264 (1993) 

X. Jiang, J. Hu, Planet. Space Sci. 49, 1281-1283 (2001) 

D. Koschny, J. Mc Auliffe, G. Barentsen, Earth, Moon, and Planets 102, 247-252 (2008) 

D. Koschny, J. Diaz del Rio, WGN 30:4, 87-101 (2002) 

D. Koschny, P. Reissaus, A. Knöfel, R. Trautner, J. Zender, Proc. Asteroids, Comets, Meteors (ACM 2002), 29 July – 092 

August 2002, TU Berlin, Berlin, Germany, ESA-SP-500 (2002) 

D. Koschny, R. Trautner, J. Zender, A. Knöfel, O. Witasse, Proc. Asteroids, Comets, Meteors (ACM 2002), 29 July – 092 

August 2002, TU Berlin, Berlin, Germany, ESA-SP-500 (2002) 

I. Murray, M. Beach, M. Taylor, P. Jenniskens, R. Hawkes, Earth, Moon and Planets 82-83, 351-367 (2000) 

SonotaCo, S. Molau, D. Koschny, EPSC Abstracts, Vol. 5, EPSC2010-798 (2010) 


An Investigation of How a Meteor Light Curve is Modified by Meteor Shape and 

Atmospheric Density Perturbations 

E. Stokan1• M. D. Campbell-Brown1

Abstract This is a preliminary investigation of how perturbations to meteoroid shape or atmospheric 

density affect a meteor light curve. A simple equation of motion and ablation are simultaneously solved 

numerically to give emitted light intensity as a function of height. It is found that changing the 

meteoroid shape, by changing the relationship between the cross-section area and the mass, changes the 

curvature and symmetry of the light curve, while making a periodic oscillation in atmospheric density 

gives a small periodic oscillation in the light curve. 

Keywords meteor · meteoroid ablation modeling 

1 Introduction 

The ablation of small objects, meteoroids, in the atmosphere produces light that may be observed on the 

ground. As the meteoroids enter the atmosphere, particles are removed from the rapidly heating body 

and excited or ionized. Atmospheric particles may also be excited and ionized in smaller numbers. 

These excited atoms and ions emit photons in narrow bands that may be analysed for meteoroid 

chemical composition using a spectrometer, or examined in their time-dependence to suggest velocity, 

structure, or other physical properties of the meteoroid. Thus, meteors, the streaks of light that occur as 

meteoroids burn up in the atmosphere, reveal information about the composition and properties of 

meteoroids when observations are combined with ablation models. Since the meteoroids originate from 

parent bodies throughout the Solar System, one is able to learn about the structure and history of the 

Solar System without sending exploration or sample return missions. 

When examining the light curve, the graph of meteor magnitude versus time, properties such as 

the shape and symmetry of the curve can reveal whether the meteoroid is fragmenting, or what sort of 

cross sectional area it is presenting to the atmosphere, as examined in Beech (2009). In some cases, 

light curves with varying symmetry may be observed for particles belonging to a single shower, such as 

the Leonid particles modeled by Campbell-Brown and Koschny in 2004. Periodic oscillations in the 

light curve, such as those examined by Beech and Brown (2000), or Beech, Illingworth, and Murray 

(2003), may indicate meteoroid rotation that is as rapid in frequency as 102

 Hz, but is not rapid enough 

to make the meteor appear like an evenly-heated sphere. These oscillations occur as local maxima in the 

light curve, flares, which are distinct from noise. 

The purpose of this brief investigation is to qualitatively comment on how a meteor light curve is 

influenced by two phenomena: variation in meteoroid shape and ablation, and periodic oscillations in 

atmospheric density. Specifically, we examine whether either of these perturbations can result in flares 



E. Stokan ( ) • M. D. Campbell-Brown 

Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada, N6A 3K7. Phone: 1 (519) 661-2111 

ext. 87985; Fax: 1 (519) 661-2033, E-mail: estokan@uwo.ca 


in the meteor light curve. To model meteoroid shape variation, the equation relating an object’s crosssection area to mass employed by Beech (2009) is utilized. Periodic atmospheric density oscillation is 

modelled by introducing an oscillation to the isothermal atmosphere profile. Meteoroid motion and 

ablation is modeled using the standard equations. Solutions for velocity, mass, and intensity as a 

function of height are obtained numerically. 

2 Method 

The fundamental equations of motion and ablation are as follows: 

op"qhr

  op"qhrC  s

ef

e_

f

e

e_

(1)

 trp"qh (2)

where is the dimensionless heat transfer coefficient, B is the dimensionless drag coefficient, atm is the 

n area is made a function of the mass of the object with power , following 

Beech,

rB 

f7

Bp7

%

density of the atmosphere, S is the cross-sectional area of the object, V is the object’s velocity, and m is 

the mass of the object. 

The cross-sectio

 2009: 



 CD



f

f7



u

(3)

Here, mi is the initial mass of the object, and i is the initial density (assumed constant throughout the 

ajectory).  may take any value, with larger positive values of  indicating that the cross-sectional 

  pVH	 <

tr

area is a more sensitive function of the mass of the object.  = 0 gives an object with a constant crosssection, possibly representing a cylinder that ablates along the height axis, while  = 2/3 gives a 

spherical object that ablates radially, or self-similarly. Negative  gives an object that experiences a 

larger cross-section area as the mass depletes, which may represent an object that fragments as it ablates. 

The atmospheric density profile is represented by an isothermal atmosphere with a small relative 

oscillation: 

pv ? #$%wvIx^  v

vV

 (4)

Oscillation amplitudes between 2% and 10% are employed, as well as wavelengths between 1 and 10 

km. Oscillation in atmospheric density may originate from two main sources: physical phenomena such 

gravity waves or transient oscillations in the atmosphere (small amplitude and large vertical 

wavelength), or other physical phenomena observed in radiosonde data, which is usually smoothed out 

(amplitude of about 10%, and possible wavelength of 1 km), as noted in Hedin (1991). 

The equations of motion and ablation are recast as the following: 


e

ev  Bt 

f7

Bp7



 CD fu/!v

u

v

pv  yfu/!vvpv (5)

f7 #$% z

ef

ev  Bo

s 

f7

Bp7



 CD

{

fv

f7

|

u v

#$% z pv  \fuvvpv (6)

These equations are solved numerically using simple Euler integration. This gives the velocity and mass 

f the object as a function of height. The light curve is then produced assuming that the luminous 

ity I is proportional to the loss of kinetic energy: 

}~

e

o

intens

 ~ 

	 ef

 < f

e

e_  e_ e_   ~ #$% z 

ef

< f

e

 ev ev (7)

used in the numerical simulation. 

3 Results and Discussion 

Table 1. Summary of qualitative observations of light curves for objects ablating with different 

metry of Maximum brightness Height of maximum 

brightness 

Ending height 

The natural logarithm of the intensity gives a scale that approximates the magnitude for the light curve. 

Appendix 1 gives meteoroid properties and parameters 

Varying the shape of the object by varying  produced light curves with different properties. Table 1 

summarizes the properties, while Figure 1 shows the light curves and mass loss graphically. 

 Concavity, sym

light curve 

 < 0 Upward, highly Highest Highest Same as height of 

asymmetric maximum brightness 

 small 

(0 <  < 1) 

Downward, highly 

asymmetric 

Moderate Moderate Above h = 0 

 large 

( > 1) 

Lowest, more symmetric Lowest Lowest h = 0 

on wi 

appl

 

Figure 1. a) Mass and b) rough light curve for ablati

ies to both figures. 

th modified shape (-parameter). The same legend

150 100 50 0

2

4

6

8

10

Height(km)

Lightoutput(log10W)

b)

150 100 50 0

0

0.2

0.4

0.6

0.8

1

Height(km)

Mass(k

a) g)

=2/3

=2/3

=8/3

=2/3>8/3

=2/3>0.2


For  < 0, the light curve is concave upward, with the meteoroid burning up at the highest altitude 

compared to other choices for . This represents an object that reveals more cross-section area as the 

mass decreases, perhaps a fragmenting, pancaking object: 

r 

	

fEuE (8)

For  = 2/3, the light curve is concave downwards and is asymmetrical with a slow rise to a peak

brightness, and a rapid drop. This is the standard single-body light curve, that of a self-similar spherical 

bject. As  increases, the object’s maximum brightness decreases and is moved to lower heights, 

h light 

In even the largest oscillations with the smallest wavelengths, 

orresponding to transient oscillations in the atmospheric density data, produce small oscillations in the 

ght curve. Such small oscillations in a measured light curve would likely be indistinguishable from 

o

making the light curve more symmetric. In the limit of large  > 1, the object survives to the ground. 

This may represent an object that becomes more aerodynamic or resistant to ablation as the mass 

decreases. In any case, no flares, or local maxima in the light curve, are created if  has a constant value 

through the trajectory of the object. Even varying  from one value to another during object ablation, 

representing a quickly rotating object that becomes oriented, gives a light curve that initially resembles 

the curve of first  value, then slowly merges towards that of the second  value, with no flares being 

observed. 

The light curve associated with the oscillatory atmospheric density profile displays oscillations 

about the light curve with the smooth atmospheric density, as shown in Figure 2. 

Figure 2. a) Rough light curve and b) enlarged roug

= 2/3. The same legend applies to both figures. 

curve for ablation with oscillating atmosphere density, 

this case, small flares are observed, but 

c

li

noise. This suggests that periodic flares in a light curve are not likely to be caused by oscillations in 

atmospheric density. Perhaps some other mechanism, such as meteoroid rotation or periodic charge 

separation is responsible for oscillatory flares observed in some light curves. This will be investigated 

in more detail in the future. 

100 98 96 94 92 90

7.3

7.4

7.5

7.6

7.7

7.8

7.9

Height(km)

Lightoutput(log10W)

Nonosc.

A=2%,k=0.1km1

A=2%,k=1km1

A=10%,k=1km1

b) 9

160 140 120 100 80 60

4

5

6

7

8

Height(km)

Lightoutput(log10W)

a)


References 

Beech, M., On the shape of meteor light curves, and a fully analytic solution to the equations of meteoroid ablation, Mon. 

ron. Soc. 397, 2081-2086 (2009) 

wn, P., Fireball flickering: the case for indirect measurement of meteoroid rotation rates, Plan. Space Sci. 48, 

8, 751-758 

ppendix: Values used for numerical simulation 

h

Not. R. Ast

Beech, M., Bro

925-932 (2000) 

Beech, M., Hargrove, M., Classical meteor light curve morphology, Earth, Moon, and Planets 95, 389-394 (2004) 

Bee s of a “flic ch, M, Illingworth, A., Murray, I. S., Analysi kering” Geminid fireball, Meteoritics & Plan. Sci. 38 (7), 1045-

1051 (2003) 

Cam D, and Koschny, D., Model of the ablati pbell-Brown, M. on of faint meteors, Astronomy and Astrophysics 41

(2004) 

Ceplecha, Z., Borovicka, J., Elford, W. G., Hawkes, R. L., Porubcan, V., Simek, M., Meteor phenomena and bodies, Space 

Science Reviews 84, 327-471 (1998) 

Hedin, A. E., Extension of the MSIS thermosphere model into the middle and lower atmosphere, J. Geophys. Research 96, 

1159-1172 (1991) 

Holton, J. R., Beres, J. H., Zhou, X., On the vertical scale of gravity waves excited by localized thermal forcing, J. Atm. 

Sciences 59, 2019-2023 (2002) 

Vargas, F., Gobbi, D., Takahashi, H., Lima, L. M., Gravity wave amplitudes and momentum fluxes inferred from OH 

airglow intensities and meteor radar windows during SpreadFEx, Ann. Geophys. 27, 2361-2369 (2009) 

A

% 1 0 6.5 km 

Q 6@106

 J/kg mi 1 kg 

B 1 i 3.5 kg/m 3

> 0.1 Z 45A

0 1.01 kg/m3 Vi 35 km/s 


Dependences of Ratio of the Luminosity to Ionization on Velocity and Chemical 

Composition of Meteors 

M. Narziev1

Abstract On the bases of results simultaneous photographic and radio echo observations, the results 

complex radar and television observations of meteors and also results of laboratory modeling of 

processes of a luminescence and ionization, correlation between of luminous intensity Ip to linear 

electronic density q from of velocities and chemical structure are investigated. It is received that by 

increasing value of velocities of meteors and decrease of nuclear weight of substance of particles, lg Ip / 

q decreased more than one order. 

Keywords meteors · meteor luminosity · ionization

1 Introduction 

Studying the interaction of processes of luminescence and ionization and investigating their dependence 

on the velocity of meteors belongs to the actual questions of meteor physics. Knowledge of these 

dependences need to address such important and yet unresolved until the end of questions, as a 

refinement of the scale radio magnitudes, as well as the mass scale as the photo and radar meteors. 

Attempts to study the interaction of processes of luminescence and ionization of meteors, as well as 

finding the dependence of the ratio coefficient of luminous to the ionization on the velocity in the range 

32 < V < 62 km /s were made earlier than on the basis of data parallel visual-radar (Greenhow and 

Hawkins 1952), as well as photographic and radar observations (Davies and Hall 1963; Babadjanov 

1969). 

 However, because of the low accuracy in the first method, and because of statistical 

heterogeneity and lack of observational data in the second, the results obtained by different authors were 

significantly different. The dependence of the relationship of light intensity to the linear electron density 

on the velocities in the range 11 - 31 km/s generally has not been investigated. 

2 Dependences of Ratio of the Luminosity to Ionization on Velocity and Chemical Composition of 

Meteors 

In this paper, on the bases of results of simultaneous optical and radio echo observations and the results 

of laboratory simulation of the luminescence and ionization, the correlation between the intensity of 

luminescence Ip to linear electron density q from the velocity and chemical composition of meteors are 

investigated. 

 

M. Narziev ( ) 

Institute of Astrophysics of Academy of Sciences Tajikistan, Bukhoro str. 22, Dushanbe 734042, Tajikistan. E-mail: 

mirhusseyn_narzi@mail.ru


 According to the physical theory of meteors, the ratio of luminous intensity If to the initial 

electron line density q is related with the parameters of the meteor body equation: 

Ip / q = > V 3

! / 2 C (1) 

where  is the luminous efficiency,  - the ionizing probability, V- velocity of the meteor and  - the 

mean mass of a meteor atom. According to the equation (1), the ratio Ip /q depends not only on the 

coefficients of luminous efficiency and ionization, but also on the velocity and chemical composition of 

meteor bodies. 

 To investigate the Ip /q from velocity and other factors, we used the results of parallel television 

and radar observations conducted during periods of maximum activity of meteor showers from 1978 - 

1980 in Dushanbe (Narziev and Malyshev 2006, 2009), as well as the data of similar observations of the 

fainter (4 < M < 8) and low-velocity meteors (10 < V < 36 km/s) at Cambridge (Massachusetts) (Cook et 

al., 1973), the results of parallel photo - radar in Dushanbe (Babadjanov 1969), and the Jodrell Bank

(Davies and Hall 1963). The basic equipment used for the observations, the method of processing the 

observational data and initial data on the individual meteors in the aforesaid sources are given in Davies 

and Hall (1963); Babadjanov (1969); Narziev and Malyshev (2006, 2009); and Cook et al. (1973). 

 Table 1 confirmed the following dates: N - number of the meteor, V - velocity, H - the height of 

the point of specular reflection, M and q - the absolute magnitude and the linear electron density at the 

point of specular reflection, Ip - luminous intensity, calculated from the known formula: 

 lg If = 9.72 - 0.4 M (2) 

 The linear electron density for our joint meteors and meteor joint given in [2, 3], was determined 

from the measured duration of the radar echo. The value of lg Ip /q, calculated for each meteor is given 

in the sixth column, and in the seventh column source is indicated, which undertook the initial data. For 

meteors, given in Cook et al. (1973), the table gives the values of lg Ip /q calculated by n - Settlements. 

 According to the results given in Table 1, the calculated values of lg Ip /q are in the range -5.2 to 

-2.7. Figure 1 illustrates the distributions lg Ip /q and shows that the values lg Ip /q change in a fairly wide 

range from -5.5 to -2.5, with a maximum range of -5 to - 4.5. A large spread of values lg Ip /q, as already 

noted, possibly related to the dependence of the relationship lg Ip /q on the velocity and the difference in 

the chemical composition of meteors. 

0

10

20

-6 -5 -4 -3

N

 Figure 1. Observed distributions of ratio lg Ip /q. 

lg Ip /q


Table 1. Ratio of luminous intensity Ip to the initial electron line density q by the results combined optical and radio observations of meteors. 

(Sources: (A) Narziev and Malyshev 2006, 2009; (B) Davies and Hall 1963; (C) Babadjanov 1969; (D) Cook et al. 1973) 

N V ëì/î H ëì M lg q lg Ip /q Source

1 56.70 104.4 1.50 13.70 - 4.62 (A)2 36.50 92.0 1.10 13.60 - 4.28 --”--3 59.99 102.9 - 0.30 13.96 - 4.12 --”--4 - 98.0 - 0.90 14.73 - 4.55 --”--5 43.90 101.0 - 1.50 14.60 - 4.28 --”--6 40.80 99.0 1.63 13.16 - 4.22 --”--7 57.90 102.3 1.90 13.67 - 4.71 --”--8 46.20 105.0 1.10 13.98 - 4.70 --”--9 40.10 92.0 2.50 13.98 - 3.67 --”--

10 21.90 86.0 0.20 13.07 - 3.43 --”--11 41.40 96.3 1.60 13.60 - 4.52 --”--12 29.10 90.0 - 1.60 15.08 - 4.72 --”--13 39.20 95.1 2.20 13.56 - 4.72 --”--14 29.90 92.3 2.16 13.11 - 4.25 --”--15 43.40 92.0 0.50 13.77 - 4.25 --”--16 41.80 91.6 1.90 12.60 - 3.64 --”--17 41.80 93.0 1.70 13.44 - 4.40 --”--18 40.60 92.6 1.80 13.30 - 4.30 --”--19 40.20 92.0 0.20 13.97 - 4.33 --”--20 30.80 90.9 1.80 13.28 - 4.28 --”--21 47.70 102.2 2.20 13.49 - 4.65 --”--22 44.97 93.5 1.60 13.50 - 4.42 --”--23 42.90 92.7 1.20 13.45 - 4.21 --”--24 40.80 98.9 2.50 12.88 - 4.16 --”--25 41.40 94.2 1.00 13.83 - 4.51 --”--26 37.50 98.5 2.50 12.84 - 4.12 --”--27 31.00 88.0 - 13.11 - --”--28 22.60 86.5 0.0 13.73 - 4.01 --”--29 43.90 95.0 1.40 13.70 - 4.54 --”--30 14.30 88.5 - 1.00 14.21 - 4.09 --”--31 69.40 110.5 - 0.15 14.59 - 4.81 --”--32 60.90 102.4 1.50 13.55 - 4.43 --”--33 60.90 106.4 - 14.36 - --”--34 62.20 107.5 0.80 14.20 - 4.80 --”--35 38.50 91.4 - 1.00 14.75 - 4.63 --”--36 38.00 84.2 0.0 13.34 - 3.62 --”--37 40.90 87.0 2.05 12.33 - 3.43 --”--38 52.90 106.6 0.22 14.50 - 4.86 --”--39 55.50 106.1 2.05 13.92 - 5.02 --”--40 57.80 105.8 2.28 13.88 - 5.07 --”--41 59.90 104.1 1.00 13.76 - 4.44 --”--42 60.90 106.7 1.10 14.04 - 4.76 --”--

N V ëì/î H ëì M lg q lg Ip /q Source

43 55.70 102.5 2.00 13.64 - 4.72 (A)44 63.60 99.0 - 1.75 14.77 - 4.35 --”--45 65.80 102.0 - 1.20 14.84 - 4.64 --”--46 63.90 102.7 1.82 13.62 - 4.63 --”--47 58.10 106.2 1.50 13.99 - 4.72 --”--48 62.20 106.0 0.80 14.20 - 4.75 --”--49 65.70 101.1 1.53 14.09 - 4.98 --”--50 62.30 103.5 1.05 13.63 - 4.33 --”--51 59.80 105.5 0.20 14.29 - 4.65 --”--52 60.50 102.5 1.50 13.56 - 4.44 --”--53 60.40 100.8 2.60 13.27 - 4.59 --”--54 65.70 99.0 - 3.20 15.71 - 4.71 --”--55 55.00 105.2 1.40 13.85 - 4.69 --”--56 61.00 108.0 1.70 14.27 - 5.23 --”--57 56.10 106.3 0.40 14.12 - 4.56 --”--

1 37.00 94.9 - 1.7 14.99 - 4.59 (B)2 40.00 110.3 - 1.80 14.88 - 4.44 --”--3 29.00 92.8 2.00 12.19 - 3.27 --”--4 27.50 81.5 2.70 12.54 - 3.90 --”--

5Ü 33.00 101.9 3.30 12.39 - 3.99 --”--

5ï 33.00 96.5 1.60 13.75 - 4.67 --”--

6 34.00 96.4 1.60 12.39 - 3.31 --”--7 26.00 89.0 1.50 12.88 - 3.52 --”--

661345Ü 71.50 97.8 - 6.30 15.93 - 3.69 (C)

661345ð 71.60 97.3 - 4.40 15.19 - 3.71 --”--

670805 60.10 98.2 - 2.10 14.25 - 3.87 --”--670821 60.50 99.0 - 2.90 15.28 - 4.40 --”--670866 61.70 107.5 - 3.00 15.50 - 4.58 --”--670931 61.00 95.0 - 5.80 16.73 - 4.69 --”--670954 63.70 93.6 - 4.80 14.96 - 3.32 --”--

1 31.20 83.7 5.50 10.16 - 3.08 (D)2 14.70 97.3 6.87 10.12 - 2.97 --”--7 17.90 91.9 4.85 10.80 - 3.02 --”--9 28.80 99.3 4.95 11.10 - 3.36 --”--

12 16.20 90.1 7.75 9.65 - 3.03 --”--14 36.00 84.0 6.13 10.77 - 3.51 --”--15 30.10 92.9 6.30 10.72 - 3.52 --”--19 30.40 100.7 6.20 10.40 - 3.28 --”--21 32.00 92.3 6.78 10.22 - 3.21 --”--23 35.70 84.3 7.15 10.24 - 3.38 --”--24 27.10 91.0 6.50 10.08 - 2.96 --”--25 20.20 88.9 5.53 10.13 - 2.79 --”--


Dependence of lg Ip /q on the velocity are investigated by observations of 66 meteors that have 

absolute magnitudes, the prisoners in the interval -1 <  < +8. Meteors brighter than magnitude -1m are 

excluded for the following reasons: a) In most of the observed cases, these meteors are registered on 

turning trails. The number of such meteors in our case was 7. b) In addition, bright meteors features with 

multicenter radio echo duration and displacement of the mirror reflection along the trail. These factors 

tend to lead to an underestimation of the values of the radio echo duration and the line electron density. 

 The rest of the meteors were divided into groups according to velocity intervals of 10 km/s and 

for each group the average value of V and lg Ip /q was calculated. The results are shown in Figure 2 (red 

circles), where the values of lg Ip /q are on the axis of ordinates and the X-axis shows meteor velocity. 

From the data presented in the figure, the ratio of lg If /q in the range 14 – 25 km/s does not change 

significantly, and it is shown that in further increasing the velocity to 62 km/s, this ratio decreases more 

than an order of magnitude. 

 According to the equation (1), the ratio lg Ip /q can be determined if we know the value of > and 

C considering the given value of velocity and chemical composition. Such data for the velocity range of 

11 - 53 km/s were obtained from laboratory simulation of the emission and ionization for particles 

consisting of Fe, Ca, Si, Mg, etc. (Becker and Friichtenicht 1971; Boitnott and Savage 1970; Boitnott 

and Savage 1971; Friichtenicht and Becker 1973; Slattery and Friichtenicht 1967). 

 These elements are the parts of stony meteoroids and are often observed in the spectra of 

meteors. The results of these experiments confirm the dependence of V on > for model B (Lebedinets 

1980). The dependence of C on V for the case of iron particles is obtained in the form (Slattery and 

Friichtenicht 1967): 

C(Fe) = 1.5 @10-21 V 3.12 (3) 

 By specifying the chemical composition of dust particles and the numerical values of > and C

according to these experiments, using equation (1), we can calculate the ratio of lg Ip /q for different 

values of velocity. The calculation results are shown in Figure 2 (white circles on the - Fe). Similar 

calculations are carried out for copper particles in Figure 2 (triangle 9 - Cu). As from observational data 

and the results of laboratory simulation it is shown that changing the value of lg Ip /q on the velocity of 

this change > from V in model B. The differences between the curves is likely due to difference of 

chemical composition, partly to measurement errors that occur in the case of observations and data in the 

laboratory simulation, as well as conditions of the laboratory experiments, which correspond to heights 

of 70 km. On the basis of the results of simultaneous observations of meteors, lg Ip /q is found with 

velocity dependence: 

 lg Ip /q = (6.66 D 0.73) - (1.63 D 0.35) lg V

where V expressed in cm/s. 

We can estimate the influence of chemical composition of meteoroids in the scatter in the value 

of lg Ip /q, using the results of laboratory simulations. To do this, from (Lebedinets 1980; Becker and 

Friichtenicht 1971; Boitnott and Savage 1970; Boitnott and Savage 1971; Friichtenicht and Becker 

1973; Slattery and Friichtenicht 1967) we had taken numerical values of lg > and lg C for the velocity V 

= 40 km/s. Data of lg > and lg C are calculated values of lg Ip /q for micron-sized dust particles, 


lg Ip/q 

-6

-5

-4

-3

10 20 30 40 50 60 70 V 

Figure 2. Variation of mean values of lg Ip /q as a function of velocity V. 

 

containing in its composition Mg, Si, Ca and Fe are presented in Table 2. According to the results given 

in the table, the value of lg Ip /q is not constant, but in all probability is a function of the atomic weight 

of the substance. For a given value of the velocity, value of lg Ip /q depending on the chemical 

composition of matter varies from -5.46 to -4.33. If the observed values of lg Ip / q, according to the 

results of parallel observations at 40 to 42 km/s, vary in the range -4.52 to -3.43. The average observed 

value lg Ip / q at a velocity V = 41 km/s is -4.2. Thus, based on how the results of parallel optical and 

radar observations and data from laboratory simulation of the emission and ionization, it follows that the 

ratio of light intensity to a linear electron density is a function of velocity and chemical composition of 

meteors. 

Table 2. Ratio of lg Ip /q as a functions of chemical composition of the substance.

Elements lg > lg C lg Ip /q 

Mg - 3.40 - 0.821 - 5.46 

Si - 2.97 - 0.523 - 5.27 

Ca - 2.88 - 0.208 - 5.33 

Fe - 2.03 - 0.225 - 4.33 

3 Conclusions 

1. For the range of meteor velocities from 14 to 71 km/s and a brightness of up to 7m – -7m

meteors obtained as a result of parallel optical and radar observations, we calculated the ratio of the 

logarithm of light intensity to a linear electron density. It was found that the calculated values of the 

ratio of light intensity to the linear electron density in the range -5.1 to -2.7. The average value of lg Ip /q

is -4.5. 

2. According to the results of parallel optical and radar observations and the data of laboratory 

modeling of the phenomenon of a meteor, we studied the relation between the logarithm of the ratio of 

light intensity to the linear electron density lg If /q on the velocity and chemical composition of the 

meteors. It is received from simultaneous results observations of meteors, and results of laboratory 


modeling follows that by increasing value of velocities of meteors lg Ip /q decreased more than one 

order. 

References 

1. Babadjanov P.B Report of Academy of Sciences USSR, 4, 800, 800-802 (1969) 

2. Becker D.G., Friichtenicht J.F. Astrophys. J., 166, N 3, pt 1, 699 - 716 (1971) 

3. Boitnott C.A., Savage H.F. Astrophys. J., 161, N 1, pt 1, 351 - 358 (1970) 

4. Boitnott C.A., Savage H.F. Astrophys. J., 167, N 2, pt 1, 349 - 355 (1971) 

5. Cook A.F, Forti G., McCrosky RE, Posen A., Southworth R., Williams J.T. Evolutionary and physical properties of 

meteoroids. IAU - Colloquium.Washington. 23-44 (1973) 

6. Davies J.G., Hall J.E. Proc. Roy. Soc., A271, N 1344, p. 120-128 (1963) 

7. Friichtenicht J.F., Becker D.G. In: Evolutionary and physical properties of meteoroids. Ed. C.L. Hemenwey, P. M. 

Millman, A. F. Cook. N.Y.: NASA SP – 319, 53 - 82 (1973) 

8. Greenhow J.S., Hawkins G.S. Nature. 170, N 4322, p. 355-357 (1952) 

9. Lebedinets V. N. Dust in the upper atmosphere and space. The Meteors. Leningrad, Gidrometeoizdat, 248 (1980) 

10. Narziev M., Malyshev, I. F. Bulletin of the Institute of Astrophysics Academy of Sciences of the Republic of Tajikistan. 

85, 35-45 (2006) 

11. Narziev M., Malyshev, I. F. Proceedings of the Academy of Sciences of the Republic of Tajikistan. 4(137), 36-45 (2009) 

12. Slattery J.C., Friichtenicht J.F. Astrophys. J. 147, N 1, 235-244 (1967) 



CHAPTER 6: 

CHEMICAL AND PHYSICAL PROCESSES RESULTING 

FROM METEOROID INTERACTIONS WITH THE 

ATMOSPHERE 


Atmospheric Chemistry of Micrometeoritic Organic Compounds 

M. E. Kress1• C. L. Belle2• G. D. Cody3• A. R. Pevyhouse1• L. T. Iraci4

Abstract Micrometeorites ~100 μm in diameter deliver most of the Earth’s annual accumulation of 

extraterrestrial material. These small particles are so strongly heated upon atmospheric entry that most 

of their volatile content is vaporized. Here we present preliminary results from two sets of experiments 

to investigate the fate of the organic fraction of micrometeorites. In the first set of experiments, 300 μm 

particles of a CM carbonaceous chondrite were subject to flash pyrolysis, simulating atmospheric entry. 

In addition to CO and CO2, many organic compounds were released, including functionalized benzenes, 

hydrocarbons, and small polycyclic aromatic hydrocarbons. In the second set of experiments, we 

subjected two of these compounds to conditions that simulate the heterogeneous chemistry of Earth’s 

upper atmosphere. We find evidence that meteor-derived compounds can follow reaction pathways 

leading to the formation of more complex organic compounds. 

Keywords micrometeorite · organic chemistry · atmosphere 

1 Introduction 

Micrometeorites 100 μm in diameter carry most of the extraterrestrial material striking the top of the 

atmosphere, approximately 40 million kg annually [3]. The majority of these particles are most closely 

related to CM chondrites, and thus should carry a few percent organic material by weight, initially. 

These particles experience severe heating upon atmospheric entry, reaching their peak temperatures at 

altitudes of >85 km [2] (see also [4] in this volume for more details on atmospheric entry temperatures). 

Most micrometeorites are melted either partially or completely, indicating that they reached 

temperatures sufficient to melt silicate, >1600 K [2] [3]. Such strong heating had been assumed to cause 

complete destruction of the organic content of the particles in this size range. 

 In recent years, the new field of astrobiology has generated much interest in the relationship of 

extraterrestrial organic compounds and the prebioitic environment of early Earth. The process of 

delivering material to habitable planets generates tremendous heat whether it is via micrometeorites or 

km-sized objects; thus, this step seems to be a potential dealbreaker for a relationship between 

interstellar or meteoritic organic compounds and the origin of life. However, in recent years the 



M. E. Kress ( ) • A. R. Pevyhouse 

Department of Physics & Astronomy, San José State University, CA 95192-0106 USA. Phone: +1-408-924-5255; E-mail: 

mkress@science.sjsu.edu 

C. L. Belle 

Department of Biology, The Colorado College, Colorado Springs, CO 80903 USA 

G. D. Cody 

Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Rd NW, Washington, DC 20015 USA 

L. T. Iraci 

Earth Science Division, NASA Ames Research Center, Moffett Field, CA 94035 USA


questions have been further refined to investigate how infalling material is modified during the delivery 

process, as opposed to whether this or that molecule can ‘survive’ delivery. For instance, Court and 

Sephton [1] found that methane evolves from the pyrolysis of carbonaceous chondrite particles. 

 Here, we report preliminary results on two sets of experiments: 1) atmospheric entry was 

simulated by flash-pyrolyzing micrometeorite analogs, producing methane and a variety of organic 

compounds, and 2) heterogeneous chemistry in Earth’s upper atmosphere was simulated with sulfuric 

acid-catalyzed reactions among two of the pyrolysis products, resulting in the formation of more 

complex organic compounds. 

2 Atmospheric Entry 

A fresh fragment from the interior of the Murchison CM 2 carbonaceous chondrite was crushed and 

sieved to yield 300 μm diameter particles. To reproduce the effects of atmospheric entry encountered by 

micrometeorites, these particles were flash-heated at 500 K/second to temperatures in excess of 1300 K 

in a CDS 1000 pyroprobe with heated injector interface. This instrument has been used in pyrolytic 

analysis of ancient biomacromolecules and extraterrestrial organic solids. Upon release from the solid 

particle, the pyrolysis products were entrained in a helium stream and deposited on a cold finger (a loop 

of the GC column immersed in liquid nitrogen). Upon liquid N2 boil off, the molecular products 

(pyrolysate) are chromatographically separated on the GC column (a Supleco SPB 50, 50% phenyl-50% 

dimethyl silicone) employing an Agilent 6890 series GC and analyzed with a HP5972 mass 

spectrometer. 

 3.5 wt % of the Murchison meteorite is composed of organic material; of this approximately 30 

wt % of these organics are converted into volatiles during flash pyrolysis, the remaining 70 % is a char. 

The resulting mass spectrum is shown in Figure 1. The majority of the organics were evolved in a 

temperature range of 500 to 1000 K. The volatile organics appeared to have been completed removed 

from the particle by a temperature of 1000 K. 

Figure 1. Products evolved upon flash pyrolysis of micrometeoritic analog particles 


The compounds that were identified as pyrolysis products included relatively simple compounds 

including CO, CO2, H2O, CH4, and H2S. Also evolved from the meteorite during pyrolysis were 

complex organics, including alkylbenzenes, phenol and alkyl phenols, alkylthiophenes, benzonitrile, 

benzothiophene, a variety of light hydrocarbons, naphthalene and alkyl-naphthalenes, styrene, and a 

minor amount of larger polycyclic aromatics including anthracene and phenanthrene. The absolute and 

relative abundances of these compounds have not yet been quantified. 

3 Heterogenous Chemistry in the Upper Atmosphere 

Sulfuric acid particles exist in Earth’s upper atmosphere, and organic compounds often react strongly 

with this acid. We have studied the reaction of phenol and styrene, two of the compounds identified in 

the pyrolysis experiments that are known to independently undergo reactions with sulfuric acid. The 

sulfuric acid solution was used as a surrogate matrix to mimic upper atmospheric particles. 

 Theory predicts an acid-catalyzed reaction between phenol and styrene to produce 4-(1-

phenylethyl) phenol (shown in Figure 2), and our experiments showed spectral evidence consistent with 

this pathway (Figure 3). The reaction mixture is compared with 4-cumylphenol which serves as an 

analog for 4-(1-phenylethyl) phenol, which was not commercially available but has a very similar 

infrared spectrum. The only difference between these two structures is that 4-cumylphenol has an 

additional methyl group on the § carbon atom in place of the hydrogen atom. H2SO4 concentrations 

higher than 30 wt% are required to obtain reaction at all temperatures and in a short amount of time. In 

general, reaction occurs more readily at colder temperatures (5°C compared to 65°C). 

Figure 2. Theoretical acid-catalyzed reaction between phenol and styrene yields 4-(1phenylethyl) phenol. Note loss 

of =CH2 in step 1 and addition of -CH3 group. 


Figure 3. Comparison of 4-cumylphenol IR spectrum (upper curve) with that of the of reaction mixture (lower 

curve). This reaction mixture was 70wt% sulfuric acid heated to 40°C for 5 minutes and then remained at 20°C for 

one day. 4-cumylphenol is an analog for the predicted product, 4-(1-phenylethyl) phenol, shown in Figure 2. 

4 Summary and Future Work 

The fate of organic material entering Earth’s atmosphere from space is not well understood. The 

preliminary results from our experiments show that 1) a wide variety of organic compounds may be 

released from micrometeorites during atmospheric entry, and 2) these compounds may then go on to 

react with each other under conditions in the Earth’s upper atmosphere. In particular, we found that 

phenol and styrene are released from flash-pyrolyzed CM chondrite micrometeorite-analogs. We also 

found that, under conditions analogous to those of the upper atmosphere, phenol and styrene react to 

produce a compound with a para-disubstituted aromatic ring. 

 Meteor-derived organic compounds are susceptible to destruction by solar UV, which has a 

higher flux at altitudes where most of the organic compounds will be released (>85 km). Organic 

compounds will be destroyed by prolonged exposure to solar UV; this issue is discussed in more detail 

in Pevyhouse & Kress ([4], this volume). If organic compounds are to persist in the atmosphere, they 

must be readily mixed to lower altitudes over timescales that are short compared to their photochemical 

lifetimes. Aromatic compounds are generally more stable to photolysis than are aliphatic hydrocarbons 

and thus are more likely to participate in heterogeneous chemical reactions leading to greater chemical 

complexity in the Earth’s modern atmosphere. 

 Future work will entail quantifying the compounds released during entry conditions. Once the 

abundances these species are measured, they can be incorporated into atmospheric chemical models. 

The questions of astrobiological interest include investigating the roles that aromatics and light 

hydrocarbons play in planetary atmospheres. These compounds are strong greenhouse gases, and they 

also drive smog production in low-O2 environments. Aromatic compounds also may be important in 

organic haze production, and they are excellent absorbers of ultraviolet radiation. On the early Earth, 


high levels of aromatic compounds from infalling debris may have shielded the prebiotic planetary 

surface from stellar UV. An understanding of these chemical processes may also be critical to preempting false positives that masquerade as biomarkers in the atmospheres of exoplanets. 

Acknowledgements 

MEK and ARP acknowledge research support from the NASA Astrobiology Institute’s Virtual Planetary 

Laboratory (PI: V. Meadows). CLB was supported via the Undergraduate Student Research Program / 

Universities Space Research Association. 

References 

1. R.W. Court and M.A. Sephton, Investigating the contribution of methane produced by ablating micrometeorites to the 

atmosphere of Mars, Earth and Planetary Science Letters, 288, 382-385 (2009) 

2. S.G. Love and D.E. Brownlee, Heating and thermal transformation of micrometeoroids entering the earth’s atmosphere, 

Icarus, 89, 26-43 (1991) 

3. S.G. Love and D.E. Brownlee, A direct measurement of the terrestrial mass accretion rate of cosmic dust, Science, 262, 

550-552 (1993) 

4. A. R. Pevyhouse and M.E. Kress, Modeling the entry of micrometeoroids into the atmospheres of Earth-like planets, in 

Meteoroids 2010, NASA Conference Proceedings, held in Breckenridge, CO, May 2010. Edited by D. Janches (in 

preparation) 


Formation of the Aerosol of Space Origin in Earth’s Atmosphere 

P.M. Kozak1• V.G. Kruchynenko 

Abstract The problem of formation of the aerosol of space origin in Earth’s atmosphere is examined. 

Meteoroids of the mass range of 10-18-10-8 g are considered as a source of its origin. The lower bound of 

the mass range is chosen according to the data presented in literature, the upper bound is determined in 

accordance with the theory of Whipple’s micrometeorites. Basing on the classical equations of 

deceleration and heating for small meteor bodies we have determined the maximal temperatures of the 

particles, and altitudes at which they reach critically low velocities, which can be called as “velocities of 

stopping”. As a condition for the transformation of a space particle into an aerosol one we have used the 

condition of non-reaching melting temperature of the meteoroid. The simplified equation of deceleration 

without earth gravity and barometric formula for the atmosphere density are used. In the equation of 

heat balance the energy loss for heating is neglected. The analytical solution of the simplified equations 

is used for the analysis. 

As an input parameter we have used the cumulative distribution of space matter influx onto earth 

on masses in large mass range. Basing on this distribution we have plotted three-dimensional probability 

density distribution of influx of particles as a function of parameters, which determine the heating and 

stop altitude of a meteoroid: initial mass m0, velocity of entry into the atmosphere 0 and radiant zenith 

angles zR0. The obtained three-dimensional distribution had been presented first as a product of three 

independent distributions on the mentioned parameters, then it was transformed using the equation of 

deceleration into the distribution on the following parameters: m0, 0 and “altitude of stopping” HS. The 

final 2-dimensional distribution on parameters 0 and HS of the aerosols of space origin in the 

atmosphere was obtained by means of integration of the previous distribution over 0. 

Keywords meteoroids · meteors · atmosphere aerosol · aerosol formation · space origin 

1 Introduction 

There are aerosols of both ground and space origin in Earth’s atmosphere. Aerosols of the ground origin 

are presented basically in the lower atmosphere: in the troposphere. The most powerful aerosol layer of 

the ground-based origin, known also as Junge Layer, is placed at altitudes of 10-25 km. It originated 

from the condensation of some components of the atmosphere appearing from the photo-chemical 

transformations of some products of volcano eruptions, for example sulphuric acid vapors. The second 

confidently established aerosol layer in the atmosphere is placed at altitudes of 80-85 km, corresponding 

to the minimal atmospheric temperature, in the mesopause. The origin of this aerosol layer in not finally 

established. Most of scientists, and the authors as well, hold an opinion that all the particles there to be 

of space origin. Under some special conditions the condensation of water vapors on these particles 

becomes possible, and we can see, probably, the high-latitudinal silvery clouds. 

 

P.M. Kozak ( ) • V.G. Kruchynenko 

Astronomical Observatory of Kyiv Taras Shevchenko National University, Kyiv, Ukraine. Phone: 044-4862762; Fax: 044-4862630; Email: kozak@observ.univ.kiev.ua 


 According to meteor physics investigations (Whipple 1950; Whipple 1951; Levin 1956; Öpik

1956; Lebedinets 1980; Lebedinets 1981; Voloshchuk et al. 1989) most of low-mass particles coming 

into the atmosphere with initial velocities ~11.2-72.5 km/s lose their energy at altitudes of 140-80 km. 

Small fragments detaching from already heated bigger particles in the atmosphere cannot be decelerated 

without almost entire loss of their masses due to evaporation. The deeper penetration of a particle to the 

atmosphere the lower the probability to save its macro size. This task of motion, deceleration and 

destruction of a separated particle in “abnormal environment” according to the terminology of Öpik

(1956) we were considering in Voloshchuk et al. (1989). Such a conclusion is also given from the 

experimental investigations of chemical analysis of particles, caught in the atmosphere with the help of 

high airplanes and balloons. Such particles are similar to coaly chondritics (Nady 1975), having a big 

amount of helium in their surfaces, which penetrated there from the solar wind. Therefore, these are the 

primary interplanetary particles, which have come though the atmosphere without intensive heating and 

are not the products of fragmentation of larger bodies (Brownlee and Hodge 1973). 

 The amount and distribution of the aerosol of space origin in the atmosphere is connected by 

some authors with planetary global warming. In this work we will try to examine the problem of 

formation of the aerosol of space origin in Earth’s atmosphere basing on the initial meteoroid 

distributions on the Earth’s heliocentric orbit and the equations of classic meteor physics. 

2 Meteor Physics Equations to be Used 

In this chapter we consider the basic equations of meteor physics to be used in the work, namely the 

equation of heating of the meteoroid, and the equation of its deceleration. In addition, the simplification 

of the equations in order to realize the final investigation analytically is substantiated. 

2.1 Complete Equations of Meteoroid Deceleration and Heating 

The base assumption for the transformation of a small meteoroid into an aerosol particle, not into a 

meteor, consists in non-reaching by the meteoroid its melting temperature. Therefore, we have to 

determine the mass interval, and other parameters of meteoroids, which coming into the Earth’s 

atmosphere, do not reach the melting temperature because of their deceleration and heat radiation. 

2.1.1 Heating Balance Equation 

The theory of heating of low-mass meteoroids with their deceleration, which plays an important role in 

this case, were developed by Whipple (1950), Whipple (1951) and later by Fecenkov (1955). They have 

obtained the name of Whipple’s micro-meteorites. It is known (Levin 1956) that the particles having the 

size less than x0 warm up to the same temperature (x0 is the warming up depth at which the temperature 

of the body is less to e times relatively the surface). According to Öpik (1937) and Levin (1956) such 

particles have radius r0 Á 10-3 cm. The change of temperature of such a particle with taking into account 

the energy loss for heating and radiation can be written as: 

 , (1)   4 4

M 00 0 S Edt m cdT T T S dt 
 C' F 0

where SM0 = const and SF0 = const are the middle section and entire surface area of the particle 

accordingly, m0 = const is its initial mass, c is the specific heat capacity and ' is Stefan’s constant, T and 


T0 are the current temperature for time t and initial temperature of the particle in the field of solar 

radiation at the distance of 1 a.u.,  Á 1 is a coefficient of thermal radiation of the meteoroid 

characterizing the digression from black body radiation, E = òA

3

/2 is the energy incoming to unity of 

the meteoroid surface due to its collision with atmosphere molecules, % is the dimensionless coefficient 

of heat conductivity, A is the atmosphere density. 

2.1.2 Deceleration Equation 

If the space particle is not warmed up to the melting temperature it becomes the aerosol particle. So, the 

next question we should answer: at which altitude will it stop? In order to solve this problem we 

consider the equation of deceleration, which can be written in the most common vector view as 

0 0 RM A

d m cS

dt


  E



 g m0 , (2) 

or separated into constituent parts: 

2

0 00 cos RM A R

d m cS mg dt

z

E


  E (3) 

sin R

R

dz

g z dt

E 
 , (4) 

where  is the meteoroid velocity, zR is the zenith angle of its radiant, cR is the resistance coefficient, g is 

the free fall deceleration constant. 

2.2 Accepted Assumptions 

In our calculations we use some assumptions and simplifications. First, we suppose the particles of 

space origin producing the aerosol are of meteor mass range. Lower bound of meteoroid initial mass is 

10-18 g according to meteoroid mass distributions presented in literature (Ceplecha et al. 1992), higher 

bound corresponds to the r0, and is approximately equal to 10-8 g (Öpik 1937). The second assumption is 

that we consider just warmed up and evaporated particles and neglect the mass loss due to blowing 

meteoroid molecules away in its “cold” state. The next, the most doubtful assumption consists in the fact 

we use the barometric formula for the atmosphere density: 

* ( ) (0) exp( ) A A

H H

H   
 . (5) 

Here A(0), H*

 are the atmosphere density at the sea level and altitude of the homogeneous atmosphere 

accordingly. For precise calculations one should use the numerical solution of the equations (1) and (2) 

and take the real atmosphere density distribution from modern models of atmosphere, especially for 

altitudes over approximately 120 km. We use the formula (5) here just for the purpose of obtaining the 

analytical solution of (3) and (4) in order to understand the physics of the aerosol layer formation. Then, 


we consider the sporadic meteoroids as the main source of aerosol particles, i.e. the particles which are 

supposed to be of the stone composition. Finally, we calculate the mean aerosol influx during a year. 

2.3 Simplification of the Equations 

According to Öpik (1937), the small meteoroid spends almost all its energy for the thermal radiation if 

its radius r Á 10-3 cm (corresponds to m0 ä 10-8 g for spherical particles), so we can neglect the first term 

in the equation (1): 

3

4 4 0

0

0 2

M A

F

S T T

S

 E

C'

% 
 . (6) 

Since we deal with low-mass particles we can suppose they are decelerated relatively fast, so we 

can neglect the gravity term in the equations (2). The equations (3) and (4) in this case transform into the 

equation 

2

0 RM A

d m cS

dt

E 
  E , (7) 

and . R R0 z z cons 
 
 t

Also we use the relation between the time t and altitude H of the particle 

 cos R dH z dt 
 E (8) 

and express the middle section and surface area of the particle through the shape parameter A: A = 

SM/V2/3, where V is the meteoroid volume. Supposing the particle is spherical SF0 = 4SM0 = 4A(m0/M)

2/3, 

the shape parameter for spherical particles to be A = 	(3/4	)

2/3. 

2.4 Variation Parameters, Constants and Final Equations 

Using (6), (7), (8), the shape parameter and barometric formula (5) we obtain 

3 *

4 4 0

0 1/3 2/3

0 0

3

exp 8 co

A R

s

A

M R

c AH T T

m z

 E  C' 

% 
 

 



 (9) 

*

0 1/3 2/3

0 0

exp

cos

R

A

M R

c AH

m z

E E



  
 

 

 . (10) 

Reaching by the particle of maximal temperature along its trajectory can be derived from 0 A dT d 
 , 

and so from (9): 

1/3 2/3

0 0

max *

cos

3

M R

AT

R

m z

c AH

  
 . 


Putting it back into (9) we obtain 

1/3 2/3 3

4 4 0

max 0 *

cos

24 exp(1)

M R

R

m z T T

c AH

 0 0 E

C'

% 
 . (11) 

Thus, the condition of transformation of space particle into the aerosol can be expressed now as 

 , (12) T T max F melt

where Tmax has to be expressed from (11), Tmelt is the melting temperature of the particle. 

 Looking at the equations (10) and (11) we can note that there are three parameters of a meteoroid 

(under the assumptions made above) having an influence onto its belonging to the class of aerosols or 

meteors, and to the altitude of stopping in the case of the aerosols. These are initial mass of the particle

m0, velocity 0, and zenith radiant angle zR0. The ranges of their variations are: m0 = 10-18 – 10-8 g 

according to Ceplecha et al. (1992) for the lower limit and Öpik (1937) for the higher limit (see above), 

0 = 11.2 – 72.5 km/s, i.e. the particles belonging to the solar system are considered, zR0 = 0° - 90°, all 

possible entrance angles are taken into account. 

Expressing (12) through the variation parameters we obtain the final inequality of separation of 

the meteoroids onto aerosols and meteors 

 , (13) 1/3 3

00 0 cos m z E R F CT

where * 44

0 24 exp(1)( ) C c AH T T T R melt

2/3 
 % C'  M . 

 If the condition (13) is realized we can find the altitude of stopping HS of the aerosol particle 

from (10), supposing the velocity of stopping S is a small enough value. Here we continue to use the 

equation (10) except the Stokes formula for low velocities, where the deceleration is proportional to the 

first power of the velocity, so HS can be found from the expression 

*

0 1/3

0 0

(0)exp( )

exp

cos

S

V A

S

R

H C

H

m z



E E

    
 

   

, (14) 

where . * 2/3 C c AH VR M 


During the calculations the following values of constants are taken (Levin, 1956): ò = 1, « = 

5.67032×10-5 erg@cm-2@K-2@s

-1, ± = 1, cR = 1, H* = 7×105

 cm, A(0) = 1.6×10-3 g/cm3, M = 3 g/cm3, T0 = 

276 K, Tmelt = 1600 K, S = 0.5 km/s. For an iron particle ò = 0.75; M = 7.6 g@cm-3; cR = 1.25; Tmelt = 

1800 K. 

3 The Statistical Approach to the Process of Space Origin Aerosol Formation in the Atmosphere 

Here we propose the statistical model for the description of atmospheric aerosol formation from 

meteoroids. We will construct the 3-dimensional distribution on variation parameters having an 


influence onto the probability of the aerosol formation and onto the altitude of the aerosol layer. Let’s 

represent the distribution as a multiplication of three independent single-parameter probability density 

distributions: 

00 0 0 0 0 ( ,, ) ( ) ()( ) mz R m z R p m z pmp pz E E E E 
 . (15) 

It is obvious that this distribution should be normalized to unity over all three parameters, i.e. there must 

be 

00 0 0 0 0 (,, ) 1 mz R R p m z dm d dz E E E 
 """ , 

where the integration is carried out inside all possible ranges of parameter values. 

3.1 Primary Distribution of Meteoroids 

Let us find all three 1-dimensional primary probability density distributions, and start from the 

distribution on mass. 

3.1.1 Probability Density Distribution on Initial Mass 

There can be found in the literature distributions of space matter onto Earth as cumulative distributions 

of number of particles on their masses, for example Ceplecha (1992), Kruchynenko (2002), 

Kruchynenko (2004). We will use the linear dependence (Kruchynenko 2002, Kruchynenko 2004) for 

the further calculations: 

 , (16) '

10 0 0 0 10 0 log ( ) log Nm m C k m 7 


where N(m0 ¿ m0) is a number of particles with masses not less than m0 coming into all Earth 

atmosphere during a year, C0 = 7.86, k = 0.892. 

The probability density distribution on mass pm(m0) according to cumulative distribution (16) can 

be described by Pareto distribution: 

0 0

0

0 0 1

0

( ) 0 

( )

m l

k

l

m l k

pm m

km

pm m

m 

; 


7 
 (17) 

where m0l is chosen freely. The probability density function is normalized to unity in the value range 0 – 

+õ. There are the following obvious consequences: 

0

0 0

0

0 00 00

0

() () 1 () 1

l

m k

l

m m k

m m

m F m p m dm p m dm

m




 

 " " , (18) 


0

0 0

0 0

( ) () () ( ) m

l l

dN m dF m p m dm Nm m 
 
 F F  0 , (19) 

where F(m0) is the cumulative probability, Nl(m0 ¿ m0l) is a sample of all particles in the chosen range, 

which can be found from (16) as 0

0 ( ) 10C k Nm m l l 
 0l . We suppose m0l = 10-18 g, so Nl = 8.24×1023. 

3.1.2 Probability Density Distribution on Initial Velocity 

The probability density distribution on velocity (0) will be chosen according to radar meteor 

observations, for example (Voloshchuk et al. 1989): 

0 11 2 p PG P G ( ) ( , ) (1 ) ( , ) E E E E' E' 
 E 2 , (20) 

where 

2

2

1 ( ( ) exp( ) 2 2

G

E E

E E

E

'  '


 )

!

 

are Gaussians with the following parameters:    km/s, 1 = 6.51 km/s,   i

0

km/s, 2 = 

5.15 km/s. The value P is changing during a year. For the mean value we choose P ä 0.33 (Voloshchuk

et al. 1989). It is obvious that the probability density function is normalized to unity in the range 0 – +õ. 

3.1.3 Probability Density Distribution on Initial Radiant Zenith Angle 

The probability density distribution on radiant zenith angle z(zR0) will be derived from the following 

thoughts: let suppose that the number of particles dN(r, r + dr) entering into earth atmosphere from some 

direction in the range dr in some spatial angle d
 (see Figure 1) per time unity can be expressed as dN(r, 

r + dr) ~ 2n0	rdrd
dt, where n0 is a spatial concentration of meteoroids. Since r = R;+%(+zR, we have 

dN(zR, zR + dzR) ~ 2n0	R;sinzRcoszRdzRd
dt. So we have to use the sine-cosine distribution sin zR0 cos 

zR0. 

After normalization to unity we obtain the final distribution on zenith radiant angle 

0 0 ( ) 2sin cos Z R RR p z z 
 z

vation of the probability density function on radiant zenith ngle. R; is Earth’s radius. 

. (21) 

Strictly saying, this distribution will be distorted by the Earth gravity, but we use it due to its simplicity. 

 

ZR

 Figure 1. To the deri a

r 

R?


3.2 Se

a geometrical 3-dimensional cube, where 

e three considered parameters m ,  and z determine the dimensions along its three ribs-axes, limited 

Figure 2. The separation of meteoroids onto aerosols and meteors. Letter A and dark gray color 

orresponds to aerosols, otherwise to meteors (letter M and light gray color). The picture a

 

Figure 2 that the region of aerosols (denoted in the picture with the letter A and 

ark gray color) is increasing while the mass is decreasing (the region of meteors denoted as M with 

0

paration of the Distribution into Aerosols and Meteors 

The primary distribution of meteoroids can be conceived as 

th 0 0 R0

by the permissible parameter values. The “intensity” in each point inside such a cube is expressed by the 

value of pmz(m0, 0, zR0). The real number of particles dN in the range of dm0, d0, and dzR0 can be found 

from (19). If we make a few sections perpendicularly to the cube rib describing the mass m0 we will 

obtain the 2-dimensional pictures in coordinates 0 ÷ zR0 for the fixed mass values, where the relative 

value of pmz can be expressed with the help of lines of the similar values, for instance. In the Figure 2 

we show only two maximums of the pmz corresponding to modal values of bimodal distribution of 

velocity and the maximum of zenith radiant angle value zR0 = 45°. Figure 2a corresponds to m0 = 10-12 g, 

Figure 2b to m0 = 10-9 g. The regions of aerosols and meteors are separated by solid line according to 

inequality (13). 

c

corresponds to mass m0 = 10-12 g, b to m0 = 10-9 g. Dashed lines describe the equal altitudes of 

stopping. Signs “+” show positions of modes of the distribution. 

 We can see in 

d

lighter gray color is decreasing accordingly). Therefore, there must be a mass value lower of which all 

particles remain aerosols. The probability for a meteoroid to become a meteor is proportional to its 

velocity and cosine of zenith radiant angle. Setting according parameters to their maximal values 0 = 

72.5 km/s and cos zR0 = 1 we get the critical mass value m0cr ä 1.7×10-14 g. Finally, all space particles 

entering into the Earth atmosphere remain aerosols if their masses are lower than the critical value, then 

the rate of aerosols is decreasing almost down to zero while the mass is increasing up to the value of 

approximately m0 = 10-8 g. This rate gA(m0) can be easily calculated with the help of the formula 

 

0 0 / 2 ( )

( ) ( ) ()

Rz

A z g m p z dz p d

 E

E

0

0 00 0

0 MIN

R R

E


 E E " " . 

0 10 20 30 40 50 60 70 80

E, km/s

0

10

20

30

40

50

60

70

80

90 ZR, deg

0 10 20 30 40 50 60 70 80

E, km/s

0

10

20

30

40

50

60

70

80

90

ZR , deg

108.1

85.8

84.4

A M

b

108.1

101.9

99.3

A M

a


The power coefficient in cumulative mass distribution k from (16) is running a range of values: k = 

92 f r m0 Á 1.7×10-14 g, then k = 1.087 for m0 ä 10 / 10-12 g, k = 1.189 for m0 ä 10-11 / 10-10 g, k = 

1.438 for m ä 10-9 / 10-8 g (the average value for all the mass range m ä 10-13 / 10-8 g is k = 1.232). 

he relation (14) connects four variation parameters: three ones included into the primary distribution, 

an be called conditionally the “free” 

arameter. The dotted curves corresponding to some of its values (minimal altitude of stopping, minimal 

H of the aerosol 

0.8 o -13

0 0

3.3 Transformation of the Primary Distribution to New Variables 

T

and the fourth one, the altitude of stopping HS. This parameter c

p

and maximal velocities altitudes) to be expressed in kilometers are shown in Figure 2. 

 Since the main aim of our investigations is to plot the two-dimensional distribution pmH(m0, HS) 

of the aerosol formation into the atmosphere, we will solve it in two steps. The first one is to change the 

variable zR0 in the primary distribution pmH 0 (m , 0, zR0) to the altitude of stopping S

particle. The second step will be consisting in the reducing of 3-dimensional distribution pmH(m0, 0, HS) 

to pmH(m0, HS) by means of integration of pmH(m0, 0, HS) over all range of 0. 

 According to statistical probability density distribution transformations and taking into account 

that only one variable is changing (zR0ø HS) we can write 

0

() 0

( ) ( ) ( ( )) S

R S

H S zH R S

z H pH p z H H

6 
 6 , 

S

(22) 

zR0(HS) and determinant of transition 0 z ( where ) R S

S

H

H

6

6 can be found from (14). Let us denote 

1/3

00 0 0 0 ( , , ) cos ( ) ln Cm H z C H m Z E  EE S RV S 3 
 A S . 

Then we can write 

  2

0 ( ( )) 2 1 Z RS Z Z p zH C C 
 , 0

* 2

1

1

R Z

S Z

z C

H H C

6 
 6 , 

and put them into (22): 

2

00 00 *

2 (,, ) (,, ) H SZ S p m H Cm H

H

E E 
 (23). 

The final view of the obtained distribution

shown in Figure 3 for the same masses as in Figure 2. The “free” parameter now is the cosine of the 

enith radiant angle, and the dashed curves correspond to different values of z expressed in degrees. 

The va

pmH(m0, 0, HS) while taking into account (23) is 

z R0

lue zR0 = 0 is placed lower than others in Figure 3 and shown with a solid curve. The region to be 

placed lower than value zR0 = 0 is forbidden for both aerosol and meteor particles. 

An interesting fact is that the inequality (13) is now transformed in the “stable” state in new 

coordinates and does not depend on the mass: 

 

3

* 0 (0) ln

ln /

V A

S

C H H

C

 E

E E

 

7  

  T S 0

It is shown in Figure 3 with a solid diagonal line. 


Figure 3. The same distributions as in Fig. 2 but in new variables. Dashed lines describe the equal 

radiant zenith angles of meteoroids. 

3.4 Resultant Distribution Reducing 

The final tr n (23) consists in reducing it to the two-dimensional state by 

eans of integration over 0. The limits of the integration can be easily determined from Figure 3 and 

ansformation of the distributio

m

according formulae. We obtain the following

2 0

1 0

0 0 0 00 0

(, )

( , ) ( ) () (,, )

S

S

mH S m H S

m H

(, ) m H

p mH p m p p m H d E

E

E


 E EE " . (24) 

If we denote the integral, which has to be taken numerically, as 

02 0

01 0

(, )

0

0 0 2

(, ) 0

( ) (, ) ln ( / )

S

S

m H

S

m H S

p I mH d

E

E

E

E

E

E

E E 
 " , 

the final formula for the formation of the aerosol of space origin in the atmosphere can be written as 

2 *

0

00 0 * 1/3

0

2 exp( / ) (, ) () (, ) V S

mH S m S

C HH p mH p m ImH H m E

   
    

. (25) 

The function pmH(m0, HS) is shown in Figure 4. 

0 10 20 30 40 50 60 70 8

E, km/s

0

70

80

90

100

110

120

H, km

A

0 10 20 30 40 50 60 70 8

E, km/s

0

70

80

90

100

110

120 H, km

A

M

b

0

45

60

85

89

a

0

0

85

45

6 M


80 90 100 110 120 130

H, km

Figure 4. Final two-dim origin into Earth’s atmosphere. 10-

logarithm scale 

4 C

s it can be seen from the Figure 4 the minimal altitude which can be reachable by the aerosol stone 

e origin is approximately ~79.6 km. This value corresponds to the meteoroid which is 

ly with the velocity ~16.6 km/s. A particle of the same mass and with lower velocity will 

-14 -8

o

.E. Brownlee, P.W. Hodge Space Res., 13/2, 1139-1151 (1973). 

on. Astrophys., 263, 361-366 (1992). 

Meteoritics, 12, 3 – 14 (1955). 

ruchynenko V.G. Kin. And Phys. Nebesn. Tel, 18, 2, 114 – 127 (2002). 

2004). 

0). 

F. L. Whipple Proc. Nat. Acad. Sci. Amer., 37, 1, 19-29 (1951). 

ensional distribution of influx of aerosol of space 

onclusion 

A

particle of spac

moving vertical

stop higher, with higher velocity will transform into a meteor. 

 The meteoroids with the mass less or equal to ~1.7  10-14 g remain the aerosols always. For 

masses 10-14 / 10-8 g cumulative distribution coefficient k increases from 0.892 to 1.438 while the mass 

increases. 

 The Figure 4 also demonstrates that aerosols of mass range 10 / 10 g stop in relatively thin 

altitude range 80-120 km. Evidently, the aerosols do not stay at these altitudes forever but immediately 

start to m ve downwards under gravitational force and the resistance force of air, which can be 

described by Stokes formula. How it occurs is the goal for the future work. 

References 

D

Ceplecha Z. Astr

Fecenkov V.G. 

K

Kruchynenko V.G. Kin. And Phys. Nebesn. Tel, 20, 3, 269 – 282 (

B.Y. Levin Moscow: AN SSSR, 296 pp. (1956). 

V.N. Lebedinets Leningrad: Hidrometeoizdat, 250 pp. (198

V.N. Lebedinets Leningrad: Hidrometeoizdat, 272 pp. (1981). 

B. Nady Amsterdam - New York, 747 pp. (1975). 

E.J. pik Publ. Obs. Astr. Tartu, 29, 5, 67 (1937).

E.J. pik Irish Astron. J., 4, 3/4, 84-135 (1956). 

Y.I. Voloshchuk, B.L. Kashcheev, V.G. Kruchynenko Kyiv: N




F. L. Whipple Proc. Nat. Acad. Sci. Amer., 36, 12, 6

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

1E+1

-8

-9

-10

-11

-12

1E+2

1E+3

1E+4

1E+5 p(m,H)

-13

-14


Composition of LHB Comets and Their Influence on the Early Earth Atmosphere 

Composition 

C. Tornow1• S. Kupper1• M. Ilgner2• E. Kührt1• U. Motschmann1, 3

Abstract Two main processes were responsible for the composition of this atmosphere: chemical 

evolution of the volatile fraction of the accretion material forming the planet and the delivery of gasses 

to the planetary surface by impactors during the late heavy bombardment (LHB). The amount and 

composition of the volatile fraction influences the outgassing of the Earth mantle during the last 

planetary formation period. A very weakened form of outgassing activity can still be observed today by 

examining the composition of volcanic gasses. An enlightenment of the second process is based on the 

sparse records of the LHB impactors resulting from the composition of meteorites, observed cometary 

comas, and the impact material found on the Moon. However, for an assessment of the influence of the 

outgassing on the one hand and the LHB event on the other, one has to supplement the observations with 

numerical simulations of the formation of volatiles and their incorporation into the accretion material 

which is the precursors of planetary matter, comets and asteroids. These simulations are performed with 

a combined hydrodynamic-chemical model of the solar nebula (SN). We calculate the chemical 

composition of the gas and dust phase of the SN. From these data, we draw conclusions on the upper 

limits of the water content and the amount of carbon and nitrogen rich volatiles incorporated later into 

the accretion material. Knowing these limits we determine the portion of major gas compounds 

delivered during the LHB and compare it with the related quantities of the outgassed species. 

Keywords impacts · solar nebula · hydrodynamic · chemistry 

1 Fate of Volatiles During Planet Formation 

Table 1 shows that the major gasses (CO2, H2O, N2, O2) making 98-100% of the atmospheres of the 

three large rocky planets clearly vary in their concentrations. However, a completely different situation 

is observed for Mercury. Its atmosphere is incredible thin, contains relatively large hydrogen and helium 

concentrations, and, in addition to oxygen, one finds a high fraction of sodium (29%). Both, the amount 

of hydrogen and helium and the existence of a large Na fraction indicate a strong interaction between the 

planet and the solar wind. This strong interaction is supported by the small distance to the Sun which 

causes a high radiation intensity (see Table 1) as well. Compared to the small radius and mass of the 

planet, it has an outsized iron core (note, its high density in Table 1) which could have been the result of 

a large mantle-stripping impact (Benz et al., 1988). Since the pressure and chemical composition of 

 

C. Tornow ( )

1

• S. Kupper • E. Kührt • U. Motschmann

Inst. of Planetary Research, German Aerospace Research Center (DLR), Berlin. Phone: +493067689427; Fax: +493066055340: E-mail: 

carmen.tornow@dlr.de 

M. Ilgner 

Astrophysical Institute and Observatory, Friedrich Schiller University, Jena 

U. Motschmann 

Institute of Theoretical Physics, Technical University Braunschweig 


Mercury's atmosphere differ so largely from the corresponding values of the other planets, we 

concentrate our study to Earth and partially Mars and Venus. 

Table 1. Bulk, orbital and atmospheric parameter of the four rocky planets as observed today 

(http://nssdc.gsfc.nasa.gov/planetary/factsheet, Prinn & Fegley (1987), and). Note, that Mercury atmosphere 

additionally contains a large fraction of Na (29 %). The normalisation values used in column 1 are: R? = 6.37106

m, M? = 5.971024 kg, ? = 5.515 g/cm3

, L? = 1.37103 W/m2, 1 AU = 1.4961011 m, B? = 510-5 T, and 1 bar 

= 105

 Pa. 

Parameter Mercury Venus Earth Mars 

mean radius / R? 0.383 0.950 1.00 0.532 

mass / M? 0.0553 0.815 1.00 0.107 

mean density / ? 0.984 0.951 1.00 0.713 

solar irradiance / L? 6.67 1.91 1.00 0.431 

semi-major axis / AU 0.387 0.723 1.00 1.52 

magnetic field / B? ~10-2 < 10-5 1.00 - 

surface pressure / bar 10-15 92 1.014 6.3610-3

atmospheric 

composition 

with respect to 

major gasses in 

% 

CO2 - 96.5 0.038 95.3 

H2O - 210-4 ~ 1 310-4

N2 - 3.5 78.08 2.7 

O2 42 - 20.95 0.13 

H2 22 10-3 5.510-5 - 

atmospheric 

composition 

with respect to 

rare gasses in 

ppm 

4

He 6104 12 5.24 1.4 

20Ne - 7 18.2 2.5 

36Ar - 31 9.34104

 1.6104

84Kr - 0.025 1.14 0.3 

130Xe - < 0.009 0.09 0.08 

 

1.1 Planet Formation 

Two aspects influence the chemical composition of a planetary atmosphere, the formation process of the 

planet and the planetary evolution due to internal forces (e.g. magnetic fields, volcanism, plate motion, 

erosion, evolution of life) and external phenomenons (e.g. solar wind, impacts). The formation process 

needs to be considered since it has influenced the amount and composition of the volatile fraction of the 

accretion material. This fraction was produced by hydrides and oxides of N and C bearing molecules in 

the SN. Its amount and composition depend on the formation time of the planet and the distance to the 

protosun. The evolution effect is characterised on the one hand by relatively short and powerful events 


(e.g. impacts or volcanism) and on the other hand by continuous processes with a low immediate 

influence (e.g. magnetic fields or solar wind). 

 The influence of Earth evolution on the fractional abundances of the major gasses in the 

atmosphere is shown in Figure 1. Due to the sparse records not much is known about the Hadean eon 

(4.6-3.810-9 years) which also comprises planet formation. However, in order to understand where the 

carbon dioxide, water, and nitrogen content of the early atmosphere was coming from, one has to 

consider the scenario of inner planet formation in detail. It is based on core accretion and can be divided 

into four periods: 

 pebble formation (> 1 mm) by dust coagulation and settlement into disk midplane with a ~ 104 y 

timescale, 

 planetesimal formation (> 102 km) due to gravitational collapse of pebble clusters formed in 

various turbulence producing instability regions with a 103

 - 104 y timescale, 

 protoplanet formation (102-103 km) by gravitational cleaning of related feeding zones with a 105 - 

106 y timescale and in two phases, which are 

o a runaway accretion phase with a relative growth rate given by dM/Mdt ~ M 1/3, and 

o an oligarchic accretion phase with a relative growth rate given by dM/Mdt ~ M -1/3

 planet formation (104 km) by chaotic accretion due to giant impact events causing mergers of 

protoplanets (e.g. Moon forming impact) with a time-scale between 107

 and 108 years. 

 Concerning the first two phases, it was shown by Johansen et al. (2007), Lyra et al. (2008), and 

Brauer et al. (2008) that the planetary embryos with a radius larger than 103 km could have been formed 

after a period of coagulation and settling. Planetesimal formation causes a mainly a physical 

modification of the accretion material. If one compares porosity values observed for cometary dust PCD

~ 0.85 (Greenberg & Li, 1999) with porosities of the C-and D-type asteroids (0.5 - 0.6) (TrigoRodriguez & Blum, 2009) one realises the increased compactification due to collisions. This fits 

perfectly to observations of enstatite chondrites (Macke et al., 2009) coming from large solid bodies 

which are highly compactified (porosity F 0.06). In addition to compactification protoplanet and planet 

formation leads to chemical modification resulting in an increase of insoluble organic matter and a 

decrease of the soluble fraction. This modification results in an increase of carbonaceous matter and a 

decrease of H and N containing molecules. 

Figure 1. Concentration in percentage, C, shown for the major atmospheric gasses of the Earth versus time in Gyr (1 Gyr = 

108

 years) whereby today is set to 0 Gyr (data except for NH3 are from Kasting, 2004 and Kaltenegger et al., 2007). Note, 

that the time is logarithmically scaled and the concentrations of the reducing molecules CH4 and NH3 are given in 100% 

C(CH4) and 100% C(NH3), respectively. 


 In the simulations of O'Brien et al. (2006) a mixture of protoplanets with Mars-like masses and 

many large planetesimals is assumed to be the initial population of the accretion of rocky planets. This 

assumption agrees with the products of runaway and oligarchic accretion and describes the final, chaotic 

period of accretion. The chaotic period explains why the volatile concentration of the Earth does not 

agree with an equilibrium condensate formed at the pressure and temperature in the SN at 1 AU (Prinn 

& Fegley, 1987). In this period one has to take into account an outgassing of the planetary mantle of the 

three planets. 

 There is much evidence that water and CO2 are typical substances outgassed from the mantle. 

According to Matsui (1993), Zahnle (1998) and references therein during the chaotic accretion period a 

magma ocean (depth: ~ 2000 km) with a steam atmosphere of 7100 bar and a surface temperature of ~ 

1500 K has been formed on Earth. In the course of 5107

 years (Elkins-Tanton, 2008) the surface has 

cooled enough to allow the formation of a proto-ocean. According to model results (Kuramoto & 

Matsui, 1993, Elkins-Tanton, 2008) a local magma ocean could have been formed for Mars as well, but 

the ocean must have been more shallow in order to form a wet mantle and allow water outgassing. In 

contrast, due to the more intensive solar radiation on Venus (see Table 1) a hydrosphere was probably 

not formed on this planet (Abe, 1988). 

1.2 Water 

Now, we have to ask for the sources of water, carbon dioxide, and nitrogen which are contained in the 

early atmosphere (Figure 1). At first, there are indications that the planetesimals contained water 

gathered by physisorption and chemisorption (Stimpfl et al., 2006). The high adsorption energy of 

chemisorption found for forsterite ensures that water is held by the mineral surface at environmental 

temperatures of 700 K -1000 K. These values are typical for the inner region of the SN. Consequently 

water could have contained already in protoplanets formed in the inner SN. According to Morbidelli et 

al. (2000) during chaotic accretion a further reservoirs results from the outer asteroid belt. The parent 

bodies of carbonaceous chondrites and, if their number was large, main belt comets (Hsieh and David 

Jewitt, 2006) could have contributed to a large fraction of water. Observations have shown that D/H 

ratio of these bodies (~ 1.310-4; Kerridge, 1985) is comparable to D/HSMOW = 1.5610-4, whereby 

SMOW stands for standard mean ocean water. 

1.3 Carbon 

In the inner region of the SN carbon is contained in the dust grains since main components are SiC 

compounds and refractive organic matter (e.g. kerogen-like substances). In addition large amounts of 

carbon is stored in polycyclic aromatic hydrocarbons (PAHs) which are nano-size particles collected by 

the larger dust grains during their settling to the midplane (Zubko et al., 2004). In the outer region of the 

SN, i.e., behind the snow line, carbon bearing molecules were incorporated in the ice mantle of dust 

grain or later as CH4 clathrates in pebble clusters (Lunine & Stevenson, 1985). 

1.4 Nitrogen 

The sources of nitrogen are less known. It is very likely that the SN has contained N2, but observations 

(Armitage et al., 2003; Sicilia-Aguilar et al., 2007) suggest that the gas of the nebula was blown away 

after less than 10 Ma, depending on the frequency range and intensity of the stellar UV radiation in the 

environment of the SN. A protoplanet, which can be formed in 105

 to 106 years, has gathered enough 


mass to keep the SN gas as a primary atmosphere. According to the calculations of Genda & Abe (2003) 

in which the Moon forming impact was considered, it is likely that the Earth was able to keep at least 70 

% of its primary atmosphere. In addition, an N-bearing substance (Si3N4) was found in ordinary 

chondrites (Lee et al., 1995). Clément et al. (2005) have detected features in the infrared spectrum of 

carbon stars which coincide well with the main features of laboratory Si3N4 spectra. Consequently, these 

nitrides are of interstellar origin. Further, N2 could have been added to the Earth atmosphere during the 

LHB. We will consider this possibility in more detail in section 3. 

2 Atmospheric Composition After Earth Formation 

Due to the formation of life on Earth the current atmospheric composition differs clearly from the 

composition directly after the formation of the planet. In order to understand the influence of the LHB 

comets on the early Earth atmosphere we need a solidified assumption concerning the composition 

directly after planet formation as a starting point. According to the reflections in the previous section the 

atmosphere of the rocky planets contained as major gases CO2 and N2. Table 1 shows that for Mars and 

Venus the carbon dioxide fraction is large (95 - 96%) while the nitrogen fraction is relatively small (3 -

4%). The water fraction disappeared on both planets. Mars has lost its water due to the disappearance of 

its magnetic field. Thus, in addition to thermal ejection the solar wind could have stripped away its 

atmosphere. The surface cooling and pressure decreasing have given a situation in which water ice 

sublimated and due to the solar UV radiation the molecule dissociated. H2 has left the planet and O has 

oxidised minerals on the planetary surface. However, a part of the water ice has survived and is probably 

buried under the dust. Concerning Venus, it was already mentioned that no hydrosphere was formed due 

to the high temperature. Similar to Mars, Venus has presumably no magnetic field and the water vapour 

molecules have been dissociated by the strong solar UV radiation. In contrast to Mars, Venus has lost 

large amounts of hydrogen and oxygen by nonthermal processes such as ion pick-up (Lammer et al., 

2006). If one assumes no large differences in the chemical composition of the accretion material and 

compares the current D/H ratios (Lammer et al., 2008) of Earth (1.510-4), Mars (8.110-4), and Venus 

(210-2) it follows that the loss of H2O molecules on Earth was least important. 

 If one constructs an atmospheric composition of the early Earth we take a CO2/N2 ratio as 

observed for today for Mars and Venus. As a result, 78% N2 of the Earth atmosphere today correspond 

to 3-5 % N2 for the early case. The resulting early pressure varies between 15-26 bar produced by a CO2

atmosphere. Is the related amount of carbon available on Earth? Table 2 presents the current mixing 

ratios for the most important volatiles at the time directly after planet formation. We see, that on Venus 

nearly the complete amount of carbon dioxide, nitrogen, and water are contained in the atmosphere. On 

Mars and Earth this is true for nitrogen only. A large amount of CO2 on Earth and Mars is in a 

condensed phase. On Mars we have CO2 ice and on Earth the equilibrium reaction 

Mg2SiO4 + 4CO2 + 4H2O 2Mg2+ + 4HCO3



 + H4SiO4

which describes weathering via hydrolysis and carbon dioxide dissolution in water, controls the amount 

of carbon in the condensed and gaseous phase. The mineral Mg2SiO4 symbolises olivine, i.e. forsterite, 

HCO3



 denotes a bicarbonate ion, and H4SiO4 is silicic acid. Other, more complex, weathering reactions 

are possible as well, for instance with feldspar (KAlSi3O8). According to Pidwirny (2006) there are 7-

101022 g carbon dioxide available on Earth and the resulting pressure ~ 20 bar. From Table 2 one 

realizes a much larger amount of water (Lide, 2001) which is given by 1.41024 g which would produce 


a pressure of ~ 290 bar. This is close to the upper limit of the calculations of Zahnle, 1998. However an 

outflow during the phase of magma ocean and steam atmosphere as well as a large water component 

stored in the planetary mantle cannot be excluded. As the surface has cooled down sufficiently a shallow 

oceans formed about 4.410-9 years ago (compare with Wilde et al., 2001). The CO2 and water amounts 

fit well to the data given in Table 2. 

Table 2. Global mass fraction of volatile substances stored in the bulk planet and in the atmosphere today. The 

masses of the planets follow from Table 1. The data are given in Goody & Walker (1972). 

Substance Site Venus Earth Mars 

carbon 

dioxide 

bulk planet 1.210-4 1.810-5 3.110-6

atmosphere 8.710-5 4.410-10 3.010-8

nitrogen bulk planet 1.510-6 1.210-6 2.010-10

atmosphere 1.110-6 5.810-7 1.710-10

water 

bulk planet 2.010-9 2.310-4 3.910-6

atmosphere 1.610-9 2.510-9 2.210-12

Finally we have to consider the different types of accretion material. Based on equilibrium calculations 

and for an atmospheric state derived from an impact atmosphere (Abe & Matsui, 1987) a gas 

composition is determined by Schaefer & Fegley (2010). The obtained data important to evaluate our 

assumed atmospheric composition are shown in Table 3 for four different chondrite types (CI, CM are 

carbonaceous chondrites with very pristine material, L is an ordinary chondrite with a low amount of 

oxidized iron, and EH is an enstatite chondrite with a high amount of iron and non-oxidized iron). 

The most pristine material is fond for carbonaceous chondrites of the type CI while the CM chondrites 

experienced an extensive aqueous alteration. L and EH chondrites contain reducing material and CI and 

CM produce a neutral composition. For our evaluation we use the CO2/N2 ratio, which is given for an 

early atmosphere by a value ranging between 15-32. A composition of CM and L chondrites produces 

nearly the same range: 15-33. The same order of agreement was not reached for the ratio H2O/CO2 which 

gives ~ 15 for the early atmosphere and 3-5 for CM and L chondrites. We have not used the EH values 

since in this case the agreement to early Earth rations becomes worse. 

Table 3. Gas compositions of impact generated atmospheres from chondritic planetesimals at 1500 K and 100 bars. 

substance CI CM L EL 

H2O 69.47 73.38 17.43 5.71 

CO2 19.39 18.66 5.08 9.91 

N2 0.82 0.57 0.33 1.85 

H2 4.36 2.72 42.99 14.87 

CO 3.15 1.79 32.51 67.00 

H2S 2.47 2.32 0.61 0.18 

 Now we have determined an early chemical composition and found that the early atmosphere 

was mainly neutral. However for the formation of life one needs a more reducing environment. Since 

SN chemistry is hydrogen chemistry the LHB comets could have a more reducing influence. Thus, the 

retention of the primary atmosphere and the delivery of volatile molecules by LHB comets will increase 


the reducing character of the Earth atmosphere and improve the chances of life formation. Observations 

from Schopf (1993) and Brazier et al. (2002) have shown that life on the Earth probably formed 

somewhere around 3.5109 years or perhaps even earlier (Mojzsis et al., 1996; van Zuilen et al., 2002; 

Cate & Mojzsis, 2006). Unfortunately, there is not much evidence left from this time to describe the 

geological state of the planet and the thermodynamic one of its atmosphere. 

3 Calculation of Nitrogen Bearing Molecules in SN 

We simulate chemical processes in each of the three evolution periods considered in our solar nebula 

model. We discriminate between 

a quasi-static prestellar core, 

a collapsing protostellar core, and 

an evolving turbulent disk. 

Our purpose is to identify chemical species that were incorporated into comets in a sufficiently large 

number. Especially, we have made great efforts in order to derive a realistic and compact hydrodynamic 

models to describe the evolutionary periods of the solar nebula. 

Table 4. The three phases of the multi-zone solar nebula model. 

 

 

 dark cloud with quasi-static collapsing protostellar core evolving turbulent disk with 

 prestellar cores protosun 

3.1 Quasi-static Prestellar Core 

The quasi-static evolution of a prestellar core is modelled with a linear time dependency of the 

temperature and density. Systematic flow processes are not considered. The negligence of flows and 

unsteady evolution events such as shock waves or cloud collisions is justified since the temperature and 

density of the cloud core change over the large time interval of nearly 15 million years. The relative 

abundances of species i in the gas and ice phase xi and xi

*

, respectively, are calculated from a set of 

kinetic equations. The rates for the chemical reactions are computed from data of Woodall et al. (2007) 

and Aikawa et al. (1997). 

Table 5 contains the initial abundances. We have restricted our set of species to compounds 

having no more than seven atoms. From the calculated abundance evolution we obtain the time 

dependence of the ratios shown in Figure 2. One recognises an increasing amount of non-polar ice and 


bounded heavy isotopes in the course of the prestellar core evolution. A large H2 to H ratio seems to be 

advantageous for the formation of CO2 relative to H2O. 

Table 5. Initial abundances relative to hydrogen abundance. 

H H2 D He O C+ N Si 

0.9 0.1 1.510-5 0.14 1.810-4 7.310-5 2.110-5 6.010-11

Figure 2. Time dependency of the nitrogen isotope ratio in the gas phase (note the factor of 50 to present all curves 

in the same figure), the D/H ratios in the ice phase and the CO2/H2O ratio for the polar to non-polar ice fraction 

calculated for the slowly evolving quasi-stationary prestellar core. 

3.2 Collapsing Protostellar Core 

The gravitational collapse of a cloud core causes the central density to increase over more than 15-16 

orders of magnitudes. At the end of this process a stellar core, the T Tauri star, and a young disk have 

formed in the centre of the solar nebula. Therefore, a numeric simulation of this type of collapse is a 

complex task. 

 We have derived an analytical solution to solve the continuity, momentum and Poisson equation 

for a collapsing cloud core in four radial zones using spherical symmetry. According to Saigo et al. 

(2008) the spherical symmetry has no serious drawbacks as long as the rotation rate is low 10-15 s-1. The 

mathematics of this solution will be described in a different publication. In Figure 3 we present the 

calculated radial density, mass, velocity, and temperature profiles at different times. In order to include 

the influence of the formed protostellar disk we have coupled our collapse solution to the disk model 

derived by Stahler et al. (1994). 

The values of the four radial profiles in Figure 3 are given for an Eulerian grid. However, the 

computation of the chemical abundance evolution of the gas and ice phase following from the continuity 

equation of each species can be simplified if one uses a transformation to a Lagrangian grid defined by 

the initial positions of the gas-ice parcels at the beginning of the collapse. The resulting total time 

dependencies of the density and temperature are calculated for an inner gas parcel moving from 2.5 to 

1.3 AU. In this case the temperatures are high enough to guarantee the loss of the ice phase due to the 


evaporation of the icy grain mantles. In order to study the temporal progress of depletion of the ice 

phase species we have computed the ratio of the current to the initial abundance for selected compounds. 

The obtained values are presented in Figure 4. 

Figure 3. Radial profiles of density, mass, mass flow, and temperature for selected time points calculated with our 

analytical multi-zone model of the solar nebula. The vertical dotted lines in the left plots show the distribution of the 

zones at the beginning (upper plot) and at the end of the collapse period (lower plot). 

Figure 4. Time dependency of the ratio of the current to the initial abundance for CO, H2O, and NH3 calculated for 

the period of the collapsing protostellar core. 


3.3 Evolving Turbulent Disk

The disk model of Stahler et al. (1994), is valid for a young disk only. In order to study the chemical 

evolution of the gas and ice species in a mature disk we have used the non-stationary model of Davis 

(2003). This model describes the disk cooling and depletion in the course of its evolution. Due to the gas 

flow we have to switch to the Lagrangian grid again in order to compute the abundance values. The 

necessary initial data follow from the final abundance results calculated for the collapse period. In 

contrast to our collapse model the Davis model is based on axial symmetry. In order to keep a simple 

radial dependency without angular variations, the relative abundances are derived with respect to the 

column density. For time intervals much larger than 107

 the corresponding number density would be less 

then 0.01 cm-3, i.e. a gas disk is not existent anymore. Therefore, at most 10 million years are of physical 

interest only. Figure 5 shows the time behaviour of the same ice ratios as seen in Figure 2. However, one 

recognizes clear differences although in both cases the ice phase abundancies are growing with respect 

of their initial values. For the evolving disk, there is a superposition of the time dynamics of the disk

parameter itself and the time dynamics of the chemical processes. Thus, the shapes of the disk related 

abundance ratios versus time are less monotonic than the same curves of the prestellar core. Further, 

disk density of the considered gas parcel decreases whereas core density increases slowly. 

 

Figure 5. Time dependency of the D/H ratios in the ice phase and the CO2-H2O molecular ratio for the polar to nonpolar ice fraction calculated for the evolving disk. 

4 Conclusion and Outlook 

We have motivated the assumption that the ratio of CO2/N2 was nearly similar (i.e. ~ 15) for the 

atmospheres of Earth, Mars, and Venus directly after planet formation. In order to calculate the 

primarily reducing contribution of LHB comets to the Earth atmosphere we have combined a 

hydrodynamical model of the SN with a kinetic model to simulate the chemical evolution. Especially we 

have developed an analytical solution for the collapse period that gives the chance to simulate this 

process very efficiently. Both models, the hydrodynamic and the chemical, were thoroughly tested to 

guarantee the consistency of merging the evolution periods of the solar nebula using the transition from 

an Eulerian to a Lagrangian grid. However, the transition from the spherically collapsing cloud core to 


the disk is complicated and further research needs to be done for the transition between the different 

temperature models. 

From chemical calculations a distinct difference between disk and prestellar core chemistry 

becomes conspicuously. It is related to the higher dynamics in the disk on the one hand and to its 

complex initial chemical state on the other. The effects of both phenomenons are entangled and further 

research needs to be done to investigate their influence independently. Figure 6 allows to estimate the 

amount of nitrogen bearing molecules. According to Gomes et al. (2005) nearly 1022 g of material from 

LHB comets have reached the Earth surface. The ice formed by soluble matter amounts 25 - 33%. Thus 

one gets 2.51021 g and the corresponding N amount is not more than 1 - 5 % giving 7 2.51019 g (see 

indications in Figure 6). If we compare this contribution with the current mass of the biosphere (1019 g). 

Consequently, the LHB comets might have delivered an amount of reducing and soluble material 

important for life formation in a otherwise neutral atmosphere. In a next study we will calculate the 

amount of reducing gasses from the SN retained by the Earth during its formation process. 

Figure 6. Abundance ratios versus time in years. The evolution of the three major nitrogen bearing molecules in the 

ice phase of the solar nebula is illustrated, whereby "CN" stands for the abundance of HCN + HC3N. 

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Modeling the Entry of Micrometeoroids into the Atmospheres of Earth-like Planets 

A. R. Pevyhouse1• M. E. Kress1

Abstract The temperature profiles of micrometeors entering the atmospheres of Earth-like planets are 

calculated to determine the altitude at which exogenous organic compounds may be released. Previous 

experiments have shown that flash-heated micrometeorite analogs release organic compounds at 

temperatures from roughly 500 to 1000 K [1]. The altitude of release is of great importance because it 

determines the fate of the compound. Organic compounds that are released deeper in the atmosphere are 

more likely to rapidly mix to lower altitudes where they can accumulate to higher abundances or form 

more complex molecules and/or aerosols. Variables that are explored here are particle size, entry angle, 

atmospheric density profiles, spectral type of the parent star, and planet mass. The problem reduces to 

these questions: (1) How much atmosphere does the particle pass through by the time it is heated to 500 

K? (2) Is the atmosphere above sufficient to attenuate stellar UV such that the mixing timescale is 

shorter than the photochemical timescale for a particular compound? We present preliminary results that 

the effect of the planetary and particle parameters have on the altitude of organic release. 

Keywords atmospheric entry · micrometeor · modeling · organic chemistry 

1 Introduction 

Micrometeorites 200 μm in diameter carry most of the incoming mass to the modern Earth, 

approximately 30 million kg annually [2]. Love and Brownlee (1991) [3] found that micrometeors in 

this size range experience severe heating upon atmospheric entry. Peak heating occurs at an altitude of > 

85 km within seconds of atmospheric entry, typically to temperatures in excess of 1600 K, sufficient to 

melt silicate and metals [3]. 

 Recent experiments have simulated the flash-heating experienced by micrometeors upon 

atmospheric entry [1], [4]. Both of these groups found that methane is released, and Kress et al. [1] also 

found that other light hydrocarbons and a variety of more complex organics are released at temperatures 

of  500 to 1000 K. In the current study, we identify the altitudes at which these temperatures are 

reached, which is an essential first step to determining the ultimate fate of these compounds. 

The influence that PAHs and methane could have on a planetary atmosphere depends on the 

altitude at which they are released from an incoming particle. The altitude at which a molecule is 

released determines its fate. Vertical mixing will bring a molecule deeper down into the atmosphere, 

where its photochemical lifetime is longer. The photochemical lifetime of a substance is the time it takes 

for destruction mechanisms to reduce its concentration to 1/e its original amount. The deeper in the 

atmosphere an organic compound is released, the greater the probability of it being vertically mixed. 

Methane, CH4, for example, will be broken into residual compounds by photolysis if released above 

Earth’s stratopause due to Lyman-alpha radiation (¶ = 121.6 nm). Methane also is destroyed at this 



A. R. Pevyhouse ( ) • M. E. Kress 

Department of Physics and Astronomy, San Jose State University, San Jose, CA 95192. Phone: 650-219-9502; E-mail: 

apevyhouse@santarosa.edu


altitude by reactions with O(1

D) and OH [5]. After several steps, these reactions will convert methane to 

CO2. However, if released at an altitude of 70 km or lower, methane has a long enough photochemical 

lifetime to allow mixing [5]. 

We first apply the atmospheric entry model to the Earth. We then extend this study to plausible 

Earth-like planets of different masses and atmospheric densities to identify the parameter space in which 

micrometeors release organics close to a planet’s surface. Varying planet mass was found to not result in 

organics being ablated under a greater portion of atmosphere. 

We find that, for the modern Earth, organics are typically released at an altitude such that the 

timescale for methane to mix lower into the atmosphere is very long compared to its photochemical 

destruction timescale at that altitude [5]. 

2 Modeling the Atmospheric Entry of Micrometeorites 

In this study, infalling micrometeorites were simulated numerically to generate temperature profiles for 

a variety of particle sizes and entry parameters. Entry parameters of interest were initial velocity and 

entry angle. The physics of atmospheric entry is that of Love and Brownlee (1991) [3]. 

Numerical modeling using an Euler algorithm was done to simulate atmospheric entry of 

micrometeorites. This model takes a continuous evaporation approach while the particle is treated as an 

isothermal sphere of density met = 3 g/cm3

. Incoming micrometeorites are heated due to collisions with 

atmospheric molecules. Particle temperature is determined by balancing the power imparted to it from 

atmospheric molecules, Pin, to the rate at which thermal energy is being dissipated by radiative and 

evaporative mechanisms, such that 

 

7  
ip"qhdgC

 

(1)

and 

 7

B

! D

e  j
i 3l1



(2)

where ! is the emissivity of the particle, T is the particle’s temperature, is the Stefan-Boltzmann 

constant, s is the particle’s geometric cross section, v is the particle’s velocity with respect to the 

atmosphere and atm is the density of the atmosphere (a function of altitude). The change in velocity due 

to atmospheric drag and gravity is 

g < m e_.(3)

We first reproduced the Love and Brownlee (1991) [3] results using the United States Standard 

Atmosphere of 1976 [6] as the atmospheric model. These calculations served as a benchmark for those 

for hypothetical earth-like planets, whose mass and surface atmospheric density were treated as free 

parameters, and whose atmospheric density was assigned a simple exponential decay law. 

To estimate the altitude at which organic compounds may be released in the atmospheres of 

hypothetical Earth-like planets, atmospheric pressure and planetary mass were treated as free 

parameters. The atmospheric density profiles for these worlds were approximated by assigning a simple 


exponential decay function. This exponential decay model treated the atmosphere as isothermal at a 

temperature of 288.15 K with a constant molecular weight of 28.97 g/mol. Using this atmospheric 

profile, the effect of varying a planet’s mass and atmospheric pressure on the altitude at which a 

micrometeorite first reaches 500 K was investigated. Results obtained for a world with 1 Earth mass and 

1 atm surface pressure were compared against the results obtained using the U.S. 1976 Standard 

Atmosphere [6]. 

3 Results 

The altitude at which volatile organic compounds are released is defined as the altitude range for which 

an incoming particle would be between 500 and 1000 K. 

 Results for a 1 Earth mass planet with 1 atm atmospheric pressure were compared to those of 

Love and Brownlee (1991) [3] who used the 1976 Standard Atmosphere as the atmospheric model. Use 

of an exponential decay function to model a planetary atmosphere consistently resulted in a higher 

calculated altitude of organic release compared to the altitude calculated using the U.S. 1976 Standard 

Atmosphere [6] (Figure 1). Heating rates also differed between the two atmospheric models. A 100 μm 

diameter particle entering at 80 deg and 20 km/s experienced a heating rate of 56 K/s under the 

exponential decay model compared to 43 K/s using the U.S. 1976 Standard Atmosphere [6]. Heating 

rates were determined between 500 to 1000 K. 

Figure 1. Comparison of results from the U.S. 1976 Standard Atmosphere [6] and exponential decay model for a 50 

μm diameter particle entering at 80 deg and 12 km/s. Top: Particle temperature as a function of altitude. Bottom: 

Particle temperature as a function of time. Note that the particle reached its peak temperature later when in the 

standard atmosphere compared to an atmosphere whose pressure is exponentially decaying. 


 Figure 2 shows the dependence of organic release altitude on planetary mass and atmospheric 

pressure. Planetary mass was shown to have a greater effect on the altitude of organic release compared 

to planetary surface pressure. A micrometeorite falling through the atmosphere of a planet with a mass 

of 0.1 Earth mass and 0.1 atm surface pressure first reached 500 K at an altitude of 345 km. Increasing 

atmospheric pressure to 10 atm increased this altitude to 494 km. The same difference in atmospheric 

surface pressure resulted in only an 11 km difference for a planet of 10 Earth masses. 

Figure 2. The altitude at which a 100 μm diameter particle first reaches 500 K as a function of planetary mass. The 

initial velocity of the particle is 12 km/s with an entry angle of 45°. Note the effect of increasing planetary mass on 

lowering the altitude at which a particle first reaches 500 K. 

4 Discussion 

Approximately 2 × 107 kg/yr of extraterrestrial material is deposited into Earth’s atmosphere each year. 

The amount of organic carbon deposited can be estimated to be 10% of this total [2]. The level of 

ablated micrometeoritic organic compounds in a planetary atmosphere is determined by the competing 

rates of material deposition and degradation. Degradation of organic molecules occurs by photolysis due 

to exposure to solar UV radiation and chemical reactions with atmospheric molecules. The rate of this 

degradation depends on the altitude at which these organic compounds are released. 

 Uncertainties in the determination of the altitude range volatile organics are released from 

incoming micrometeorites originate from four factors. 

 The first factor is the Love and Brownlee (1991) [3] model. It does not take into account that 

meteorites have more than one phase. Micrometeorites in this model are treated as generic silicates. 

Therefore, an organic phase that evaporates at lower temperatures compared to silicates is not taken into 

consideration. The limitation of this model comes from the physics of the micrometeorite being 

determined to the 90% level by the silicates that are present. In reality, the loss of organics and ice will 

keep the particle cooler for longer due to the energy used for the phase change of these components. 

This lower temperature will allow for the particle to reach a lower altitude before reaching 500 K. The 

use of the Love and Brownlee (1991) [3] should therefore be considered as providing a conservative 

estimate on the altitude at which organics are released from micrometeorites. 


 The atmospheric model used is the second factor. The size of micrometeorites makes them very 

sensitive to any changes in atmospheric density. The difference in results between the U.S. 1976 

Standard Atmosphere [6] and the Exponential Decay model makes the point that better representations 

of exoplanet atmospheres should be used. 

 The other two factors are the estimation of a heat transfer coefficient and lack of a rate equation 

for the release of volatile organics. A heat transfer coefficient will determine the percentage of input 

power that goes into heating the particle. A rate equation for the evaporation of organics determines 

were in the temperature range 500 to 1000 K organics are released. This is critical in determining the 

lower altitude boundary a particle will release organics. The need for an organic evaporation rate 

equation is discussed below. 

 The rate at which a particle is heated will determine the range of time organic compounds are 

released. Slow heating rates will give more time for volatile organics to be outgassed from a particle 

compared to quicker rates. Heating too quickly can result in organic compounds in the particle to be 

transformed to char before they are able to diffuse out of the particle. 

 A particle entering at 12 km/s and an angle of 0 deg was found to have a heating rate  300 K/s. 

The same 12 km/s particle entering at 80 deg had a reduced heating rate of  40 K/s. The heating rate of 

500 K/s used by Cody was higher than any rate found for particles with an initial velocity less than 20 

km/s. Such a high heating rate should be considered a worse case scenario of heating. Under such a high 

rate of heating, it is unknown if the volatile organics contained in a particle are all outgassed before 

being charred. 

 Further experiments on Murchison samples are needed to determine a rate equation for the 

evaporation of organic compounds. A rate equation will give insight into where in the temperature range 

of organic release organics are ablated. It is unknown if the majority of organics are released when a 

particle reaches 500 K, volatilization of organics is a continuous process over the entire temperature 

range of organic release, or if the majority of organics are ablated as the particle approaches 1000 K. 

4.1 Effect of Stellar Class on Lyman-alpha Exposure 

The further into a planetary atmosphere micrometeorites release organics, the greater the protection from 

lyman-alpha radiation. Lyman-alpha will degrade organic molecules on a time scale less than 

atmospheric vertical mixing times if released under too little atmosphere. The intensity of planetary 

exposure to Lyman-alpha depends on the temperature of a planet’s home star and its distance to it. The 

liquid water habitable zone (LW-HZ) is defined as the region in space around a star in which a planet 

would be able to maintain liquid water on its surface [7]. Figure 3 shows the continuum flux of Lymanalpha through the LW-HZ of F0, G2, and M0 stars as defined by Kasting et al. [7]. 

 M-stars comprise about 75% of all main-sequence stars. Their hydrogen burning lifetimes are 

much longer than G2V stars like our Sun. Comparison of the intensity of Lyman-alpha radiation 

between a G star and an inactive M dwarf indicates  10-7 reduction in Lyman-alpha intensity. This 

reduction in Lyman-alpha could slow the rate of rate of organic degradation in the atmosphere on an Mstar planet. However, too low a level of UV radiation has been thought to inhibit the biogenesis of 

complex macromolecules. The volatile UV output from M-star flares have been hypothesized to be 

needed for the synthesis of large complex macromolecules [8]. 

The spectral distribution of radiation incident on an M-star planet has been theorized to result in a 

thicker ozone layer compared to the Earth [9]. A broader ozone layer could increase the photochemical 

lifetime of ablated molecules.


Figure 3. Irradiance at the top of the atmosphere (TOA) of Lyman-alpha for M0, G2, and F0 stars. Irradiance values were 

calculated from Planck’s function. The range of habitable zone for each stellar class follows those published by Kasting et al. 

[7] 

 Another source of protection could come from the high probability of planets with the LW-HZ 

being tidally locked. Synchronous rotation does not necessarily mean atmospheric freeze out [10]. 

Therefore, the side of the planet always facing away from the star could provide a protected 

environment for ablated volatile organics. Future work should include modeling atmospheric mixing on 

tidally locked planets to investigate further the micrometeoritic contribution of volatile organics to these 

worlds. 

5 Conclusion 

For organic compounds to reach altitudes were exposure to UV radiation is low enough that it will not 

degrade, the compounds need to be either photochemically stable (e.g. PAHs) or the parent 

micrometeorite reaches 500-1000 K at lower altitudes. Although survival of methane in our modern 

atmosphere looks grim, that does not mean the release of organics in other atmospheres is not important. 

Smaller stars radiating less UV than our Sun may provide a longer time frame for ablated material to be 

vertically mixed into the atmosphere. At constant planetary density, increasing planet mass lowers the 

altitude 500 K and is first reached by an incoming particle but does not necessarily result in organic 

ablation occurring under a greater percentage of a planets atmosphere. 

 The need for atmospheric models of exoplanets was demonstrated in this study. Results differed 

by 35 km in altitude between the U.S. 1976 Standard Atmosphere [6] and exponential decay model 


atmosphere. This is due to the exponential decay model calculating a denser atmosphere compared to the 

U.S 1976 Standard Atmosphere [6] for altitudes above 100 km. This result was independent of entry 

angle for a 50 μm diameter particle entering at 12 km/s. 

 Progress into the micrometeoritic contribution of volatile organics to the atmosphere of planets 

and moons has been made in this study. Heating rates for further lab experiments have been clarified as 

well as the need to determine a rate equation for the release of volatile organics. Determination of an 

upper altitude for when a particle first reaches 500 K under a worst case scenario of heating has been 

made. Although progress has been made, further work needs to be done in three main areas: (1) 

determine a rate equation for the evaporation of organics under different rates of heating. (2) investigate 

the altitude range a particle first reaches 500 K while varying the heat transfer coefficient. (3) use the 

exponential model to simulate atmospheres with various combinations of atmospheric temperature and 

pressure that are favorable for liquid water to be present on a planetary surface. This will allow the study 

to be extended to a broader variety of exoplanets. 

Acknowledgements 

MEK and ARP acknowledge research support from the NASA Astrobiology Institute’s Virtual Planetary 

Laboratory (PI: V. Meadows). 

References 

1. M.E. Kress, C.L. Belle, G.C. Cody, A.R. Pevyhouse and L.T.Iraci, Atmospheric chemistry of micrometeoritic organic 

compounds, NASA Conference Proceedings from Meteoroids 2010, D. Janches, editor (2010) 

2. S.G. Love and D.E. Brownlee, A direct measurement of the terrestrial mass accretion rate of cosmic dust, Science, 262, 

550-552 (1993) 

3. S.G. Love and D.E. Brownlee, Heating and thermal transformation of micrometeoroids entering the earth’s atmosphere, 

Icarus, 89, 26-43 (1991) 

4. R.W. Court and M.A. Sephton, Investigating the contribution of methane produced by ablating micrometeorites to the 

atmosphere of Mars, Earth and Planetary Science Letters, 288, 382-385 (2009) 

5. G.P. Brasseur and S.Solomon, Aeronomy of the Middle Atmosphere, 3rd edn. D.Reidel Publishing Company (1984) 

6. R.A. Minzner, The 1976 Standard Atmosphere Above 86-km Altitude. NASA SP-398, NASA Special Publication, 398 

(1976) 

7. J.F. Kasting and D.P. Whitmire and R.T. Reynolds, Habitable Zones around Main Sequence Stars, Icarus, 101, 108-128 

(1993) 

8. A.P. Buccino and G.A. Lemarchand and P.J.D Mauas, UV habitable zones around M stars, Icarus, 192, 582-587 (2007) 

9. A. Segura and J.F. Kasting and V. Meadows and M. Cohen and J. Scalo and D.Crisp and R.A.H Butler and G. Tinetti, 

Biosignatures from Earth-Like Planets Around M Dwarfs, Astrobiology, 5, 706-725 (2005) 

10. M. Joshi, Climate Model Studies of Synchronously Rotating Planets, Astrobiology, 3, 415-427 (2003) 


A Numerical Study of Micrometeoroids Entering Titan’s Atmosphere 

M. Templeton1• M. E. Kress1

Abstract A study using numerical integration techniques has been performed to analyze the 

temperature profiles of micrometeors entering the atmosphere of Saturn’s moon Titan. Due to Titan’s 

low gravity and dense atmosphere, arriving meteoroids experience a significant “cushioning” effect 

compared to those entering the Earth’s atmosphere. Temperature profiles are presented as a function of 

time and altitude for a number of different meteoroid sizes and entry velocities, at an entry angle of 45°. 

Titan’s micrometeoroids require several minutes to reach peak heating (ranging from 200 to 1200 K), 

which occurs at an altitude of about 600 km. Gentle heating may allow for gradual evaporation of 

volatile components over a wide range of altitudes. Computer simulations have been performed using 

the Cassini/Huygens atmospheric data for Titan. 

Keywords micrometeoroid · Titan · atmosphere 

1 Introduction 

On Earth, incoming micrometeoroids (~100 μm diameter) are slowed by collisions with air molecules in 

a relatively compact atmosphere, resulting in extremely rapid deceleration and a short heating pulse, 

often accompanied by brilliant meteor displays. On Titan, lower gravity leads to an atmospheric scale 

height that is much larger than on Earth. Thus, deceleration of meteors is less rapid and these particles 

undergo more gradual heating. This study uses techniques similar to those used for Earth meteoroid 

studies [1], exchanging Earth’s planetary characteristics (e.g., mass and atmospheric profile) for those of 

Titan. Cassini/Huygens atmospheric data for Titan were obtained from the NASA Planetary 

Atmospheres Data Node [4]. 

 The objectives of this study were 1) to model atmospheric heating of meteoroids for a range of 

micrometeor entry velocities for Titan, 2) to determine peak heating temperatures and rates for 

micrometeoroids entering Titan’s atmosphere, and 3) to create a general simulation environment that can 

be extended to incorporate additional parameters and variables, including different atmospheric, 

meteoroid and planetary data. 

 The micrometeoroid entry simulations made using Titan atmospheric data assume that, as on 

Earth, micrometeors are heated by collision with molecules in the atmosphere. Unlike on Earth where 

heating pulses last a few seconds and reach temperatures sufficient to melt silicates (> 1600 K [1]), 

micrometeors on Titan experience a more gradual thermal exchange lasting several minutes and the 

particles do not reach such high temperatures. The long duration of this gradual heating and cooling may 

allow ices and volatile organic species (such as small PAHs) to be evaporated throughout Titan’s upper 

atmosphere. 



M. Templeton ( ) • M. E. Kress 

Dept. of Physics & Astronomy, San José State University, San José, CA 95192-0106. Phone: +1-408-924-5255; E-mail: 

templeton100@gmail.com 


2 Atmospheric Entry Model 

The method used in these simulations is that of Love & Brownlee [1] for micrometeoroids entering 

Earth’s atmosphere. Meteoroids are assumed to be spherical and of uniform composition and density, 

met = 3 g/cm3, with a starting radius r of 100 μm and an entry angle of 45°. g is the acceleration due to 

gravity for Titan, 1.352 m/s2

. A full two-dimensional simulation is performed to correctly account for 

Titan’s curvature. 

 The change in velocity due to atmospheric drag and gravity is 

e  
i p"qhg

ph4q

g <  e_

7  
ip"qhdgC

   7

B

(1)

where atm is the local density of Titan’s atmosphere calculated from the Huygens probe’s pressure and 

temperature data and v represents the velocity of the meteoroid with respect to the atmosphere. Heating 

of meteoroids is due to the impacts with atmospheric molecules, in this case primarily nitrogen and 

methane. The rate of energy transfer, Pin, to the meteoroid is described by: 

(2)

where s is the geometric cross section of the meteoroid under study. The temperature T of the particle is 

determined by a balance of frictional heating and radiative cooling: 



! D

Fi mission [4] 

(3)

where is the Stefan-Boltzman constant and ! is the meteoroid’s emissivity. 

 Atmospheric data were obtained from NASA’s Planetary Data System Atmospheres Node 

website. The data set id is HP-SSA-HASI-2-3-4-MISSION-V1.1 [4]. Figure 1 shows a plot of 

atmospheric temperature versus altitude for the combined Huygens data set. 

gure 1. Temperature prole of Titan’s atmosphere from the Cassini Huygens


3 Results 

 this analysis, the only parameter that is varied is the entry velocity of the micrometeoroid. Figure 2 

Figure 2. Micrometeoroid temperature as a function of altitude for entry velocities of 1 to 15 km . 

The evaporation of meteoroid material due to heating was modeled by the Langmuir formula 

 heating at 

 Discussion 

eteors decelerate once they have encountered roughly their own mass of atmospheric molecules. 

In

shows altitude versus temperature for meteoroid entry velocities from 1 to 15 km/s, chosen to span the 

range from Titan’s escape velocity (2.6 km/s) and orbital velocity (5.6 km/s) to Saturn’s orbital velocity 

(9.7 km/s). 

/s

The curve that peaks at the highest temperature is 15 km/s. 

using a variety of values for the vapor pressure as have been used in other meteor evaporation studies 

[3]. Varying the vapor pressure value over this range did not significantly alter these results. 

 This result agrees well with previous studies [2] in that the micrometeors reach peak

approximately 600 km, and are heated over a timescale of minutes. The slowest particles (1 km/s) only 

reach a temperature of about 200 K, whereas the fastest particles (15 km/s) are heated to 1200 K. 

4

M

Compared to Earth [1], micrometeors entering Titan’s atmosphere will experience significantly less 

severe heating, because Titan’s gravity is only ~ 14% that of Earth. Titan’s atmospheric scale height is 

thus larger than Earth’s, making it a more diffuse medium through which to decelerate and allowing for 

more time to radiate away the frictional heat of atmospheric entry. 


Figure 3. Micrometeoroid temperature as a function of time for entry velocities of 1 t km/s. The curve that 

peaks at 200 K and ~ 12 minutes is that for 1 km/s and the curve that peaks at ~ 1200 K at 2 minutes is for 15 km/s. 

/s micrometeor of 100μm diameter and 45° entry angle will reach a peak temperature of 

800 K after 13 seconds [1]. By comparison, the same micrometeor entering Titan’s atmosphere will not 

he assumptions made 

ere as

 Conclusions 

ity and large scale height means that micrometeors undergo relatively slow heating and 

ooling compared to those entering Earth’s atmosphere. Molecules liberated from meteoroids during 

1000 K [5]. 

milar

o 15

 A 12 km

1

exceed 1000 K and will require about two minutes to reach its peak temperature. 

 Detailed knowledge regarding ranges of input velocities, size distribution, average composition, 

etc. is incomplete for meteor sources in the neighborhood of the outer planets. T

h sume similarity to the situation observed in our part of the solar system. If meteoritic material in 

the area of the outer planets is more cometary in origin with a higher percentage of water ice, then a 

lower meteoroid density and a modified entry velocity range may be more appropriate. The specific 

heats of vaporization and melting are very different for water ice compared to that used in Earth-based 

meteor studies [1]. This difference will keep the particle’s temperature lower since energy is more 

efficiently partitioned into melting and evaporation. The slowest micrometeors may possibly retain some 

water ice, while the fastest will likely lose all of the ices and most of their organic compounds. 

5

Titan’s low grav

c

their descent will likely be able to participate in photochemical and heteorgeneous reactions 

 Recent experiments have shown that flash-heated CM chondrite micrometeorites will evolve 

organic compounds, including PAHs and light hydrocarbons, at temperatures from 500 to 

Si experiments should be conducted at slower heating rates to observe what organic compounds 


may be released under the more gentle heating expected in Titan’s atmosphere. These compounds can be 

incorporated into chemical models for Titan’s atmosphere. In particular, micrometeorites may be involved in the presence of oxygen-bearing compounds and also small polycyclic aromatic hydrocarbons 

in Titan’s atmosphere. 

Acknowledgements 

research support from the NASA Astrobiology Institute’s Virtual Planetary 

aboratory (PI: V. Meadows). 

eferences 

and D.E. Brownlee, Heating and thermal transformations of micrometeoroids entering Earth’s atmosphere. 

-43 (1991) 

try of micrometeoritic organic 

MEK acknowledges 

L

R

1. S.G. Love 

Icarus 89, 26

2. S.G. Love and D.E. Brownlee, Heating and thermal transformations of micrometeoroids entering Earth’s atmosphere. 

Icarus 89, 26-43 (1991) 

3. E.J. Öpik, Physics of Meteor Flight in the Atmosphere. Wiley-Interscience, Hoboken, NJ 

4. NASA Planetary Atmospheres Data Node, Data Set ID: HP-SSA-HASI-2-3-4-MISSION¬V1.1 (2006) 

5. M.E. Kress, C.L. Belle, G.C. Cody, A.R. Pevyhouse and L.T.Iraci, Atmospheric chemis

compounds, NASA Conference Proceedings from Meteoroids 2010, D. Janches, editor (2010) 


Global Variation of Meteor Trail Plasma Turbulence 

L. P. Dyrud1• J. Hinrichs2• J. Urbina2 

Abstract We present the first global simulations on the occurrence of meteor trail plasma irregularities. 

These results seek to answer the following questions: when a meteoroid disintegrates in the atmosphere 

will the resulting trail become plasma turbulent, what are the factors influencing the development of 

turbulence, and how do they vary on a global scale. Understanding meteor trail plasma turbulence is 

important because turbulent meteor trails are visible as non-specular trails to coherent radars, and 

turbulence influences the evolution of specular radar meteor trails, particularly regarding the inference 

of mesospheric temperatures from trail diffusion rates, and their usage for meteor burst communication. 

We provide evidence of the significant effect that neutral atmospheric winds and density, and 

ionospheric plasma density have on the variability of meteor trail evolution and the observation of nonspecular meteor trails, and demonstrate that trails are far less likely to become and remain turbulent in 

daylight, explaining several observational trends using non-specular and specular meteor trails.

Keywords meteor trail · plasma· turbulence · simulation 

1 Introduction 

The daily occurrence of billions of meteor trails in the Earth’s upper atmosphere presents a powerful 

opportunity to use remote sensing tools to better understand the meteoroids that produced them, and the 

atmosphere and ionosphere in which their trails occur. One of the most promising tools employed in 

this endeavor are high-power-large-aperture (HPLA) radars. Such radars routinely observe two distinct 

types of meteor echoes, head echoes and non-specular meteor trails. Head echoes are the radar 

reflection from targets with short durations, usually less than 1 millisecond at a given range, and moving 

at apparent meteoroid velocities [Close et al., 2002; Janches et al., 2000; Mathews et al., 2001, Janches 

et al. 2008, Chau and Galindo, 2008, Dyrud et al.. 2008]. When radars are pointed perpendicular to the 

magnetic field, head echoes are often, but not always, followed by echoes lasting seconds to minutes 

[Dyrud et al., 2005; Zhou et al., 2001, Malhotra et al., 2007]. Because these echoes occur 

simultaneously over multiple radar range gates, the term non-specular echoes has been adopted by many 

authors in order to differentiate them from the meteor echoes from specular meteor radars, which require 

a trail to align perpendicular to the radar beam [Ceplecha et al., 1998; Cervera and Elford, 2004]. It is 

now understood that non-specular trails are reflections from plasma instability generated field aligned 

irregularities (FAI) [Chapin and Kudeki, 1994a, Oppenheim et al., 2000, Zhou et al., 2001, Dyrud et al., 

2001, Dyrud et al., 2002, Dyrud et al., 2007, Close et al., 2008]. However, the influence that turbulent 

trails has on specular observations of meteor trails has only been briefly studied [Hocking, 2004, 

 

L. P. Dyrud ( ) 

Communications and Space, Sciences Laboratory, Pennsylvania State University, University Park, PA, USA. E-mail: 

Lars.Dyrud@jhuapl.edu 

J. Hinrichs • J. Urbina 

Applied Physics Laboratory, John Hopkins University, Columbia, MD, USA


Galigan et al., 2004], and we do not yet understand the degree to which meteor trails are inherently 

plasma unstable. This paper seeks to address some of these unknowns. 

 We focus on the role that neutral atmospheric wind and density, and ionospheric plasma density 

has on the development of meteor trail turbulence and evolution. Our goal is to understand how 

regional, diurnal and seasonal variability in these background parameters will influence the role that 

plasma turbulent meteor trails has on various applications and scientific studies. Most prominently, 

turbulent trails are thought to have a diffusion rate that can exceed the nominal cross-field ambipolar 

diffusion rate by up to an order of magnitude, significantly altering trail evolution, duration and 

reflectability [Dyrud et al., 2001]. The effects of this turbulent evolution are important for specular 

radar derivations of diffusion rate and therefore neutral temperature ("#) [Hocking et al., 1999, Kumar, 

2007], meteor burst communication [Fukuda et al., 2003], and scientific studies involving non-specular 

trail observations in general [Dyrud et al., 2005, 2007, Malhotra et al., 2007]. 

In order to understand the global variation of meteor trail turbulence, we expanded a model of 

the evolution of an individual meteor from atmospheric entry to trail instability and diffusion (See 

Dyrud et al. [2005, 2007] for a detailed description of the model) by incorporating climatological 

models for the relevant ionospheric and atmospheric parameters. For readers interested in the global 

modeling of the incoming meteor flux see Janches et al., [2006] and Fentzke and Janches [2008]. 

Our model was originally used to simulate artificial radar Range-Time-Intensity (RTI) images 

for comparison with facilities like the 50 MHz Jicamarca Radar and other coherent radars [Chau et al., 

2008, Oppenheim, 2007, Dyrud et al. 2004, Dyrud et al., 2007, Hinrichs, 2008]. This program simulates 

head echoes and non-specular trails for meteoroids of a chosen velocity, mass, and composition, 

entering the Earth’s atmosphere. Our new program runs this individual meteor model, and then 

measures several key parameters pertaining to trail plasma instability, with this paper focusing on the 

duration of trail plasma instability. Instability duration is closely associated with the duration of an 

individual non-specular trail observation. Further, duration also acts as a guide for researchers interested 

in specular meteor trail observations, and meteor burst communication, by indicating when, where and 

to what degree they can expect turbulent versus laminar meteor trail evolution. By analyzing trail 

variation on a global scale, we show that properties of the atmosphere and ionosphere play a critical role 

in the observation and interpretation of meteor trails observations, and that as a result, the characteristics 

of meteor trail evolution are considerably more variable then previously expected. 

2 Model Description 

The model used here simulates meteoroid entry into the atmosphere, including ablation, ionization, 

thermal expansion and plasma stability based upon the meteor Farley-Buneman Gradient-Drift (FBGD) 

instability [Dyrud, 2001, 2002, Oppenheim, 2000, 2003a,b]. We have now enhanced the capability of 

this program by automating location and time specific ionospheric and atmospheric data from three main 

climatological models: Cospar international reference atmosphere (CIRA) [CIRA, 2005], the 

International Reference Ionosphere (IRI2000) [Bltiza, 2001], and the Horizontal Wind Model (HWM) 

[Hedin et al., 1996]. The parameters required from these models include electron density, atmospheric 

mass density, neutral temperature and wind speed, and from these we also derive ion and electron 

collision frequencies based upon the formulas from Banks and Kockarts, [1972] for a given location and 

time. This information is used to make location specific meteor simulations, which are then called 

multiple times to build up global maps of the meteor trail characteristics. While we recognize that these 

climatological models do not capture the full variability of aeronomical and ionospheric parameters, 


they do allow for an examination of the resulting climatological and global variation expected for 

meteor trail evolution. An aspect which previously has never been explored in light of the known 

influence of plasma turbulence. 

An example meteoroid comparison to model results from an individual meteoroid simulation, for 

a single location and local time are displayed in Figure 1a. We display the results of this model as a 

simulated Range-Time-Intensity image of a head echo and non-specular trail, similar to those produced 

by a coherent radar observations [Chapin et al. 1994, Close et al. 2002, Oppenheim et al. 2007, Dyrud 

al. 2005, Malhotra et al. 2007]. This figure displays the head echo trace as diagonal colored line, with 

color corresponding to electron line density per meter divided by 106

, such that it may appear on the 

same color bar as FBGD growth rate. We have worked on numerous head echo models (See Dyrud and 

Janches, [2008]) but have opted to plot a parameter which is related to head echo strength, but is also of 

direct physical relevance to the development of plasma instability. To the right of the head echo, this 

plot displays the calculated, non-negative, FBGD growth rate as a function of time and altitude for a 

diffusing meteor column. Examination of Figure 1a reveals that only a limited altitude portion of the 

trail is immediately plasma unstable, with the width of this unstable portion decreasing in time. The 

total duration of plasma instability for this example is approximately 15 seconds, which is defined as the 

time from trail generation at a given altitude to the time the growth rate becomes negative at that same 

altitude. In order to test our model, data comparison was done with trail observations from Fort Macon 

North Carolina with simulated meteors. This comparison is shown in Figure 1b. We continue with a 

presentation of the duration of trail turbulence if such a meteor where to occur simultaneously across the 

globe. 

Figure 1a. A simulated RTI simulation for a meteoroid near North Carolina compared to a observed meteoroid in North 

Carolina (Latitude = -35o

 and Longitude = -55o) conditions for 00:00 UT, on June 27th . The simulated meteoroid mass is 10 

μg, traveling at a velocity of 70 km/s, composed of an atomic mass of 30 AMU. The duration of the trail turbulence is 

approximately 15 seconds. The color bar shows instability growth rate in s-1 for the trail, and the simulated head echo 

displays electron line density per meter divided by 106

 (units chosen such that they appear on the same scale). 


Figure 1b. A bar graph comparing meteor trail simulations from North Carolina with data observed at Fort Macon 

North Carolina. The data was obtained by taking the average of the top 5 largest meteors at each hour and 

comparing it with meteor simulations from the model previously described. Data was not taken for 6 hours, starting 

at 6am, because the radar was not on. Notice how much of the data points compare well with the simulated data, yet 

some outliers occur in the data. 

3 Global Model Results 

Here we examine the duration of meteor trail turbulence as function of location, for a trail produced by a 

10 microgram meteor traveling at 70 km/s on June th at 00:00 UT, with a zenith angle of 45o

. These 

characteristic meteoroid parameters were chosen because this is a commonly measured size class of 

meteoroids among the billions of daily meteors [Mathews, 2001, Chau, Dyrud and Janches, 2008]. The 

meteor simulation of the type shown in Figure 1a, is repeated several hundred times across a 2o latitude 

and longitude grid, with the analyzed results displayed in Figure 2a. This plot shows, in color, the 

duration of plasma instabilities within the meteor trail for each location, which are seen to vary between 

9 seconds and 0, where 0 indicates no trail turbulence is generated. The first striking observation from 

this figure is the dramatic global variation of meteor trail evolution, even for trails produced by the very 

same meteoroid. Some of the features shown are: a clear day to night variation, i.e. that duration is 

significantly longer in the dark regions of the globe, and since we show a January day one can see that 

more of the Northern hemisphere contains longer turbulent durations than the more sunlit southern 

hemisphere. We also see that that duration is in general longer near equatorial regions with 

enhancements that appear in the Northern Atlantic Ocean, over South America and Africa. The 

variation in this figure is caused by variation in the main drivers for instability, which are primarily 

background ionization levels, and the magnitude of the neutral wind blowing both perpendicular to the 

trail and the geomagnetic field. 


We point out here that only the HWM was used for determination of meteor zone winds, and 

therefore these results will likely not to apply near the equator and at the highest latitudes where 

ionospheric drifts due to electrojets dominate the neutral winds. Hinrichs et al. [2008], has specifically 

analyzed a 24 hour meteor simulation for the Jicamarca radar location with inclusion of an electrojet 

drift model to show that the magnitude of the electrojet drift strongly modulates trail duration. We 

expect to incorporate climatological models for the high and low latitude electrojets into this global 

simulator in the future. We continue with a presentation of both the meteoric and atmospheric 

parameters responsible for variability in meteor trail evolution. 

4 Meteor Properties 

We now investigate meteoric properties and their influence on meteor trail duration. Two meteoric 

properties that have the greatest effect on meteor trail duration are mass and velocity. Figure 2b is a 

global simulation with identical parameters as 2a except the mass of the meteor has been decreased from 

1.0 μg to 0.1 μg in order to investigate the effect of mass. As seen by comparing Figures 2a and 2b, a 

meteor with a mass of 1.0 μg will produce longer duration meteor trails compared to a smaller massed 

meteor. A more massive meteor produces steeper plasma density gradients, and penetrates to lower 

altitudes where polarization fields are the strongest. Not only do meteors of larger mass produce longer 

duration meteor trails at night, but during the daytime meteors of higher masses are now turbulent in 

regions where 0.1 μg meteors were not. 

Unlike mass, an increased meteoric velocity doesn't always have a complementary effect to 

meteor trail duration. Yet, velocity has a significant impact on meteor trail duration. Figure 3 shows the 

drastic effect velocity has on meteor trails duration. A slow meteor traveling at 15 km/s has less 

ablation and ionization, which produces a relatively short lived meteor trail, if any trail at all. A very 

fast meteor traveling at 75 km/s has so much energy that all of its mass becomes ionized at such high 

altitudes that short trails are produced, due to weak polarization fields above ~100 km. The longest 

meteor trails observed are created by meteors of speeds in between both extremes. A velocity ranging 

from 35-40 km/s allows the meteor to reach lower altitudes where polarization electric fields become 

stronger, yet still generates steep density gradients. The impact that meteor velocity has on global 

meteor trail variability is shown by comparing Figure 2b and Figure 4. Figure 4 shows a global 

simulation of a 0.1 μg meteoroid, identical to that in Figure 2b, but with a velocity of 35 km/s. One may 

see that the slower velocity results in longer duration trails and more daytime trails. 

5 Atmospheric Properties 

 In order to understand the atmospheres role in meteor trail evolution we investigate the parameters 

which have profound effects on trail evolution. We find that these parameters are electron density 

present in the ionosphere and the horizontal winds that a meteor experiences. Small changes in 

atmospheric properties result in dramatic global variability. Since electron density and winds effect 

meteor trail duration we must further investigate the variability seen in these parameters to understand a 

global meteor trail outlook.


Figures 2. (a) A global simulation of the duration of meteor trail turbulence of a single 1 μg meter simulated across the 

world traveling a 55 km/s at 00:00 UT on January 1st. The units of the color bar are in seconds after meteor trail creation. 

Each pixel results from the measured duration of a simulation of the type shown in Figure 1a. The location of the meteor 

presented in Figure 1 is denoted by a (*) near North Carolina. Figure 2a illustrates the effect that the atmospheric properties 

electron density and horizontal wind speed have on a meteor's trail duration. (b) A global simulation of the duration of 

meteor trail turbulence of a single 0.1 μg meter simulated across the world traveling a 55 km/s at 00:00 UT on January 1st

. 

The units of the color bar are in seconds after meteor trail creation. Each pixel results from the measured duration of a 

simulation of the type shown in Figure 1a. Notice that a meteor of lesser mass meteor experiencing the identical atmosphere 

as Figure 2a will produce meteor trails of shorter duration or no meteor trail at all depending on the location. 

 


Figure 3. The duration of 3 meteors of different atomic masses (8, 30 and 60) and how its velocity effects meteor 

trail duration. The duration of a meteor trail is plotted in seconds and the meteors velocity is in km/s. Notice how 

slow and fast traveling meteor will produce short duration meteor trails in comparison with mid range meteor 

velocities. A velocity of 35-40 km/s has the right amount of energy to create a long duration trail. 

Figure 4. A global simulation of the duration of meteor trail turbulence of a single 0.1 μg meter simulated across 

the world traveling a 35 km/s at 00:00 UT on January 1st. The units of the color bar are in seconds after meteor trail 

creation. Each pixel results from the measured duration of a simulation of the type shown in Figure 1a. Notice the 

impact that a meteors velocity has on meteor trail evolution and trail duration. In comparison with Figure 2b which 

has a speed of 55 km/s, a meteor traveling at 35 km/s has a preferred velocity for producing a long duration meteor 

trail. Not only are longer duration trails produced but also trails in areas where they were absent in Figure 2b.


 Electron density is the first atmospheric property we look at since its effect on trail duration is 

quite evident. Electron density is important because densities in the day differ from nighttime densities 

by a factor of two and electron density directly effects meteor trail evolution and duration. A meteor 

subject to high electron densities will produce a shorter plasma turbulent trail than if lower densities 

were present. Figure 5 shows the diurnal cycle of electron density at 0:00 UT on January 1st. The global 

structure of present electron density determines the area across the globe in which conditions favor 

meteor trail evolution. 

Figure 5. The electron density of the Earth’s ionosphere that is present in Figure 2a and b. Density is measured in 

1/m3 at 0:00 UT on January 1st. The color bar shows densities that range from high density present during daytime 

hours and low densities present at night. Notice the distinct diurnal cycle of high density daytime located at the east 

and west and the nighttime low density area located at the center of the world. Higher electron densities inhibits 

meteor trail evolution.

 

 Electron density is an important factor in meteor trail evolution, but identical meteors that 

encounter constant electron density still have variability in trail duration around the globe. This is 

attributed to the winds that a meteor encounters. A meteor that is exposed to high winds will have a 

longer duration than the same meteor that is exposed to lower wind speeds. The impact that wind speed 

has on trail duration of meteors of different speeds is shown in Figure 6. To demonstrate the effect that 

global winds have on meteor trail duration we examined the horizontal wind speed at the altitude where 

maximum duration of the meteor trail occurs, this is shown in Figure 7. In the figure wind speeds vary 

from 0.5 m/s to 107 m/s. Although this is not the total wind that a meteor encounters, the wind speed at 

the altitude of maximum duration gives a good picture of the winds that directly influence a meteors 

plasma trail. Both the distinct global structure of winds at the altitude of maximum duration and the 

diurnal cycle of electron density are essential in understanding the global variability presented in this 

paper. 


Figure 6. A plot of trail duration versus wind speed for 4 different velocities of 1.0μg meteors. The influence that the 

increased magnitude of horizontal wind speeds have on a meteor's plasma trail and its duration. The plot used data from 

simulations of the meteors trail durations of 4 identical meteors traveling at different speeds ( 15, 35, 55 and 75km/s). 

These meteors are simulated at different wind speeds. Notice that meteor trail duration is directly linked to wind speeds. 

Figure 7. A global plot of the magnitude of horizontal wind speed present on January 1st at 0:00 UT at the altitude at 

which the simulated meteor has maximum trail duration in Figures 2a and b. The color bar shows wind speed in m/s. 

The wind pattern shown here is present throughout the day and is fixed in local time. Notice the large variations in the 

magnitude of horizontal wind speed which effects trail evolution. 


6 Seasonal Variability 

The effects of the atmosphere on meteor trail evolution can be seen not only globally, but seasonally 

as well. We now look as seasonal variability of meteor trails since the atmospheric properties we 

presented vary seasonally. We investigate seasonal variation by inspecting simulations near the 

equinoxes and solstices. Seasonal variability in meteor trail duration can be seen by comparing Figure 

2b and 8. Differences in the global plots of meteor trail duration of identical meteors on January 1st and 

March 20th are the result of subtle yet key changes in the atmosphere throughout the seasons. 

Figure 8. A global view of the duration of a meteor's trail. This simulation is of a 0.1 μg meteor traveling at 55 

km/s on March 20th at 0:00 UT, measured in seconds. The units of the color bar are in seconds after meteor trail 

creation. Each pixel is a simulated meteor as seen in Figure 1a. Figure 8 takes place on March 20th, otherwise it is 

the identical conditions that is simulated in Figure 2b. Notice the differences in the global structure of trail duration 

compared to Figure 2b, which is simulated on January 1st. The differences are caused by the changes in the 

atmosphere throughout the seasons.

One difference in atmospheric properties is the structure of the present electron density. Figure 5 

showed winter in the northern hemisphere. The shape of this structure varies throughout the seasons and 

is based on the amount of sun present throughout the day. For example June's electron density is a 

horizontally flipped version of Figure 5 since the night is present longer in the southern hemisphere. 

Since both hemispheres experience roughly the same amount of sunlight during the months near 

equinox, electron density will reflect accordingly. The other change in atmosphere throughout the 

seasons is the horizontal winds that a meteor experiences. The structure of the magnitude of horizontal 

wind at the altitude of maximum duration changes throughout the year. 

The combination of electron density and winds along with the meteors own parameters help the 

understanding of the great differences seen in both day/night observations and seasonal variability of 

meteor trials. With this understanding we now have a better idea of the scope that small variations in 

atmosphere has on worldwide variability of meteor trail evolution. 


7 Discussion 

This paper presents a drastic global and seasonal variability in plasma turbulent meteor trail duration. 

We find that variations in trail duration are caused by two atmospheric properties, electron density of the 

ionosphere and the magnitude of horizontal winds. While the observational studies of meteor trail 

turbulence and non-specular meteor trails remain sparse in terms of geographical and local time 

coverage, several observational trends have been reported in the literature. The model we constructed is 

critical for placing data from individual sites in the context of a global meteor flux into a local 

atmosphere and ionosphere. Here we review some observations on diurnal trends. 

 [Chapin and Kudeki, 1994a] and [Chapin and Kudeki, 1994b] published some of the first 

observations of non-specular trails from the Jicamarca radar. While it was not the focus of their paper, 

the difference in trail occurrence and duration before and after sunrise can was clearly shown in their 

Figure 4. The figure shows two distinct periods of meteor observations; the first half contains over 125 

meteor echoes before sunrise near 6:20 LT, followed by an abrupt decrease in the number trails 

observed. After 6:20 only 20 meteor echoes are seen throughout the second half of observation. 

Recently, Oppenheim et al. 2008 drew specific attention to the diurnal variability of non-specular 

echoes at Jicamarca. Before dawn, 341 non-specular trails were observed for 1288 head echoes and 

only 81 trails for 1240 head echoes after dawn. They suggested that this was evidence of a previously 

published theory by Dimant and Oppenheim [2006a, b] that predicted stronger zeroth order ambipolar 

fields at night, and therefore an enhanced driver for instabilities. In contrast, we provide an alternative 

explanation for this day night variability, which involves not just background electron density but the 

presence of background electric fields or winds that drive polarization fields within the meteor trail [See 

Dyrud et al. 2007]. The results presented here show that day/night variability is a global phenomenon, 

and not limited to electrojet regions. 

Zhou et al. [2001] presented observations of head echoes and non-specular trials from the MU 50 

MHz radar in Japan. This experiment was conducted with the radar pointing both perpendicular, and off 

-perpendicular to the geomagnetic field. They noted that essentially all head echoes had a corresponding 

non-specular trail in the perpendicular to B geometry, while the off- perpendicular had essentially no 

trails, but similar counts of head echoes. Their data were collected from 00:00 to 08:30 LT over 4 

nights, but made no comment on pre and post sunrise differences. These results cemented the view that 

non-specular echoes result from plasma instability induced FAI. While not the primary focus Close et 

al. [2008] recently demonstrated that larger meteoroids are more likely to produce non-specular echoes 

than smaller. 

Simek [2005] examined the seasonal and diurnal variability of specular meteor trail durations to 

show that mean sunlit durations were 2.27 - 0.11 seconds, but that night durations were 1.95 - 0.06 

seconds. These general trends fit what we expect and report here, that enhanced diffusion as a result of 

trail turbulence during predominantly night-time meteors will reduce trail duration. However, the values 

reported here include a number of influencing factors such as changing echo altitude as a function of 

local time. However, specular echo duration as a function of altitude, which helps isolate the effects of 

trail turbulence, has been examined by Singer et al. [2008]. They showed that low altitude decay times 

decreased at high latitude in summer, and that strong echo trails had longer decay times than weaker 

echo trails (stronger echoes likely typify higher electron line densities produced by larger meteoroids). 

However, examination of this author’s Figure 2 shows that these trends are reversed at the highest 

altitude of observation (94 km). The results reported here explain this seasonal and meteor size trend 

reversal at higher altitudes. In the summer hemisphere trails are more likely to be produced in a sunlit 


ionosphere, and therefore remain turbulent for shorter periods of time or not at all. If turbulent decay 

rates are faster than laminar decay rates as reported by Dyrud et al. [2001] we expect summer trails to 

possess, on average, longer decay times. Since larger meteoroids produce larger plasma density 

gradients we also expect larger trails (or stronger echoes) to possess faster decay times. Further, these 

effects of turbulent diffusion are more pronounced at higher altitude as also discussed by Dyrud et al. 

[2001]. 

In a study of specular trail diffusion as a function of radar pointing to B, Hocking [2004] 

suggested that ” ... future theoretical analysis need to include externally imposed electric fields in order 

to produce accurate simulations of diffusion rates..”. This is what we have included in this study. 

Hocking [2004] examined decay times as a function of radar azimuth angle and time of day, and found 

that there was far stronger anisotropic diffusion at greater altitudes above 93 km, and that winds and 

electric fields appear to influence the diffusion rate in general, and the overall anisotropy. 

As the above summary of studies show, the existing non-specular and specular trial observations 

do support a day to night variation in the occurrence of meteor trail plasma turbulence. The studies also 

show that larger meteoroids are more like to produce turbulent trails. Further, our simulations here 

indicate that this day/night occurrence variation is one that is predicted to be global. However, the 

detailed variability is a result of the altitudinal wind profiles and magnitude. Understanding this 

variability will require substantially increased observations, both in terms of geographical and local time 

coverage, and comparison with data from other instruments. We conclude by noting that the driving 

factors accounting for meteor trail turbulence are many and complexly intertwined, thus it is not the 

focus of this short letter to describe all the competing forces but to publicize the predicted dramatic 

variability to researchers in various meteor related fields. We are working on a detailed analysis of the 

various contributions and expect to report them in an upcoming publication, but can summarize the 

general trends here. The primary drivers for turbulence duration are background ionization: turbulence 

lasts longer at night, wind or drift velocity: higher winds or drifts produce longer turbulent durations, 

meteoroid mass: larger meteoroids produce longer turbulent durations, velocity: velocities near 35 km/s 

(with some modification with entry angle and a particular mass) longer lasting turbulence because they 

deposit their mass at preferred altitudes for turbulence, between 90-105 km altitude. 

We expect that a complete understanding and characterization of all the driving forces behind 

meteor trail turbulence will improve our understanding of non-specular trails, but also dramatically 

improve our ability to use specular trail observations to derive atmospheric temperature and other 

parameters, by isolating decay rates from the influence of turbulence. 

Acknowledgments 

Lars Dyrud and Jason Hinrichs’ work was supported by NSF grants ATM-0613706 and ATM-0638912. 

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1399. 


CHAPTER 7: 

BOLIDE OBSERVATIONS AND FLIGHT DYNAMICS 


Passage of Bolides through the Atmosphere

O. Popova1

Abstract Different fragmentation models are applied to a number of events, including the entry of TC3

2008 asteroid in order to reproduce existing observational data. 

Keywords meteoroid entry · fragmentation · modeling 

1 Introduction 

Fragmentation is a very important phenomenon which occurs during the meteoroid entry into the 

atmosphere and adds more drastic effects than mere deceleration and ablation. Modeling of bolide 

fragmentation (100 – 106 kg in mass) may be divided into several approaches. Detail fitting of 

observational data (deceleration and/or light curves) allows the determination of some meteoroid 

parameters (ablation and shape-density coefficients, fragmentation points, amount of mass loss) 

(Ceplecha et al. 1993; Ceplecha and ReVelle 2005). Observational data with high accuracy are needed 

for the gross-fragmentation model (Ceplecha et al. 1993), which is used for the analysis of European and 

Desert bolide networks data. Hydrodynamical models, which describe the entry of the meteoroid 

including evolution of its material, are applied mainly for large bodies (>106 kg) (Boslough et al. 1994; 

Svetsov et al. 1995; Shuvalov and Artemieva 2002, and others). Numerous papers were devoted to the 

application of standard equations for large meteoroid entry in the attempts to reproduce dynamics and/or 

radiation for different bolides and to predict meteorite falls. These modeling efforts are often 

supplemented by different fragmentation models (Baldwin and Sheaffer, 1971; Borovika et al. 1998; 

Artemieva and Shuvalov, 2001; Bland and Artemieva, 2006, and others). 

 The fragmentation may occur in different ways. For example, few large fragments are formed. 

These pieces initially interact through their shock waves and then continue their flight independently. 

The progressive fragmentation model suggests that meteoroids are disrupted into fragments, which 

continue their flight as independent bodies and may be disrupted further. Similar models were suggested 

in numerous papers, beginning with Levin (1956) and initial interaction of fragments started to be taken 

into account after the paper by Passey and Melosh (1980). The progressive fragmentation model with 

lateral spreading of formed fragments is widely used (Artemieva and Shuvalov, 1996; Nemtchinov and 

Popova, 1997; Borovika et al. 1998; Bland and Artemieva, 2006). 

 The second mode of fragmentation is the disruption into a cloud of small fragments and vapor, 

which are united by the common shock wave (Svetsov et al. 1995). This fragmentation occurs during the 

disruption of relatively large bodies. If the time between fragmentations is smaller than the time for 

fragment separation, all the fragments move as a unit, and a swarm of fragments and vapor penetrates 

deeper, being deformed by the aerodynamical loading like a drop of liquid (Hills and Goda 1993 and 

others). This liquid-like or “pancake” model assumes that the meteoroid breaks up into a swarm of small 



OPopova 

Institute for Dynamics of Geospheres Russian Academy of Sciences, Leninsky prospect 38, bldg.1, Moscow 119334, Russia. Phone: +7 

495 939 70 00; Fax: +7 499 137 65 11; E-mail: olga@idg.chph.ras.ru 


bodies, which continue their flight as a single mass with increasing pancake-like cross-section. The 

smallest fragments can be evaporated easily and fill the volume between larger pieces. Initially formed 

fragments penetrate together deeper into the atmosphere and the fragmentation proceeds further. But 

large fragments may escape the cloud and continue the flight as independent bodies. 

 The formation of a fragment–vapor cloud was observed in the breakup of a meteoroid on 1 

February 1994 (McCord et al. 1995), in the fragmentation of the Benesov bolide (Borovika et al. 1998), 

and in other cases. The total picture of fragmented-body motion is comparatively complicated. Both 

scenarios are realized in the real events (Borovika et al. 1998). 

2 The Entry of TC3 2008 

2.1 Observational Data 

The entry of asteroid TC3 2008 over Sudan was observed by numerous eyewitnesses and a few detecting 

systems, including Meteosat satellites (Borovika and Charvat, 2009), infrasonic array and US 

Government satellites (Jenniskens et al. 2009). Meteorites named Almahata Sitta were recovered in 

December 2008. Meteorite searches allowed collectors to find about 300 fragments with total mass up to 

3.95 kg (Jenniskens et al. 2009). Masses (from 1.5 g to 283 g) were found along a 29 km path. 

 Almahata Sitta was classified as an anomalous polymict ureilite (Jenniskens et al. 2009). 

Different lithologies including a number of non-ureilite fragments (enstatite and ordinary chondrites) 

were found among retrieved samples. All pieces are fresh and unweathered, so they probably had been 

incorporated into asteroid TC3 2008 and did not originate from an earlier meteor event (Bischoff et al. 

2010). This indicates that the asteroid was probably a collection of different lithologies, which were 

included as distinct stones within the asteroid body. The measured bulk density of Almahata Sitta varies 

from fragment to fragment ( 2.9 – 3.1 g/cm3 ) and porosity is about 15-20% (Kohout et al. 2010). These 

values are close to the typical ureilite values (3.05 g/cm3 and 9%; Britt and Consolmagno, 2003). Welten 

et al. (2010) estimated the macroporosity of the asteroid as high as about 50%. One small piece of 

Almahata Sitta was disrupted in the laboratory and its measured tensile strength was about 56 ± 25 MPa 

(Jenniskens et al. 2009). 

 The initial diameter of this meteoroid was estimated as 4.1 ± 0.3 m based on asteroid visual 

magnitude (Jenniskens et al. 2009). Corresponding pre-atmospheric mass ( = 2.3 g/cm3

) is about 83 ± 2 

5 t (Jenniskens et al. 2009). This estimate correlates well with the mass obtained based on infrasound 

signal (87 ± 27 t). The irradiated energy recorded by US DoD satellites allows an estimated initial mass 

of 56 t, assuming an integral luminous efficiency of 9.3% based on optical events calibrated by 

infrasound registration (Brown et al. 2002a). According to theoretical estimates (Nemtchinov et al. 

1997) the integral luminous efficiency is slightly lower for this low velocity entry - 6.8-8.2%; these 

values result in initial mass of about 63-77 t. 

 The lower mass estimate (~20 t) is suggested by Kohout et al. (2010) and is based on 

assumptions of higher albedo and essential macroporosity of the asteroid. But this low mass estimate 

corresponds to very high value of integral luminous efficiency (~26%), which seems not probable. 

 The light curve recorded by US DoD satellites wasn’t published, but it was released that the 

signal consisted of three peaks, while the most energy was radiated in the middle of a 1-s pulse at 37 km 

altitude and a final pulse 1 s later (at about 33 km altitude) (Jenniskens et al. 2009). Analysis of 

Meteosat 8 images allows the estimation of bolide brightness at two random heights, 45 and 37.5 km, 

where it reached Â18.8 and Â19.7 magnitude, respectively (Borovika and Charvat, 2009). The peak


brightness was probably brighter than Â20mag (Borovika and Charvat, 2009). A schematic version of 

possible light curve is shown on Figure 1. Minimal detectable intensity is assumed to be about 2 109 

W/sr. Shapes of light peaks are arbitrary, but the total irradiated energy corresponds to reported value of 

4 1011 J (or 0.096 kt; USAF press release). 

Analysis of Meteosat 8 images allows the conclusion that dust release due to meteoroid breakup 

occurred at altitudes 44, 37 and possibly at 53 km. The broken pressures were estimated as 0.2-0.3 MPa 

(at 46-42 km altitude) and 1MPa (at 33 km) (Jenniskens et al. 2009).

 (a) (b) 

Figure 1. (a) Schematic light curve of Almahata Sitta (dashed line) and an example of model light curves of 

Almahata Sitta in the frame of pan-cake model. (b) Schematic light curve of Almahata Sitta (dashed line) and model 

curves obtained in the frame of disruption onto two fragments (pointed line) and disruption into a number of 

fragments. 

2.2 Modeling Efforts 

2.2.1 Pan-cake Model 

The presence of three peaks in the Almahata Sitta light curve indicates that there were three main stages 

of fragmentation. Similar light curves for a number of satellite observed bolides were successfully 

reproduced in the frame of pan-cake (or liquid-like) models (Svetsov et al. 1995; Nemtchinov et al. 

1997; Popova and Nemtchinov 2008). Although liquid like models mentioned above are applicable 

mainly for large impactors, which are destroyed so intensively that fragments couldn’t be separated 

(>~4-10 m in size) (Svetsov et al. 1995; Bland and Artemieva 2006), its modifications provide 

reasonable energy release. These models may be suitable for catastrophic disruption, when a huge 

number of fragments are formed. 

 The shape of light curve depends on chosen model parameters (rate of dust cloud spreading, 

mass fraction fragmented in every break up, assumed strength at the breakup). One possible light curve 

of Almahata Sitta is shown on Figure1a. The meteoroid with initial mass of 83 tons and bulk density 2.5 

g/cm3 initially disintegrated at the altitude of about 50.4 km under the aerodynamical loading about 0.15 


MPa on two-three big pieces and a cloud of small fragments and dust, which may be described in the 

frame of pan-cake model. Formation of this cloud is accompanied by the first flare in the light curve. 

The next fragment (or few fragments) is broken up by aerodynamical loading of about 0.6 MPa at 40.2 

km altitude. And the last fraction of meteoroid was disrupted at 33.9 km altitude under loading of about 

1.5 MPa. The fractions of initial mass fragmented at different altitudes are roughly 33, 47 and 20% (i.e. 

~27.6, 38.4 and 16 t). The integral luminous efficiency was about 6.5%, corresponding to a total 

irradiated energy of about 0.099 kt. Slightly different values of mass fractions (25, 65 and 10 %) and 

strengths (0.15, 0.4 and 1.5 MPa) also permits reproduction of the triple peaked light curve. About 70% 

of the initial mass is evaporated, and about of 30% of it (~25 t) remains in the atmosphere as a 

decelerated cloud of dust. 

According to the statistical strength theory (Weibull, 1951) and direct observations on natural 

rocks (e.g., Hartmann, 1969) the strength of a body in nature tends to decrease as body size increases. 

The effective strength is usually expressed as = s(ms/m)



, where and m are the effective strength and 

mass of the larger body, s and ms are those of small specimen, and  is a scaling factor. There are no 

precisely determined values of scaling factor , but for stony bodies the exponent is estimated to be in 

the range of 0.1–0.5 (Svetsov et al. 1995). It has not been proven that theses values hold for meteorite 

strength, though that is commonly assumed in meteoroid fragmentation theories (e.g., Baldwin and 

Sheaffer, 1971; Tsvetkov and Skripnik, 1991; Nemtchinov and Popova, 1997; Borovika et al. 1998; 

Artemieva and Shuvalov, 2001; Bland and Artemieva, 2006). 

The inferred strength at breakups depart from the values, which are predicted by the strength 

scaling law with exponent  ~ 0.25. Bland and Artemieva (2006) suggest using a small variation in 

strength (about 10% around predicted values), but there is much more significant deviation. Even 

application of larger variations in strength (up to 50% of predicted value) reproduces only double peak

curves, and the altitude difference between peaks is smaller than observed one. 

The pan-cake model is not capable of providing a mass-velocity distribution of meteoroid 

fragments; it cannot predict the meteorite strewn field. Besides, the same luminous efficiency is used for 

the solid fragment and for the cloud of vapor if their sizes are equal. 

2.2.2 Progressive Fragmentation Models 

The possibility to describe the fate of individual fragments, to determine meteorite strewn or crater fields 

is the main and extremely important advantage of the progressive fragmentation type models. The 

number of fragments changes in the process of the disruption from 1 (a parent body) to an arbitrarily 

large value, depending on the assumed properties of the meteoroid. These types of models usually 

incorporate the strength scaling law mentioned above and different assumptions about distribution of 

formed fragments on mass. 

Bland and Artemieva (2006) suggested that each fragmentation of a single body results in two 

fragments with smaller mass and usually higher strength (although a small (<10%) variation in strength 

was considered). Each fragment is subjected to additional fragmentations later if the dynamic loading 

exceeds the updated fragment strength. 

Disruption into two fragments supplemented with the strength scaling law leads to a single peak

light curve. Corresponding modeling efforts are shown on Figure 1b. An initial meteoroid mass ms ~ 83 

tons, initial strength s ~ 0.15-0.2 MPa and  ~ 0.25 are assumed. The observed value of strength at 

initial breakup is used as sample strength. The usage of stony meteorite sample strength (~30MPa for 

0.01 kg) results in higher initial strength and lower altitude of fragmentation beginning (~40 km). 

Masses of daughter fragments are chosen randomly in every breakup. Heat transfer coefficient Ch ~ 0.1 


corresponds to ablation parameter of about 0.016 s2

/km2 similar to the characteristic value for stony 

bodies (0.014 s2

/km2; Ceplecha et al. 1998) and to the value used by Bland and Artemieva (2006). The 

used luminous efficiencies in the satellite detectors passband were obtained in the course of radiative 

hydrodynamic numerical simulations (Golub’ et al. 1996; Nemtchinov et al. 1997). 

Fragmentation starts at 47 km altitude and proceeds down to about 29 km altitude. A large 

fraction of initial mass lands on the ground (Mfall ~ 24 t) in more than 5000 pieces. The largest fragment 

reaches 10-20 kg (size of largest fragment is mainly determined by suggested strength scaling law and 

entry velocity). Most of the fallen mass is contained in the largest fragments. The integral luminous 

efficiency is about 2.5 - 3% and total light energy in the satellite detectors passband is about 0.03 – 0.05 

kt TNT. Obtained values vary slightly from one set of calculations to another due to random choice of 

fragment size at breakup, but they are close to each other on average. The light pulse starts and ends at 

lower altitudes than the schematic one for the real event, the model light intensity and total irradiated 

energy are lower. 

The single disruption event may result in a number of fragments. The mass distribution of 

fragmented rocks is often described by a power law (Hartmann 1969; Fujiwara et al. 1989). The power 

law distribution was also used in the description of meteorites (Jenniskens et al. 1994; Hildebrand et al. 

2006) and in modeling of meteoroid entry (Nemtchinov and Popova, 1997; Borovika et al. 1998). 

Following Hartmann (1969), the cumulative fragment distribution in the breakup is assumed N ~ m

-b, 

where N is the cumulative number of fragments of mass > m; b is the negative slope in a log(N)-log(m) 

plot. The slope holds the same if a logarithmic-incremental plot is used (F ~ m

-b, where F = number of 

fragment within a logarithmic increment, dlogm). The value b ~ 0.6 is accepted (Hartmann 1969). 

Disruption into several groups of fragments is considered. The average mass in neighboring groups 

changes in 2 times. The size of the largest daughter fragment is chosen randomly in every breakup, the 

number of groups and number of fragments in a group are determined based on parent fragment mass 

and fragment distribution mentioned above. All other parameters are the same as in the previous case. 

The formation of a number of fragments causes the appearance of flashes in the light curve and 

slightly shifts the light curve to higher altitude (Figure 1b). The total fallen mass is still close to previous 

case (Mfall ~ 20-24 t), but the fallen mass has wider distribution. The total number of fragments increases 

essentially up to 104 – 105

. Nevertheless, the Almahata Sitta entry is poorly described by this and 

previous approaches. The fallen mass is too huge and irradiated energy is small. 

2.2.3 Luminous Efficiency 

The model light curves and total irradiated energy are dependent on assumed values of luminous 

efficiency. In general, luminous efficiencies vary with meteoroid size, velocity, altitude of flight and 

meteoroid composition. The dependence of luminous efficiencies f in the satellite detectors passband on 

altitude is given on Figure 2 for H-chondrite meteoroids (Golub et al. 1996; Nemtchinov et al. 1997). 

Luminous efficiencies mainly increase with meteoroid size and velocity and become higher at lower 

altitudes (Figure 2). The values of luminous efficiencies for achondrite bodies probably differ from Hchondrite ones due to the different composition of vapor in the radiative volume. In the entry modeling, 

the same luminous efficiency is used for the solid fragment and for the cloud of vapor if their sizes are 

equal. The model, which allows the determination of these coefficients, also has some limitations 

(Golub’ et al. 1996), but currently it provides the best known estimates of luminous efficiency f for 

satellite observed light curves. 


Figure 2. Luminous efficiencies for H-chondrite bodies versus altitude for two velocities (10 and 15 km/s) and two 

different sizes (R ~ 0.14 m (stars) and 1.4 m (squares)) 

Moreover, these luminous efficiencies were a basis for the determination of integral luminous 

efficiency , i.e. the relation between total irradiated energy and initial kinetic energy for satellite 

observed bolides (Nemtchinov et al. 1997). An independent estimate of integral luminous efficiency 

was obtained by Brown et al. (2002a) based mainly on infrasound registrations of 13 events. There were 

3 meteorite falls among these events, compositions of other meteoroids were unknown (Brown et al 

2002a). These estimates of  agree well with each other (Popova and Nemchinov 2008). 

Roughly, it may be estimated that the light intensity has the precision of about two times. It 

should be also noted here that the light curve on Figure 1 is not really observed, it is only a sketch. 

2.2.4 Hybrid Model 

A large number of fragments may be formed simultaneously, but the progressive fragmentation model 

considers their flight and radiation independently. This type model deals better with few fragments, 

which are well separated. The progressive fragmentation model does not well describe the case of 

production of a large number of poor separated fragments. Different configurations of fragments may 

occur during the disruption process and influence further motion and radiation of fragments (Artemieva 

and Shuvalov, 1996, 2001). A number of separated fragments may be formed whereas smaller fragments 

and dust probably have no time to be separated and form a spreading cloud. The suggestion that 

randomly chosen part of mass in the break up forms an expanding cloud of dust causes the appearance 

of the flares on the light curve (Figure 3a) and the increase of radiated energy up to 0.04-0.07 kt TNT, 

but these values are still lower than observed ones. Shape of light pulse varies from one numerical run to 

another. The total fallen mass decreases down to 6-14 t in 103

-105 fragments. Fallen mass is essentially 

overestimated. Larger fraction of mass should be converted into the dust in breakups. 


(a) (b) 

Figure 3. (a) Schematic light curve of Almahata Sitta (dashed line) and three model curves obtained under 

assumption that in every breakup some part of mass formed spreading cloud of vapor and dust. (b) Schematic light 

curve of Almahata Sitta (dashed line), two model curves obtained under assumption that in every breakup only few 

fragments are formed, some part of mass (~30% in average) formed spreading cloud (black and pointed curves); 

fragmentation onto two parts, one of which is converted into dust spreading cloud (gray curve). 

During the progressive fragmentation of Moravka meteoroid (initial mass estimate ~1.2 ton) at 

the altitudes 30-40 km (Borovika and Kalenda, 2003) every break up of parent fragment resulted in 

formation of 1-3 relatively large fragments and dust (invisible on videorecord). Dust mass reached 10-

90% of the parent fragment mass. Light curves obtained under the assumption that the number of 

fragments in the breakup is relatively small are shown on Figure 3b. Number of fragments in breakup is 

about 1-10 (2-3 in average) and some part of mass is converted into spreading dust cloud (~30% in 

average). Fallen mass in these cases is about 1.5-2.5 t, number of fragments is about 1000, integral

luminous efficiency is about 4 – 5% and Er ~ 0.07-0.08 kt, but light pulse becomes more narrow (Figure 

3b) even if the deviation of fragment strength from strength scaling law is allowed. 

In the limiting case of the disruption into two parts – one fragment and dust cloud – the fallen 

mass decreases to about 5-15 kg in one piece. Integral luminous efficiency increases up to 5-6% and Er ~ 

0.08 – 0.09 kt (Figure 3b). In order to get few peaks on the light curve the strength of fragments should 

essentially deviate from assumed strength scaling law, but the pulse is still narrow even if the strength 

may change on about 50% (Figure 3b). 

It is possible to increase the mass fraction converted into dust clouds artificially and to fit 

observed light energy and shape of light pulse, but it is done above in the frame of pan-cake model. 

Light curve may be fitted if fallen mass is smaller about 100-400 kg, which seems to be an upper 

estimate. 


3 Comparison With Other Events 

3.1 Dust Formed in the Breakups 

As it was mentioned above (Section 2.1), formation of dust clouds were directly observed during the 

entry of TC3 2008 (Borovika and Charvat 2009). The amount of warm decelerated dust was estimated 

as at least 10 t, that is in the same order as our estimates (~25 t). 

 The Almahata Sitta entry confirmed that a large part of stony meteoroid mass and energy may be 

deposited in the atmosphere during the entry. Dust clouds are often observed at breakup events during 

observations of meter-sized meteoroids. These clouds are formed typically at 30-60 km altitude, but the 

data on particle size and on the mass fraction of the parent body, which was dispersed into dust, are 

scarce. 

 Attempts to collect dust from meteoroid disruption were done for two separate events, 

Revelstoke and Allende. The air through which a fireball had been observed to pass was sampled for 

meteoritic debris. Particulate matter was collected on special filters, which was mounted on aircraft and 

flown downwind from the site of the meteorite fall at 10-12 km altitude (Carr, 1970). According to Carr 

(1970), Revelstoke and Allende represented two different types of events. In the case of Revelstoke 

(type I carbonaceouse chondrite, corresponding sound wave energy is estimated as 1012-1013 J, i.e.~1 kt) 

only a small 1 g of material was found in the fall area (possibly the result of rough terrain in the fall 

area, but may be the result of essential breakup in the atmosphere), large amount of debris still present in 

the atmosphere three days after event. Air samples contained a substantial excess over background of 

magnetite and transparent glass spherules and in addition contained a substantial number of irregular 

opaque particles high in Ni. Sizes of collected particles were mainly 2-4 ãm (<10-25 ãm). The Allende 

event was quite different (type III carbonaceouse chondrite, initial mass estimate >2000 kg, intial energy 

~1012 J) >500 kg was found on the ground. Allende filters were clean – only a small number of particles 

were collected. The difference between sample and background is less than a factor of four, although 

some amount of opaque and glass spherules (<10 ãm) were collected. Carr (1970) suggested that the 

difference in collected air samples and on fall sites resembles two different types of meteoroid breaks in 

the atmosphere. 

 A dust cloud formed due to fragmentation of large meteoroid (initial mass estimate 600 - 1900 t) 

was recorded during routine lidar observation of the atmosphere (Klekociuk et al. 2005). The meteoroid 

was fragmented at 32 km altitude and a dust cloud was recorded 7.5 hours later. The total mass of dust 

in this cloud was estimated as about 1000 t (that is lower estimates, because according to satellite 

observations, second fragmentation of meteoroid occurred at 25 km altitude). Dust size and 

concentration were estimated as 0.4-0.98 ãm and 2-6 106

ì

-3. Data on this event suggests that a large 

fraction of initial meteoroid mass may be released in the atmosphere as dust. Micron-sized particles may 

exist in the atmosphere during weeks-months and may play an important role both in climate processes 

and ozone layer dynamics (Klekociuk et al. 2005). No material was collected or found. 

3.2 Tagish Lake and Carancas 

The fraction of initial mass recovered as meteorites is mainly about fm ~ 0.1-3 % for 11 meteorite falls 

with detailed tracking data on atmospheric passage (Popova et al. 2010). The recovered mass is smaller 

than estimated total fallen mass partially due to incomplete finding. The highest fractions are obtained 

for two smallest and slowest meteorites (~10%, Lost City and Innisfree), the smallest fractions (<10-4) 


are found for Tagish Lake and Almahata Sitta meteorites, probably due to their specific structure and 

composition. 

 The Tagish Lake material is classified as ungrouped carbonaceous chondrite with a very high 

porosity of 25-49%, and the largest meteorite fragment constitutes only about 10-5 of its initial meteoroid 

mass (Hildebrand et al. 2006). Modeling efforts done to describe the entry of the Tagish Lake meteoroid 

demonstrated that about of 80-90% of instantaneous mass of the body was lost in the main breakup at 

the altitude of about 34-35 km (Brown et al. 2002b; Ceplecha 2007). Hildebrand et al.(2006) concluded 

that most of the initial meteoroid mass (~60-90 t) was deposited at 30-40 km altitude as the dust. 

Attempts to apply pan-cake and progressive fragmentation models to the Tagish Lake case also 

confirmed that essential amount of its mass was deposited as the dust in the atmosphere similar to 

Almahata Sitta case. About 1000 kg of initial mass may be converted into meteorites. This estimate is of 

the same order as the mass estimates at the end of luminous trajectory (~1300 – 2700 kg) obtained by 

Brown et al.(2002) and Ceplecha (2007). Hildebrand et al.(2006) estimated the total fallen mass as about 

100-1000 kg, and only 16.3 kg was collected. 

Borovika and Charvat (2009) compared the apparent strengths at fragmentation for a few 

bolides and suggested that the Tagish Lake meteoroid is the best analog to asteroid TC3 2008. Presence 

of non-ureilite fragments among retrieved samples of Almahata Sitta shows inhomogeneous structure of 

the asteroid body (Bischoff et al. 2010). Besides, some authors suggest high macroporosity of TC3 2008 

(Borovika and Charvat 2009; Welten et al. 2010; Kohout et al. 2010). The parent bodies of Tagish Lake 

and Almahata Sitta meteorites were probably very fragile and inhomogeneous. They were 

catastrophically disrupted during the atmospheric passage producing dust clouds, and their stronger parts 

became meteorites. 

The opposite case was observed in the Carancas event, where the fall of a stony meteorite caused 

the formation of a 13-m wide impact crater. This ordinary chondrite meteoroid probably did not 

experienced significant atmospheric fragmentation (Borovika and Spurny 2008), although there was no 

detailed observational data. The meteoroid mass was estimated as about M~1300-10000 kg (Borovika 

and Spurny 2008) or even as 10000-50000 kg. (Kenkmann et al. 2009). The Carancas event confirms 

that meteoroid strength and fragmentation scenario can vary significantly from case to case. But it 

should be noted here that small crater formation on the Earth is an extremely rare event due to disruption 

of meteoroids in the atmosphere, whereas 10-30 similar sized bodies enter the atmosphere every year 

(Nemtchinov et al. 1997; Brown et al. 2002a). 

3.3 Mbale 

If the fraction of initial mass recovered as meteorites fm exceeds about 1-5%, probably there is no large 

dust deposition during the passage. Entry of these meteoroids is reasonably described in the frame of 

progressive fragmentation models. Comparison of model predictions with strewn fields permits better 

understanding of the details of meteoroid breakups, although in many cases the incomplete recovery 

adds uncertainties in strewn field data. 

About 150 kg of material in more than 850 pieces were collected on a strewn field of a size 3x7 

km after the fall of L5/6 ordinary chondrite Mbale in 1992 (Jenniskens et al. 1994). Its pre-entry mass 

was estimated as 400-1000 kg (more probably ~1000 kg) based on cosmogenic radionuclide data. Entry 

velocity was roughly estimated as 13.5 km/s. It was assumed that small fragmentation started probably 

above 25 km, but the main catastrophic breakup occurred at 10-14 km altitude. 

Application of progressive fragmentation model to the Mbale entry allowed estimation of fallen 

mass as 200-250 kg in 100-3000 fragments (in dependence on assumed breakup model) covering a 


strewn field of about 1x7-9 km. Wind drift, which is essential for gram-sized fragments, wasn’t taken 

into account. Multiple breakups occurred at the altitudes 22-35 km under the loading of about 0.8-1.3 

MPa. Strength scaling law (with allowed random strength deviations) was used. The values of breakup 

loading are in the same range as for other observed meteoroid fragmentations (Popova et al. 2010), but it 

should be noted here that observed strength of meteoroids at breakup substantially deviates from this 

scaling law (Popova et al. 2010). The Mbale meteorite fragment distribution is better reproduced if a 

number of pieces following power law distribution are formed in every breakup. Model results 

satisfactorily describe the observed strewn field. 

More strewn fields should be modeled in the future in order to better understand the details of the 

breakup process (strength at breakup; fragment distribution at breakup, etc). 

4 Summary 

Different fragmentation scenarios occur during the passage of meteoroids 100 – 106 kg through the 

atmosphere. There are a number of events which deposited essential fraction of their masses as dust in 

the atmosphere. Observational data are still incomplete to make definite conclusion, what fraction of 

incoming bodies is fragile enough to deposit this dust and how it is related with their 

structure/composition etc. But even bodies, which deposited much of mass as a dust/vapor, are able to 

produce meteorites. The total picture of fragmented-body motion is comparatively complicated. Better 

statistics are needed to estimate parameters of incoming cosmic material and to predict its behavior in 

the atmosphere. A full set of data, including detailed light curves, photographic trajectories, spectra, 

acoustic and seismic signals, and data on the composition of found meteorites are highly desirable. 

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Constraining the Drag Coefficients of Meteors in Dark Flight 

R. T. Carter1• P. S. Jandir2• M. E. Kress3

Abstract Based on data in the aeronautics literature, we have derived functions for the drag coefficients 

of spheres and cubes as a function of Mach number. Experiments have shown that spheres and cubes 

exhibit an abrupt factor-of-two decrease in the drag coefficient as the object slows through the transonic 

regime. Irregularly shaped objects such as meteorites likely exhibit a similar trend. These functions are 

implemented in an otherwise simple projectile motion model, which is applicable to the non-ablative 

dark flight of meteors (speeds less than +3 km/s). We demonstrate how these functions may be used as 

upper and lower limits on the drag coefficient of meteors whose shape is unknown. A Mach-dependent 

drag coefficient is potentially important in other planetary and astrophysical situations, for instance, in 

the core accretion scenario for giant planet formation. 

Keyword meteorite · drag 

1 Introduction 

The scientific value of meteorites motivates many efforts to recover them quickly. To expedite the 

collection of meteorites resulting from observed fireballs, one must better constrain where they may 

have landed. Given an object’s instantaneous position and velocity (in three dimensions), its mass (as 

inferred from deceleration) and its drag coefficient, its landing site can be constrained. 

 In recent years, detailed observations of meteors have been made by the European Fireball 

Network [16] [18], the Desert Fireball Network [3], and the Southern Ontario Network [22], resulting in 

the recovery of many meteorites. These detection networks can measure a meteor’s position and velocity 

with very high precision. The Neuschwanstein Bolide was observed by the European Fireball Network; 

its angle is constrained to ±0.07°, the altitude to ±50 m, and the speed to ±800 m s-1 [17] [19]. 

Information about the mass of the object can also be derived from observations [17]. 

 Considering the high accuracy to which observables can be measured, the drag coefficient 

introduces most of the uncertainty in calculating the landing site of these observed meteors. Detailed 

analysis of the drag coefficients of meteorites is daunting because meteorites are irregularly-shaped 

objects, and thus have different drag coefficients, not only for each individual object but also for the 

infinite number of orientations each can assume as they tumble, spin and ablate during flight. 

Nevertheless, there has been much effort to determine the drag coefficient for meteorite-like shapes (e.g. 

[23] [10]). Several studies have used or derived constant values for drag coefficients (e.g. [5] [23] [10] 

[21]). 



R. T. Carter 

Department of Physics, University of Oregon, Eugene, OR 97403 USA. E-mail: rcarter2@uoregon.edu 

P. S. Jandir, Department of Physics, University of California, Riverside, CA 92521 USA 

3

M. E. Kress ( ), Department of Physics & Astronomy, San José State University, CA 95192 USA. E-mail: mkress@science.sjsu.edu


 Mach number, M, is an object’s speed relative to the local speed of sound. In Earth’s atmosphere, 

the speed of sound depends on the square root of the temperature of air and thus is primarily a function 

of altitude. At sea level, the speed of sound is approximately 340 km/s. We derived empirical equations 

for the drag coefficient as a function of Mach number from the data available in the aeronautical 

engineering literature [9] [11] [12]. In these studies, the drag coefficients for spheres were measured up 

to Mach 10 and for cubes up to Mach 3. From these data, we derive functions for the drag coefficients 

CD(M) for spheres and cubes. We use these two CD(M) functions as lower and upper limits for the drag 

on a meteor. We note that drag coefficients dependent on Mach number have been used in meteor 

physics before, e.g. [6] and often define the drag coefficient as $ , which is related to CD via the relation 

$ = 0.5CD. Here, when we refer to the drag coefficient, we use the CD convention. 

 In section 2, we present the CD(M) functions for spheres and cubes, and explain how the 

equations of motion are solved. In section 3, we show how Mach-dependent drag affects the landing site 

for the idealized cases of spherical and cubic ‘meteors.’ We illustrate how the search area is smaller 

when using a CD(M) whose limits are set by a sphere and cube, compared to a search area delimited with 

constant CD. In section 4, we discuss how CD(M) becomes increasingly important for meteors whose 

mass, velocity, altitude and entry angle cause them to spend more time at lower velocities where the 

drag coefficient varies the most. In section 5, we summarize our findings and discuss how a Machdependent drag coefficient may improve upon other planetary and astrophysical calculations. 

2 Model 

The drag coefficients for several regular shapes, including a sphere and a cube, have been 

experimentally measured over a wide range of Mach numbers [9] [11] [12]. In these ballistic range tests, 

pellets in the shape of spheres and cubes were shot out of high velocity guns. For all speeds, the drag 

coefficient for a cube is always about a factor of two greater than that for a sphere. However, spheres 

and cubes exhibit similar trends in CD(M) (see Figure 1). At low speeds, the drag coefficient of a cube is 

1.09 and that of a sphere is 0.46. These both almost double as the speed increases to Mach 1.5, and then 

they level off to 1.7 and 0.9 respectively, at high Mach numbers. Therefore, the Mach number has as 

much of an effect on drag coefficient as does the shape, when comparing spheres and cubes. 

 Using these experimental data, best fit functions were derived to estimate the drag coefficient of 

spheres and cubes as a function of Mach number (Figure 1). Both of these drag coefficient functions are 

piece-wise. At lower speeds, CD depends on M 2

, and the best fit functions are quadratic. In the 

supersonic (M > 1) regime, the best fit functions are both a sum of two exponentials. The drag 

coefficient of a cube as a function of Mach number is 

  

 < 	
>++++++++++ 
 W  W 		i


  	/!!VC  i/CVC < 	>   		i


  
i < 
>++++++++ 
 W  W 


  	/!VC  /VC < 
>   


(1)

The drag coefficient of a sphere as a function of Mach number is 

(2)

 In the hypersonic regime, (M > 5), the drag coefficient for a cube levels off to a constant value of 

1.67. That of a sphere approaches 0.92. In general, the drag coefficients of simple shapes tend to 


approach a constant value as Mach number increases. This tendency, known as Mach number 

independence, is well documented in aeronautics [2]. However, Mach number independence does not 

mean that models of meteors traveling at arbitrarily high Mach numbers should use a constant drag 

coefficient. At sufficiently high speeds, enough heat is generated to dissociate the air molecules 

surrounding a meteor. This changes the fluid properties of the air which, in turn, affects the drag 

coefficient [1]. Thus, our Mach-dependent drag coefficient is most applicable to a meteor’s ‘dark flight’, 

which commences when a meteor’s speed drops below Mach 10 [4] [20] [14]. At speeds greater than 

this, one must consider energy losses via radiation and ablation in the equations of motion. [7] [8] 

 We implement the Mach-dependent drag coefficients in a two-dimensional projectile motion 

calculation. Input parameters include the meteor’s altitude, its velocity (speed and angle), its final (postablation) mass and the drag coefficient CD(M) of the object. Our model uses the fourth order RungeKutta method to solve the differential equations of motion, 

x

_   >'f 

x

_

c

_

(3)

  fb  >-

f 

c

_

Figure 1. Drag coefficients as a function of Mach num r a sphere and a cube. Our best fit functions for a 

sphere and a cube (equations 1 and 2) are plotted along with experimental data [9] [11] [12]. Also shown are more 

current numerical results for a cube [15]. 

(4)

where x is the horizontal position along the direction of flight, y is the vertical position of the bolide, m

is the mass of the bolide, FD,x is the force due to drag in the x-direction (= 1⁄2CD(M)Acosv2

) and 

likewise for the y-direction, v is the speed of the object, A is the cross-sectional area of the meteoroid, 

is the angle of the velocity vector with respect to horizontal, and  is the density of air. Atmospheric 

density, temperature, and pressure are calculated as a function of altitude using the U.S. 1976 Standard 

Atmosphere [13]. We emphasize that this expression for the drag force is appropriate for an object that 

is in dark flight (velocity less than about Mach 10). 

ber fo


3 R

e idealized case of a sphere. This allows us to calculate the exact 

, using our Mach-dependent drag coefficient for a sphere. We compare this to the landing 

Figure 2. Landing ellipses for a meteor with Neuschwanstein parameters (see text). The length of the black ellipse is 

bound by the Mach-dependent drag coefficients CD(M) for a sphere and cube (equations 1 and 2). The gray ellipse is 

bound by using a constant drag coefficient of 0.7 and 1.6. roid of the Mach-dependent calculation is shifted 

esults 

We begin by applying the model to th

landing site

position calculated using a constant low-Mach drag coefficient for a sphere of 0.464. 

 For the initial angle, speed, and altitude of this bolide, we use the values measured for the 

Neuschwanstein main body fragment as observed just before dark flight. We chose this meteor because 

it erties were very well measured by the European Fireball Networ s prop k: studies of this event 

determined an angle of 49.23° ± 0.07° measured from the horizontal, a speed of 3.1 ± 0.8 km s-1, and an 

altitude of 16.06 ± 0.05 km [19] [17]. The mass of the Neuschwanstein main body fragment is estimated 

to be 15 kg [17]. We will refer to these as the ‘Neuschwanstein parameters’ in the discussion that 

follows. 

 When the drag coefficient of this spherical meteor is kept constant at its low-velocity value of 

0.464, the drag force is greatly underestimated. The sphere is predicted to land approximately 1880 m 

further downrange compared to the result obtained with the Mach-dependent drag coefficient given in 

Equation 1. 

We did the same analysis for a cube-shaped meteor. The landing site computed with the Machdependent drag coefficient given in Equation 2 lands about 806 m further uprange than that calculated 

with a constant drag coefficient for a cube of 1.094. The cube is less affected because its greater drag 

causes it to spend more time with a CD closer to its low-Mach value. The sphere, on the other hand, stays 

at high speeds longer, and thus spends more time with a CD that is much greater than its low-Mach 

value. The more aerodynamically-shaped the object, the more important is the use of a Mach-dependent 

drag coefficient. 

 In Figure 2, we show the landing ellipses for a meteor coming in from the left. The landing 

ellipse is the area in which the resulting meteorite is likely to fall, and is determined by uncertainties in 

th teor’s motion, shape and mass. This meteor has Neuschwanstein parameters as described above. e me

 The cent

uprange by approximately 150 m; the area of the constant-drag ellipse is 1.36 times that of the CD(M) ellipse. 


The ry, 

det he 

n 

ur Mach-dependent drag model to constrain the search ellipse for real meteors, the 

hat the object will be less aerodynamic than a sphere and more aerodynamic than a cube. 

 vertical axis of the ellipse is perpendicular to the meteor’s velocity. Its units are arbitra

ermined in practice by crosswinds and uncertainty in the meteor’s position and velocity. T

horizontal axis is parallel to the meteor’s flight. The gray ellipse is calculated with constant values for 

CD and the black ellipse is calculated using our CD(M) method. The points indicate the positions of the 

centroids of the ellipses. 

 The major axis of the constant CD ellipse is determined by the low and high drag estimates for a 

meteor, 0.7 and 1.6, respectively. The value of 1.6 is that of a cube at high Mach numbers [23], which 

we assign to be the upper limit. A CD of 0.7 is the low-Mach value from Ceplecha [6], which we use 

here as a lower limit on the drag coefficient. 

 The length of CD(M) ellipse is bound by the CD(M) functions for a sphere and cube (Equations 1 

and 2). The centroid of the CD(M) ellipse is shifted approximately 150 m uprange from the centroid of 

the constant-drag ellips . The area of an ellipse is e 	ab, where a and b are the semi-major and semi-minor 

axes, and thus the ratio of the two areas is the ratio of the semi-major axes (given the same uncertainty 

in semi-minor axes). The area of the landing ellipse calculated using constant values for drag is about 

1.36 times greater than the area of the one bound by our Mach-dependent drag coefficients for spheres 

and cubes. 

4 Discussio

When using o

assumption is t

Our discussion here also implicitly assumes that the irregularly-shaped object will have a Machdependent drag coefficient that follows the same trend as that for spheres and cubes (i.e. a decrease in 

drag coefficient as the object slows through the transonic regime). 

 The Neuschwanstein bolide was a deeply-penetrating fireball that entered dark flight at an 

altitude of just over 16 km. Dark flight often begins at much higher altitudes. A recent example is the 

Bunburra Rockhole meteorite, which began dark flight at an altitude of 30 km [20]. In these types of 

falls, the altitude introduces more time for drag to operate, which means a substantially larger search 

area, regardless of what method is used to calculate it. Thus, constraining the search area even by 27% 

(from the example of the Neuschwanstein fireball) can be helpful to meteorite hunters. 

 We conducted an exploration of parameter space to determine what meteors would be most 

affected by our Mach-dependent drag coefficient. Not surprising, the Mach-dependent drag was more 

im nt for bolides that entered dar porta k flight at higher altitudes and at shallower angles. The mass had a 

less dramatic effect: only for masses smaller than 1 kg did the landing ellipse change substantially. The 

speed also had an important influence on the landing ellipse. We show a plausible scenario in Figure 3, 

in which we constrain the landing site of a (non-ablating) meteor with a mass of 15 kg, at an altitude of 

36 km, a speed of 7.1 km s-1, and an angle of 29° measured from the horizontal. (We chose a velocity 

higher than the 3 km/s upper limit on the non-ablative phase of dark flight to force the meteor to spend 

more time in the hypersonic regime where CD does not vary as much. Meteors with lower initial speeds 

will have more of their flight take place in the M < 5 regime where the CD varies significantly.) In this 

case, the areas of the landing ellipses calculated with the constant-drag method and our method have the 

same ratio (about 1.36). However, the centroid of the ellipse found with our method is about 1.4 km 

uprange, and this ellipse is no longer entirely contained within the constant-drag ellipse (see Figure 3). 


Figure 3. Landing ellipses for a hypothetical but plausible meteor. The length of the black ellipse is b d by the 

When a meteor has been observed and successfully recovered, one can empirically derive a 

nstan

 Conclusions 

he drag coefficient, CD, is an important parameter in determining the landing site of observed meteors, 

 a function of Mach number from 

oun

Mach-dependent drag coefficients CD(M) for a sphere and cube (equations 1 and 2). The gray ellipse is bound by 

using a constant drag coefficient of 0.7 and 1.6. The centroid of the Mach-dependent calculation is shifted uprange 

by approximately 1400 m; the area of the constant-drag ellipse is 1.36 times that of the CD(M) ellipse. 

co t drag coefficient that reproduces the known landing site. However, this technique has no 

predictive power. It is unlikely that the same constant CD will work in a model of any other meteorite 

with different initial conditions, even if it has similar mass and shape. A difference in angle, speed, and 

starting altitude will affect the amount of time it spends in the high vs. low Mach/drag regimes. Instead, 

a Mach-dependent drag coefficient, similar to equations 1 and 2, can derived for meteorites that have 

been recovered after observed falls. 

5

T

but the value for CD is notoriously elusive. Aerodynamic studies of regular shapes (spheres and cubes) 

reveal that an object’s speed affects its drag coefficient as much as its shape does. This trend likely holds 

true for irregularly-shaped objects such as meteorites. All but the most oddly-shaped meteoroids likely 

have shapes such that their aerodynamic properties cause them to suffer less drag than cubes and more 

drag than spheres of the same mass traveling at the same speed. 

 We have derived functions for drag coefficients as

experimental data for spheres and cubes. These functions can be readily implemented into any model for 

meteor trajectories that currently uses a constant value for the drag coefficient. Dark flight trajectories 

and landing ellipses were then computed using these drag coefficient functions, and compared to those 

computed using constant drag coefficients. The landing ellipses bound by spheres and cubes is smaller 

compared to those calculated using constant drag coefficients from 0.7 to 1.6. We also find that the 

centroids of the ellipses are shifted uprange, sometimes by more than 1 km. 


 More work must be done to understand the changes in drag coefficients due to the dissociation of 

ach-dependent drag 

cknowledgements 

he authors thank the US National Science Foundation for supporting RTC and PSJ via a Research 

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A

T

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23. Zhdan, I.A., Stulov, V.P., Stulov, P.V., Turchak, L.I., Solar System Research, 41, 505 (2007) 


The Trajectory, Orbit and Preliminary Fall Data of the JUNE BOOTID 

Superbolide of July 23, 2008 

N. A. Konovalova1

• J. M. Madiedo2• J. M. Trigo-Rodriguez3

Abstract The results of the atmospheric trajectory, radiant, orbit and preliminary fall data calculations 

of an extremely bright slow-moving fireball are presented. The fireball had a -20.7 maximum absolute 

magnitude and the spectacular long-persistence dust trail (Fig 1 and 2) was observed in a widespread 

region of Tajikistan twenty eight minutes after sunset, precisely at 14h

 45m 25s UT on July 23, 2008. The 

bolide was first recorded at a height of 38.2 km, and attained its maximum brightness at a height of 35.0 

km and finished at a height of 19.6 km. These values are very much in line with other well-known 

fireballs producing meteorites. The first break-up must have occurred under an aerodynamic pressure 

Pdyn of about 1.5 MPa, similar to those derived from the study of atmospheric break-ups of previously 

reported meteorite-dropping bolides. Our trajectory, and dynamic results suggest that one might well 

expect to find meteorites on the ground in this case. The heliocentric orbit of the meteoroid determined 

from the observations is very similar to the mean orbit of the June Bootid meteor shower, whose 

parental comet is 7P/Pons-Winnecke (Lindblad et al. 2003). If the parent was indeed a comet, this has 

implications for the internal structure of comets, and for the survivability of cometary meteorites.

Keywords fireball · meteoroid · atmospheric trajectory · radiant · orbit · fall data

1 Introduction

On July 23, 2008 at 14h

 45m 25s UT, two minutes after sunset, an extremely bright slow-moving fireball 

and the spectacular dust trail that it left behind were witnessed by numerous casual witnesses in a 

widespread region of Tajikistan. The area from which it was seen was within a radius of about 300 km. 

The sky in the area of the fireball was completely clear. The event was bright enough to be recorded by 

video and photo cameras, and, therefore, the time of the fireball passage is reliable derived from these 

observations. The intensity of the flash was so great that at about 100 km from the epicenter it was 

possible to be noticed by persons through the windows inside rooms. The majority of the eyewitnesses 

agree that suddenly the fireball became very bright. Some observers reported intense sounds, such as 

“cracking” and “thunder” just after the fireball appearance. A sonic boom probably associated with the 

bolide fragmentation at the height of the brightest flare was heard as far as 100 km away from the burst 

location. Many witnesses watched the resulting dust trail, which was perceptible for about 20 minutes 

 

N. A. Konovalova ( ) 

Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan, Bukhoro, str. 22, Dushanbe 734042, Tajikistan. E-mail: 

nakonovalova@mail.ru. 

J. M. Madiedo 

Facultad de Ciencias Experimentales. Universidad de Huelva. 21071 Huelva, Spain 

J. M. Trigo-Rodriguez 

Institute of Space Sciences (CSIC-IEEC). Campus UAB, Facultat de Ciències, Torre C5-p2. 08193 Bellaterra, Spain 


Figure 1. The trail of the July 23, 2008 fireball 

from HisAO (Tajikistan). The photograph by U. 

Hamroev was taken at 14:45 UT 

Figure 2. The trail of the July 23, 2008 fireball 

from Vose (Tajikistan). The photograph by M. 

Ahmetzyanov was taken at 14:58:58 UT 

and was expressive distorted by the atmospheric winds. The trail of the fireball was very bright 

exhibiting a blue-white and on the end orange-red colors. The fireball was observed by a visible-light 

satellite system which detected a brightest path of fireball light. The total radiated energy was 2 × 1011 J, 

which is equivalent to a total released energy of about 0.05 kT (Brown 2008). The fireball’s flare 

reached an absolute magnitude of -20.7 putting it in the superbolide category. One day after the event 

we interrogated inhabitants and a few witnesses have furnished numerous photographs of the dust trail 

of which two double-station photographs (baseline of 11.3 km) fortunately were taken immediately after 

the flight of fireball, showing clear references for being calibrated. The trajectory of the fireball was in 

fact photographed only during the later stages of its path. The terminal point of the fireball can be seen 

close to the western horizon. 

2 Data Obtained 

On the basis of two available double-station records (baseline of 11.3 km) the astrometric calibration of 

the fireball apparent trajectory in reference to the stars was made following the standard procedure and 

method described in (Katasev 1966). The procedure to obtain the astrometric measurements was based 

on the use of a Zeiss Ascorecord device. Measuring the rectangular coordinates of the positional stars 

and any feature point (beginning, terminal, and all flares and depressions) on the fireball trail, such 

measurements were converted to equatorial coordinates by using the astrometric method of the 

METEOR software package developed by the Meteor department (Institute of Astrophysics, Tajikistan). 

As a result of the astrometric measurements we were able to determine the fireball atmospheric 

trajectory, radiant, velocity, and orbit. The exact duration of the fireball was known from the data of a 

visible-light satellite system (Brown 2008). The fireball was first recorded at a height, Hb of 38.2 ± 0.5 

km when the velocity, vb was 14.3 ± 0.5 km/s. The fireball traveled a 19-km observed luminous 

trajectory and terminated its light at a low altitude He of 19.6 ± 0.5 km when the fireball decelerated to 

5.8 ± 0.5 km/s. The slope of the trajectory was extremely steep - the zenith distance of the radiant was 

only of about 10° and the difference between the beginning and the terminal height was 18.6 km. The 


brightest flare was near the beginning of the trajectory at the height Hmax = 35.0 ± 0.5 km when the first 

break-up must have occurred under an aerodynamic pressure Pdyn of about 1.5 MPa. At the heights of 

other two small flares the aerodynamic pressure was 2.9 MPa and 3.1 MPa respectively. The apparent 

radiant was in Bootes, which suggest that the bolide belongs to the J.Bootid meteor shower. The 

resulting data on the atmospheric trajectory and coordinate of radiant, calculated by software METEOR 

are given in Table 1 and Table 2. 

 Table 1. Atmospheric trajectory data 

 Beginning Maximum light Terminal 

Velocity (km/s) 14.3 ± 0.5 13.1 ± 0.5 5.8 ± 0.5 

Height (km) 38.2 ± 0.5 35.0 ± 0.5 19.6 ± 0.5 

Abs. magnitude - - 20.7 - 

Table 2. Radiant data 

Radiant (J2000.0) Observed Geocentric Heliocentric 

R (deg) 221.83 ± 2.1 219.52 ± 2.1 - 

R (deg) +32.40 ± 2.1 +30.95 ± 2.1 - 

initial velocity v
 (km/s) 16.0 11.6 38.5 

In order to obtain an accurate orbit, it is necessary for the fireball to be observed from multiple 

stations. In spite of the presence of only two records of the 23 July, 2008 fireball, the resulting data have 

a good accuracy. The initial (pre-atmospheric) velocity, v
 = 16 km/s was used for the meteoroid orbit 

computations. The resulting elements of the heliocentric orbit for the equinox 1950.0, calculated by 

software METEOR are given in Table 3. 

Table 3. Orbital data 

Orbit (J2000.0) 

Semimajor axis (AU) 3.32 

Eccentricity 0.694 

Perihelion distance (AU) 1.015 

Aphelion distance (AU) 5.624 

Argument of perihelion (deg) 176.76. 

Ascending node (deg) 119.709 

Inclination (deg) 11.95° 

These orbital results were also tested by using the software of the Spanish Fireball Network (SPMN). It 

is remarkable that the computed orbit is very similar to the mean orbit of the June Bootid meteor shower 

(Lindblad et al. 2003). Both the %-criterion of Southworth and Hawkes (Southworth and Hawkes 1963) 

and Drummond (Drummond 1981) were applied to the obtained orbit (DSH = 0.114 and DDr = 0.082). 

The meteoroid, with a mass of about 24 tons and a kinetic energy, possible in the order of 0.5 – 0.6 kt 

(personal communication Dr. O. Popova) entered the Earth’s atmosphere with velocity of about 16 km/s. 

Penetrating deeply into the atmosphere, the aerodynamic pressure increased progressively on the front 


part of the body. At a height of 35 km the pressure on the surface reached 1.4 MPa causing the fracture 

of the body, so its mass started to break and crumble. Among the relatively few documented cases of 

collisions with bodies of such a great mass, this is a remarkable event because the body, probably of 

cometary origin, penetrated deeply into atmosphere and probably dropped meteorite. We hope to have 

the chance of recovering meteorites from this event occurred over an inhabited region. 

3 Data of Dark Flight 

The dark flight was simulated by using the standard procedure described in (Ceplecha 1987). The 

deceleration at the terminal point of the trajectory obtained from the estimated values of fireball velocity 

vs. height was -7.6 km/s2

, with a trajectory inclination of about 80o. The simulation was performed by 

taking into account the modeled atmospheric conditions (provided by the British Atmospheric Data 

Center) with a software package developed by the Spanish Meteor Network (SPMN) which uses a 

standard Runge-Kutta calculation procedure. Spherical shape was assumed and a value of the drag factor 

at the terminal point of 0.58 was used. Under these conditions, the terminal mass of the meteoroid, 

which depends on its density, would vary from 1.5 ± 0.3 kg (d = 3.7 g/cm3

) to 4.2 ± 0.3 kg (d = 2.2 

g/cm3

). Most of the surroundings near of the impact area are covered by agricultural fields, without 

stones or rocks that would complicate meteorite searches, as the soil consists basically of clay. Thus the 

favorable circumstances of an almost vertical fireball trajectory and favorable countryside give a hope of 

successful search of the meteorite. At present, the search of additional and more detailed data is in 

progress and expeditions to the impact area will be organized in short in order to try to find the 

meteorite. 

Acknowledgements

We are grateful to Dr. O. Popova for the presentation our work at the conference METEOROIDS 2010. 

We are grateful to all the witnesses of the fireball of July 23, 2008 who volunteered their observations, 

and especially to those who offered photographs of the fireball. 

References

P. Brown, htpp://astroalert.su/files/bolide, (2008) 

Z. Ceplecha, Astronomical Institutes of Czechoslovakia, Bulletin 38, (1987) 

J.D. Drummond, Icarus, 45, 545, (1981). 

L.A. Katasev, Investigations of the meteors in the Earth’s atmosphere. L.:Gidrometeoizdat ,336, (1966) 

B.A. Lindblad; L. Neshisan; V. Porubcan; J. Svoren, Earth, Moon and Planets, 93, 4, 249, (2003) 

R.B. Southworth, G.S. Hawkes, Smith. Contrib. Astrophys., 7, (1963) 


Infrasonic Detection of a Large Bolide over South Sulawesi, Indonesia on October 8, 

2009: Preliminary Results 

E. A. Silber1• A. Le Pichon2• P. G. Brown1

Abstract In the morning hours of October 8, 2009, a bright object entered Earth's atmosphere over 

South Sulawesi, Indonesia. This bolide disintegrated above the ground, generating stratospheric 

infrasound returns that were detected by infrasonic stations of the global International Monitoring 

System (IMS) Network of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) at 

distances up to 17 500 km. Here we present instrumental recordings and preliminary results of this 

extraordinary event. Using the infrasonic period-yield relations, originally derived for atmospheric 

nuclear detonations, we find the most probable source energy for this bolide to be 70 ± 20 kt TNT 

equivalent explosive yield. A unique aspect of this event is the fact that it was apparently detected by 

infrasound only. Global events of such magnitude are expected only once per decade and can be utilized 

to calibrate infrasonic location and propagation tools on a global scale, and to evaluate energy yield 

formula, and event timing. 

Keywords infrasound · bolide · fireball · airburst · impact 

1 Introduction 

Medium sized Near Earth Objects (NEOs) (>10 m diameter) may penetrate deep into the atmosphere, 

though rarely, and cause significant damage on the ground (Chapman, 2008) and could potentially 

perturb regional climate trends (Toon et al. 1997). However, currently available models cannot 

accurately define the critical impactor size at which the regional climate is affected (Bland and 

Artemieva, 2003). A part of the problem is limited observational data, as records of significant NEOs 

are scarce. Therefore, various observational methods, including infrasound, are critical to re-evaluate 

airburst models and determine with more accuracy the size at which an object can influence the local 

climate. 

Records of significant NEO impacts are rare. Klekociuk et al. (2005) and Arrowsmith et al. 

(2008) report multi-instrumental observations of two different impactors with energies of 20-30 kilotons 

of TNT (1 kT = 4.185×1012 J) occurring in the fall of 2004, while Brown et al. (2002) present infrasound 

data for two somewhat less energetic events over the Pacific in 2001. In all cases these events occurred 

over open ocean and much of the energetics information was compiled from records of the associated 

airwaves detected by infrasonic stations. 

 

E. A. Silber ( ) • P. G. Brown 

Department of Physics and Astronomy, University of Western Ontario, London, ON N6A 3K7, Canada. Phone:1-519-661-2111 x82385; 

Fax:1-519-661-2033; E-mail: elizabeth.silber@uwo.ca 

A. Le Pinchon 

CEA/DAM/DIF, F-91297 Arpajon, France


 Infrasound is low frequency sound extending below the 20 Hz hearing threshold of the human 

ear and just above the natural oscillation frequency of the atmosphere (>0.01 Hz, Brunt-Väisälä 

frequency). It has the ability to propagate over long distances with very little attenuation, thus enabling 

the study of remote explosive sources (Hedlin et al., 2002). The International Monitoring System (IMS), 

operated by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO), features as one of its 

monitoring technologies, a global network of 42 fully certified infrasonic stations designed to detect 

nuclear explosions (CTBTO web: http://www.ctbto.org). 

 Bright meteors (also known as fireballs) fall into the category of events that can be detected and 

consequently studied using infrasound (ReVelle, 1976, 1997; Brown et al., 2002a). Fireballs are 

produced by large meteoroids which may penetrate deep into the atmosphere and generate a cylindrical 

blast wave during their hypersonic passage, which decays to low frequency infrasonic waves that 

propagate over great distances (ReVelle, 1976; Edwards, 2010; Le Pichon et al., 2002a, Brown et al., 

2002; Brown et al., 2003). Global impacts detected infrasonically can provide a valuable tool in the 

estimation and validation of the influx rate of meter sized and larger meteoroids (Brown et al. 2002; 

Silber et al. 2009). Very often, infrasound offers the only available record when it comes to major 

impacts over open ocean. Infrasound observations can provide crucial trajectory and energetics 

information for interesting events which otherwise lack such information (e.g. the Carancas crater 

forming impact in Peru in 2007 (Brown et al., 2008; Le Pichon et al., 2008)). Here we present evidence 

that a significant NEO impact occurred on October 8, 2009 over South Sulawesi, Indonesia based 

primarily on infrasonic recordings of the blast wave detected across the globe; this may have been one 

of the most energetic impactors to collide with the Earth in recent history. 

2 The Indonesian Bolide 

At 2:57 UTC (10:57 a.m. local time) on October 8, 2009 a loud rumbling sound and ground shaking 

startled the people of the town of Bone, South Sulawesi, Indonesia (4.5oS, 120oE). Eyewitnesses who 

ran out their homes in fright saw a very bright object flying across the sky, subsequently disintegrating 

in the mid air, leaving a thick dusty smoke trail behind (Surya news report, in Indonesian: 

http://www.surya.co.id/2009/10/09/ledakan-misterius-guncang-sulsel.html). A news article stated that 

there are reports from local residents that the surviving remnants of the object may have crashed into the 

sea (Surya news report, in Indonesian: http://www.surya.co.id/2009/10/09/leda kan-misterius-guncangsulsel.html). 

Shortly thereafter, the national media, including Metro TV of Jakarta and two news agencies, 

The Jakarta Globe and The Jakarta Post, released a number of reports, including an amateur video of the 

smoke trail (Figure 1). Features and the appearance of the smoke trail are consistent with dust trails of 

other fireballs observed in a similar manner (e.g. the Tagish Lake fireball (Hilderbrand et al, 2006)), 

indicating a probable meteoritic origin of the event. As per The Jakarta Globe, the airburst caused 

damage to several houses in Panyula village (The Jakarta Globe, available at: http:// 

www.thejakartaglobe.com/home/astronomer-sulawesi-blast-bigger-than-atom-bomb-and-caused-by-met 

eorite/338073) and the police department in Bone was flooded with reports of audible sounds extending 

as far as 11 km from Latteko, Bone district, South Sulawesi (The Jakarta Globe: available at: 

http://thejakartaglobe.com/home/mysterious-explosion-panics-locals-in-south-sulawesi-police-stillinvestigating/334246). Unfortunately, there was one casualty, a 9 year old girl with an underlying heart 

condition who went into cardiac arrest upon hearing the thunderous sounds (The Jakarta Globe, 

available at: http://www.thejakartaglobe.com/home/astronomer-sulawesi-blast-bigger-than-atom-bomb-


and-caused-by-meteorite/338073). Initially, local people speculated that the event was caused by a 

falling airplane; however, South Sulawesi Police spokesman Sr. Comr. Hery Subiansauri confirmed that 

no aircraft was involved nor any other air incident had occurred. The extraterrestrial nature of the event 

was confirmed by Thomas Djamaluddin, head of the Lapan Center for Climate and Atmosphere Science 

(The Jakarta Post, available at: http://www.thejakartapost.com/news/2009/10/08/blast-may-be-resultfalling-space-waste-or-meteorite-lapan.html). 

Upon scrutinizing scrutinizing these reports, we undertook a thorough investigation of infrasonic 

records of all IMS infrasound stations to search for possible signals from the air explosion. 

Figure 1. A screenshot from Metro TV news report showing an amateur video of the smoke trail, twisted by the 

wind (You Tube, available at: http://www.youtube.com/watch?v=yeQBzTkJNhs&videos=jkRJgbXY-90). 

3 Data Processing and Analysis 

We were able to examine a total 31 infrasound stations in the IMS network which were providing data at 

the time of the event. Probable signals originating from 4.5°S, 120°E were detected at 17 IMS stations 

(Figure 2), which we correlated with the event. Table 1 summarizes data from all stations which 

detected the signal, sorted by distance. The signal was extraordinary in two aspects: first, it was detected 

by many infrasound stations, some of which are at extreme distances (>17,000 km), and second, that 

most of the signal energy is contained in very low frequencies, indicative of a source yielding very high 

energy. Infrasonic signals were analyzed using two independent methods, Matseis 1.7 (Harris and 

Young, 1997; Young et al., 2002) and Progressive Multi-Channel Correlation Method (PMCC) (Cansi, 

1995). 

First, infrasound data across each station have been array processed in windows (typically of 30-

60 second length) to search for coherent signals with consistent back-azimuth measurements for several 

adjacent windows using the analysis package Matseis 1.7 (Harris and Young, 1997; Young et al., 2002). 

To determine the arrival azimuth for a coherent signal, we used the standard method of cross-correlating 

the output between each sensor of an array and performed beamforming of the signals across the array 


Figure 2. A global map (courtesy of CTBTO, web: http://www.ctbto.org) showing all stations (black circles) that 

detected the Indonesian bolide event circled in red. 

Table 1. Summary of all detections, sorted by distance. We include results for two methods of signal detection 

(MatSeis and PMCC). 

Distance 

(km) Station ID

Latitude 

(deg)

Longitude 

(deg)

True Back 

Azimuth (deg)

Observed 

Back 

Azimuth 

(deg) Arrival time

Signal 

Duration 

(s)

Minimum 

Celerity 

(m/s)

Maximum 

Celerity (m/s)

Peak-topeak 

Amplitude 

via PMCC 

(Pa)

Peak-topeak 

Amplitude 

via 

MatSeis 

(Pa)

Period at 

max 

Amplitude 

via PMCC 

(s)

Period at 

max PSD 

via 

MatSeis 

(s)

Period at 

max 

Amplitude 

via 

MatSeis 

(s)

2099 I39PW 7.5 134.5 230 264 04:39:51 1235 283 340 ... 1.57 ... 13.65 14.87

2291 I07AU -19.9 134.3 316 318 04:55:46 850 287 320 2.823 3.091 6.96 7.88 5.79

3350 I04AU -34.6 116.4 7 9 05:59:18 1370 271 305 0.471 0.526 5.36 7.31 7.11

4920 I30JP 35.3 140.3 210 211 07:33:43 1280 280 302 0.642 0.6077 25.60 7.88 7.89

5009 I05AU -42.5 147.7 319 319 07:37:01 690 280 292 0.542 0.874 10.50 29.26 25.23

5386 I22FR -22.2 166.8 284 285 07:45:08 1340 290 312 0.165 0.127 5.30 20.48 21.07

5543 I45RU 44.2 132.0 196 197 08:04:54 1450 278 300 1.192 1.1873 10.70 17.07 19.79

7296 I46RU 53.9 84.8 222 224 09:46:19 1490 281 298 0.803 ... 15.20 ... ...

7323 I44RU 53.1 157.7 141 141 09:49:46 2450 268 294 0.363 0.7896 6.99 18.62 18.29

8577 I55US -77.7 167.6 311 305 10:55:07 1060 289 299 0.168 0.145 12.10 17.07 17.62

10573 I53US 64.9 -147.9 270 270 12:49:47 830 291 297 0.488 0.418 12.70 12.80 14.66

11594 I26DE 48.8 13.7 80 80 14:28:51 185 278 279 0.04 ... 5.48 ... ...

11900 I18DK 6.7 -4.9 350 340 14:15:26 1100 284 292 0.693 0.645 18.10 25.60 21.81

12767 I56US 48.3 -117.1 293 322 14:54:45 1520 286 292 0.765 0.764 14.70 13.65 11.83

13636 I13CL 15.3 -23.2 244 240 16:26:53 1310 273 281 0.618 0.606 12.10 11.38 11.31

13926 I17CI -33.7 -78.8 91 87 17:05:34 615 270 274 0.128 0.1347 12.10 9.31 8.64

17509 I08BO -16.2 -68.5 203 218 18:54:45 30 ... 305 ... 0.933 ... 17.07 16.34


(Evers and Haak, 2001). A sample output is shown in Figure 3. In total 15 positive detections were 

identified in this way, using the approximate location and timing from media reports and expected 

typical stratospheric propagation speeds as a guide to isolate the period of most probable signal arrival 

on each array. This procedure was repeated for multiple bandpasses to try and isolate any coherent 

signal from the station noise. 

Figure 3. An example of signal observed at I45RU, located 5543 km from the source. The top window is the Fstatistic, a measure of the relative coherency of the signal across the array elements in any particular window, the 

second window represents the apparent trace velocity of the acoustic signal across the array in the direction of the 

peak F-stat, while the third window shows the best estimate for the signal back-azimuth in the direction of 

maximum F-stat for each window. The fourth window shows the bandpassed raw pressure signal for one array 

element. 


The second method, PMCC, for analysing the data, sensitive to coherent signals with very low 

signal-to-noise ratio (SNR), yielded positive detections at a total of 16 IMS stations. This technique has 

been successfully implemented in detections of other bolides (cf. Arrowsmith et al., 2008), as it searches 

for coherent signals in both frequency and time windows, selecting detections of similar parameters to 

identify coherent signals (Brachet et al., 2010) (Figure 4). 

Figure 4. Results from array processing using the PMCC algorithm for the IMS station I45RU. The top window 

gives the observed azimuth, while the middle window represents the trace velocity of the signal. The bottom 

window shows the bandpassed raw pressure signal for one array element. 

 We have also established a geolocation using the nine closest stations (Figure 5) by utilizing a 

non-linear system of equations describing the propagation of the detection waves through the 

atmosphere, where the inverse location algorithm is based on Geiger's approach (1910). The location 

results are obtained assuming a homogeneous half-space with a typical celerity value of 290 m/s for 

each individual phase without azimuthal correction (Brown et al., 2002). In order to determine the 

location errors, the 95% confidence ellipses are estimated by repeatedly running the linearized leastsquares inversion with arbitrary sub-sets of the input data within ±10° and ±30 m/s ranges of 

uncertainties for the azimuths and celerity, respectively. 

The maximum peak-to-peak amplitude was determined by bandpassing the stacked, raw 

waveform using a second-order Butterworth filter and then applying the Hilbert Transform (Dziewonski 

and Hales, 1972) to obtain the peak of the envelope. The filter cutoff frequencies were typically 0.05 Hz 

for the low frequency and up to 2.1 Hz for the high frequency (with few exceptions) and were 


determined using a power spectral density (PSD) method where the signal segment of the waveform was 

superimposed over the average of the prior and post background noise (of equal length), all being 

divided into equal windows (50-170 seconds in length, depending on station), establishing a frequency 

band which lies above the noise. Therefore, the low and high frequency cutoffs would be selected where 

the signal rises above the noise on the low end or descends into the noise on the high end of the 

spectrum, respectively. 

a) 

b) 

Figure 5. Map showing the geolocation. The best fit solution was obtained using nine stations closest to the 

Indonesian bolide event. 

 To measure the dominant period at maximum peak-to-peak amplitude, two independent 

techniques were employed. First, the dominant period at maximum frequency was acquired from the 

residual power spectral density (PSD) obtained using the method described above, except the noise PSD 

was subtracted from the signal PSD. The inverse of the frequency at maximum residual PSD was used to 

obtain the dominant period. Second, the period at maximum peak-to-peak amplitude was tabulated by 


measuring the zero crossings of the stacked waveform at each station (cf. ReVelle, 1997) in the same 

bandpass. The periods obtained using these two techniques show a very strong 1:1 correlation (Figure 

6), indicating that this methodology is robust in itself. 

Figure 6. The dominant period correlation using two methods: PSD (vertical axis) and zero-crossings (horizontal 

axis). 

4 Estimating the Source Energy 

There are several empirical relations, relying on either the period at maximum amplitude or range and 

signal amplitude, which can be utilized in estimating source energy from infrasound measurements 

(Edwards et al., 2006). The yield estimates based on infrasonic amplitude are very uncertain in this 

instance as the propagation distances are much larger than is typical and outside the range limits where 

such relations have been developed (Edwards et al, 2006). In general, infrasonic period is less modified 

during propagation than amplitude (cf. Mutschlecner et al., 1999; ReVelle 1997; ReVelle 1974) and thus 

the period relationship is expected to be more robust. The Air Force Technical Application Centre 

(AFTAC) period-yield relations which are commonly used for large atmospheric explosions, are given 

by ReVelle [1997], as: 


log(E / 2) 
 3.34 log(P) 2.58 E / 2 F 100kt (1) 

 (2) log(E / 2) 
 4.14 log(P) 3.61 E / 2 7 40kt

Here, ? is the total energy of the event (in kilotons of TNT), @ is the period (in seconds) at maximum 

amplitude of the waveform. Since these relations were originally derived from nuclear explosions, the 

factor 1⁄2 must be incorporated in order to account for energy loss due to radiation for low altitude 

nuclear airbursts (Glasstone and Dolan, 1977). Even though there are a number of effects that may 

adversely influence and change the period at maximum amplitude during long range propagation of 

infrasound, this approach remains more robust than the maximum amplitude based relations, since it 

shows better agreement with energy estimates for bolide events which had their energies estimated by 

other methods (Silber et al, 2009; Brown et al., 2002). 

5 Results and Discussion 

There are total of 17 detections, 16 obtained with PMCC and 15 obtained with MatSeis (Table 1). These 

detections overlap, except for the signal detected via MatSeis at the Bolivian station (I08BO), 17 509 km 

from the source. This signal, though very weak and short in duration (~30 seconds) compared to other 

signals (>185 seconds), shows a strong correlation to the bolide. The correlation indicators are the 

arrival time, the signal velocity, the dominant period and the apparent agreement between the observed 

and expected azimuth. The first arrival was detected almost two hours after the event at the closest IMS 

station, I39PW, at 04:39:51 UTC, while it took nearly 15 hours for the last bits of the signal to arrive to 

I08BO. Duration of the signal at each station (not including I08BO) was quite significant, ranging from 

3 minutes up to 41 minutes. All infrasound signals from the event show similar characteristics, such as 

long period and very low frequency content, consistent with a large blast radius and consequently a large 

energy source (ReVelle, 1976). Furthermore, average signal celerities are between 270 m/s and 320 m/s, 

indicative of stratospheric duct signal returns. 

 The presence of high altitude winds affects the propagation of the signal in such way that it 

amplifies the downwind propagation, while it attenuates upwind propagation (c.f. Mutschlecner and 

Whitaker, 2010; Davidson and Whitaker, 1992; Reed 1969a). Most of the detecting stations are located 

east from the source and in October the stratospheric winds are predominantly westerly in the northern 

hemisphere (Webb, 1966). Average signal celerities (defined by the ratio between the horizontal 

propagation range and the travel time) are between 0.27 and 0.32 km/s, which is consistent with 

stratospheric duct signal returns. We also searched for possible antipodal signals, but found none. 

 The geolocation ellipse (Figure 5), computed using azimuths and arrival times, points to 4.9°S 

and 122.0°E with mean residuals of 2.9°. The source time estimated from this location is 02:52:22 with 

a residual of 1320 s. The accuracy of the source location strongly depends on the atmospheric wind and 

temperature profiles at the place and time of the event. 

 To establish the best possible energy estimate of the Indonesian bolide, the average global period 

as well as individual periods, using both previously described zero-crossings and PSD methods, for each 

station were utilized. Table 2 shows the summary of energy estimates. The combined average periods of 

all phase-aligned stacked waveforms at each station produce a global average of 14.8 seconds (zero 

crossings method ) and 15.3 seconds (PSD method), corresponding to a mean source energy of 42.7 kt 

of TNT and 47.3 kt of TNT, respectively. Using the measurements from nine stations with the highest 

signal-to-noise ratio energy yield is 66.1 kt of TNT (zero crossings method) and 78.1 kt of TNT (PSD 


method). The standard deviation of energy measurements across all stations is approaching the 

measurement itself, but this is expected because the signal usually emanates from different portions of 

the bolide trail as observed at different stations. Our best source energy estimate is 70 ± 20 kt TNT, with 

the error bounds representing the spread in the average from the different approaches (Table 2). 

6 Conclusions 

The Indonesian bolide of 8 October, 2009, detected infrasonically on a global scale, was perhaps the 

most energetic event since the bolide of 1 February, 1994 (McCord et al., 1995) and may have exTable 2. List of all detecting stations and their periods measured via two methods (zero-crossings at maximum 

amplitude in time domain and frequency at maximum PSD in frequency domain), as well as energy measurements 

for each station, where appropriate AFTAC relations were used (equation (1) or equation (2)). 

Station ID

Period via 

zero 

crossings 

(s)

Energy (kt 

of TNT)

Period via 

PSD (s)

Energy (kt of 

TNT) Station ID

Period via 

zero 

crossings 

(s)

Energy (kt 

of TNT)

Period via 

PSD (s)

Energy (kt of 

TNT)

IS04 7.11 3.68 7.31 4.05 IS04 7.11 3.68 7.31 4.05

IS05 25.23 312.64 29.26 577.07 IS05 25.23 312.58 29.26 577.07

IS07 5.79 1.85 7.88 5.19 IS07 5.79 1.86 7.88 5.19

IS08 16.34 59.33 17.07 68.61 IS18 21.81 155.65 25.60 332.00

IS13 11.31 17.37 11.38 17.71 IS44 18.29 86.46 18.62 91.75

IS17 8.64 7.06 9.31 9.06 IS45 19.79 112.50 17.07 68.61

IS18 21.81 155.69 25.60 332.00 IS53 14.66 41.30 12.80 26.25

IS22 21.07 138.75 20.48 126.15 IS55 17.62 76.33 17.07 68.61

IS30 7.89 5.22 7.88 5.19 IS56 11.83 20.17 13.65 32.56

IS39 14.87 43.30 13.65 32.56 Average E (kt of TNT) 90.06 134.01

IS44 18.29 86.42 18.62 91.75

IS45 19.79 112.45 17.07 68.61 Energy estimate as a function of SNR (period average)

IS53 14.66 41.25 12.80 26.25 Total 16.88 66.10 14.46 78.11

IS55 17.62 76.29 17.07 68.61

IS56 11.83 20.19 13.65 32.56

Average E (kt of TNT) 72.10 97.69

Total 14.81 42.73 15.27 47.30

Energy estimate as a function of period Energy estimate as a function of SNR

Energy estimate based on averaged global period

ceeded it in total energy. We have no other instrumental records of this event other than casual video 

records of the dust trail emphasizing again the value of infrasonic monitoring of atmospheric explosive 

sources. Low frequency waves were observed at 17 IMS stations of the CTBTO network, making it one 

of the best infrasonically documented events (DTRA Verification Database, available at: 

http://www.rdss.info). 

Using an average impact velocity for Near Earth Objects (NEO) of 20.3 km/s, the energy limits 

(50-90 kt of TNT) suggested by this analysis correspond to an object 8-10 m in diameter. Given our 

upper limit in energy and a lowest possible entry velocity of 11.2 km/s, the upper limit to the mass for 

this meteoroid is < 6000 tonnes. Based on the flux rate from Silber et al. (2009), such objects are 


expected to impact the Earth on average every 10-22 years. Additional instrumental records of this 

unique event would prove valuable in understanding in more detail its interaction with the atmosphere 

and documenting possible local atmospheric perturbations. 

Additional instrumental records of this exceptional event, such as seismic, ground video 

recordings, satellite and possible meteorites, would prove valuable in understanding such occurrences 

and documenting possible local atmospheric perturbations. Since events like this one are rather rare, it is 

essential to maximize all aspects of such observations in order to validate propagation models at global 

scale, implement and better understand the spatial and temporal influences of atmospheric dynamics 

over propagation times, especially over long distances, and to evaluate energy yield formula and 

establish what information, not available via other techniques, can be derived from infrasonic 

measurements. 

Acknowledgements 

EAS and PGB thank the Natural Sciences and Engineering Research Council of Canada and Natural 

Resources Canada, and express their gratitude to the Meteoroid Environment Office of the National 

Aeronautics and Space Administration for funding the Meteoroids 2010 conference. 

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CHAPTER 8: 

RADAR OBSERVATIONS 


Analysis of ALTAIR 1998 Meteor Radar Data 

J. Zinn1• S. Close2• P.L. Colestock • A. MacDonell3• R. Loveland 

Abstract We describe a new analysis of a set of 32 UHF meteor radar traces recorded with the 422 

MHz ALTAIR radar facility in November 1998. Emphasis is on the velocity measurements, and on 

inferences that can be drawn from them regarding the meteor masses and mass densities. We find that 

the velocity vs altitude data can be fitted as quadratic functions of the path integrals of the atmospheric 

densities vs distance, and deceleration rates derived from those fits all show the expected behavior of 

increasing with decreasing altitude. We also describe a computer model of the coupled processes of 

collisional heating, radiative cooling, evaporative cooling and ablation, and deceleration – for meteors 

composed of defined mixtures of mineral constituents. For each of the cases in the data set we ran the 

model starting with the measured initial velocity and trajectory inclination, and with various trial values 

of the quantity ms

2

 (the initial mass times the mass density squared), and then compared the computed 

deceleration vs altitude curves vs the measured ones. In this way we arrived at the best-fit values of the 

ms

2

 for each of the measured meteor traces. Then further, assuming various trial values of the density 

s, we compared the computed mass vs altitude curves with similar curves for the same set of meteors 

determined previously from the measured radar cross sections and an electrostatic scattering model. In 

this way we arrived at estimates of the best-fit mass densities s for each of the cases.

Keywords meteor · ALTAIR · radar analysis 

1 Introduction 

This paper describes a new analysis of a set of 422 MHz meteor scatter radar data recorded with the 

ALTAIR High-Power-Large-Aperture radar facility at Kwajalein Atoll on 18 November 1998. The 

exceptional accuracy/precision of the ALTAIR tracking data allow us to determine quite accurate 

meteor trajectories, velocities and deceleration rates. The measurements and velocity/deceleration data 

analysis are described in Sections II and III. The main point of this paper is to use these deceleration 

rate data, together with results from a computer model, to determine values of the quantities ms

2

 (the 

meteor mass times its material density squared); and further, by combining these ms

2

 values with 

meteor mass estimates for the same set of meteors determined separately from measured radar scattering 

cross sections, to arrive at estimates of the mass densities s. 

 The computer model, described in Section IV and Appendix A, treats the simultaneous processes 

of meteor heating through air molecule collisions, blackbody radiation emission, evaporation, sputtering, 

 

J. Zinn ( ) • P. L. Colestock • R. Loveland 

Los Alamos National Laboratory, Los Alamos, NM. E-mail: jzinn@lanl.gov 

S. Close 

Stanford University, Stanford, CA 

A. MacDonell 

Boston University, Boston, MA 


and deceleration – for meteors of specified assumed initial mixtures of mineral constituents. The model 

assumes in each case that the meteors are spherical, and remain so without fragmenting. It includes an 

imbedded table of atmospheric mass densities vs altitude, and data on (1) vapor pressure vs temperature, 

(2) heat of sublimation, (3) vapor molecular weight, and (4) melting point – for each of the assumed 

constituent species. Other inputs to the model include, for each individual case, (1) the initial meteor 

velocity and trajectory inclination (i.e. at the top of the atmosphere), (2) trial values of the initial ms

2

 

(i.e. values before entering the atmosphere). 

 The data include 32 individual meteor traces, where the meteors all appear to be in the mass 

range 10-6 to 10-4 grams, and the altitudes are such that air molecule collision mean free paths are much 

larger than the meteor dimensions. Thus air molecule collisions with the meteor can be regarded as 

isolated events, and fluid-dynamic effects do not apply (large Knudsen number). In our data analysis we 

fit the reduced data on velocities vs altitude and trajectory inclination as least-squares quadratic 

functions of the path-integrated air column densities, using tabular data on air densities vs altitude. We 

then compute the corresponding deceleration rates. We find, as expected, that for all the traces the 

deceleration rates increase with decreasing altitude. 

 The model equations and variables are listed in Appendix A. Appendix B describes a quasianalytic solution of the ablation equations for a 1-component meteor, using the steady-state 

approximation. It shows that at the lowest altitudes the meteor temperatures are determined mainly by 

an equilibrium between collisional heating and evaporative cooling. And the ablation coefficients tend 

to approach a common value equal to the vapor molecular weight divided by twice the heat of 

vaporization, and independent of the initial meteor velocity. 

2 Experimental

The ALTAIR High-Power-Large-Aperture radar facility is located on the Kwajalein Atoll (9o N, 167o

E) in the Republic of the Marshall Islands. ALTAIR has a 43-m diameter mechanically-steered 

parabolic dish, and simultaneously transmits a peak power of 6 MW at two frequencies (VHF-160 MHz, 

and UHF-422 MHz). (Close et al 2000, Close et al 2004 ). The radar characteristics are described in 

detail in those references. It is particularly suited for precise measurements of small targets at long 

ranges. Extensive measurements going back to 1983 show stable rms tracking accuracies of ±15 millidegrees in angle and ±6 m in range. In the present paper we discuss a UHF data set consisting of 32 

meteor traces obtained on November 18, 1998. The radar sample window encompassed slant ranges 

corresponding to heights mostly between 90 to 110 km. 150 !s pulsed waveforms were used, with a 

range sample spacing corresponding to about 7.5 meters . The instantaneous meteor 3-dimensional 

positions were determined from the monopulse range and angular measurements, and the velocities were 

determined by direct numerical differencing of the positions vs time (Close et al, 2002). 

 In this paper we do not yet make use of a much larger set of ALTAIR meteor data obtained in 

2007 and 2008, or results of an ongoing analysis of these data where line-of-sight velocities are 

determined from measured Doppler frequency shifts of the reflected radar signals (Loveland et al, 2010). 

We expect that the velocities thus determined will be of higher accuracy than those derived from the 

1998 data described in this paper. We will report analyses of the newer results in a later paper. 


3 Data Analysis 

For each of the 32 meteor traces (using the tabulated altitudes, velocities and vertical velocity 

components vs time) we begin by performing a quadratic least-squares fit to the velocities vs the air path 

traversed (Q), where 

Q 3 "z

  ds, (1)

 is the local air density, and ds is the element of distance along the meteor path to the altitude z. The 

’s were taken from the CIRA ’61 tabulations (COSPAR International Reference Atmosphere 1961), 

and the Q integrals were evaluated for each point along each trace using the measured trajectory 

inclination angles. (We will regard these atmospheric density data as given, and note that they are 

probably more accurately determined than are the meteor masses or mass densities that we will derive 

from the radar data). Then from the Q derivative of this fitted quadratic velocity vs Q function we 

compute the corresponding deceleration rates as functions of z. Figure 1 is a composite plot of the fitted 

velocities vs altitude for the 32 traces. It will be noted that they all show velocities decreasing with 

decreasing altitude, and all of them show some downward curvature. Likewise, the deceleration rates 

increase with decreasing altitude, as they should. Figure 2 is a composite plot of the decelerations 

(negative accelerations) vs altitude for the 32 traces, derived from the velocity fits. (Note that one 

meteor streak appears to be interstellar in origin, with a velocity exceeding 72.8 km/s. We will perform 

orbital analysis on this streak in the future to confirm this result.) We note also that in five of the cases 

the initial value of dv/dt has come out to be positive, due presumably to inaccuracies in the velocity data. 

These cases will be discarded as flawed. 

Figure 1. Composite plot of the fitted velocities vs altitude for the 32 cases – from the least-squares quadratic fits of 

the measured velocities vs Q . 


Figure 2. Composite plot of the accelerations vs altitude for the 32 cases – as derived from the quadratic fits to the 

velocities 

 In our analysis we will assume that the meteors are spherical. Then the energy flux on the 

meteor surface due to air molecule collisions is r

2

v

3

/2, where r and v are the meteor radius and 

velocity, and  is the local air density. Consistent with other authors (e.g. Pecina & Ceplecha, 1982; 

Opik, 1958; Bronshten, 1983) we will write the meteor mass loss rate as 

 dm/dt = - r

2

v

3

' , (2) 

where m is the meteor mass and ' is the “ablation coefficient”. The rate of deceleration of the meteor is 

 dv/dt = - r

2

v

2

/m . (3) 

Combining equations 1 and 2 we obtain 

 dm/m = ' v dv . (4) 

If we make the convenient (but not necessarily valid) assumption that ' is constant, then Eq 3 can be 

integrated, giving 

 ln(m/m1) = ('/2)(v2

 – v1

2

) , (5) 

where m1 and v1 are the initial values of m and v along a given meteor radar trace. The constant-'

assumption would be appropriate if, for instance, the meteor mass loss was dominated by “sputtering”. 

 In an alternative model (e.g. Vondrak et al, 2008; Janches et al, 2009; Lebedinets, 1973), the 

mass loss is dominated by thermal evaporation of the meteor constituents. The instantaneous 


evaporation rate is determined by the instantaneous temperature. In the next section we describe our 

own numerical model of these coupled processes. 

4 Numerical Model

The consensus of most current theoretical studies of the ablation and slowing down of small meteors in 

the atmosphere (Lebedinets, 1973; Janches et al, 2009; Vondrak et al, 2008) is that: (1) Very rapid 

heating occurs due to collisions with air molecules, moderated by energy losses due to blackbody 

emission from the meteor surface and due to evaporation. (2) The heating leads to vaporization of 

meteor (generally preceded by melting). (3) Some sputtering occurs, in addition to the vaporization. (4) 

The air molecule collisions also lead to deceleration of the meteor. (5) With very small meteors the rate 

of internal heat conduction is sufficient to maintain a uniform temperature distribution within the 

meteor. (6) Meteors are composed of mixtures of chemical constituents, and each will vaporize at its 

own rate. 

 It the present model we further assume that the meteor is spherical, and that after melting it does 

not disintegrate. 

 The rate of heating of the meteor through air molecule collisions is (dH/dt)coll = r

2

v

3

/2 , where 

r is the instantaneous meteor radius, v its instantaneous velocity, and  the local air density, and it is 

assumed that all the energy of a collision is transferred to the meteor. The rate of loss of energy by 

blackbody emission is (dH/dt)rad = -4r

2

'SBT4 , where 'SB is the Stephan-Boltzmann constant and T is 

the instantaneous temperature. The vapor pressure of the ith chemical constituent of the meteor is given 

by the Claussius-Clapeyron equation 

 Pvap(i) = Ai exp(-Ci/T) , (6) 

where Ai and Ci are constants characteristic of the particular constituent. The evaporative flux of each 

constituent from the surface is given by the Langmuir relation 

 Fevap(i) = Cflx Pvap(i) / (!vap(i) T)1/2 (molecules/cm2

s) , (7) 

(Taylor and Langmuir 1933), where !vap(i) is the molecular weight of the vapor. . If Pvap(i) is in 

dynes/cm2 and !vap(i) is in grams, then the constant Cflx is equal to 3.40×107

. Then the rate of energy loss 

from the meteor surface due to evaporation of each constituent is 

 (dH/dt)evap = -4r

2 9Hsblm(i) Fevap(i) , (8) 

where 9Hsblm(i) is the heat of sublimation (erg/molecule). Then the rate of change of the meteor 

temperature is 

 dT/dt = [ (dH/dt)coll + (dH/dt)rad + (i=1,N)(dH/dt)evap(i) ]/Cp , (9) 

where Cp is the specific heat. In the above equation it is assumed that each constituent vaporizes at a 

rate independent of the other constituents, as long as that constituent is still present (i.e. has not totally 

evaporated). Values of the parameters 9Hsblm(i) , Ai, Ci, !vap(i) and melting point for several likely meteor 

constituents are listed in Table 1, below. 


Table 1. Physico-chemical parameters for meteor constituents, and references. The numbered references are: 1. 

Ferguson et al, 2004; 2. Brewer et al, 1948; 3. Clarke and Fox, 1969; 4. Wickramasinghe and Swamy, 1968; 5. 

Brewer and Porter, 1954; 6. Akopov, 1999; 7.Fabian,1993; 8. Patnaik, 2002. 

 Constituent 9Hsblm A C !vap Melting Pt References

 (erg/molec) dyne/cm2 Deg K grams Deg K 

 

Fe (iron metal) 6.62e-12 5.06e+12 4.836e+4 9.30e-23 1811 1 

C (graphite) 1.495e-11 9.74e+15 1.006e+5 3.99e-23 --- 2, 3 

SiO2 9.64e-12 4.16e+11 6.99e+4 9.97e-23 1923 4 

MgO 8.65e-12 9.16e+14 6.27e+4 6.64e-23 3073 5 

FeO 1.03e-11 1.01e+16 7.47e+4 1.20e-22 1653 6, 7, 8 

 Table 1 shows the physico-chemical parameters that we have assumed for several possible 

meteor constituents, including A, C, 9Hsblm , and some references. In most cases the references do not 

give the quantities A, C and 9Hsblm directly, and in those cases we have had to calculate those quantities 

by fitting Eq 6 to data on vapor pressures measured at two or more temperatures, and assuming that 

9Hsblm is equal to the Boltzmann constant kB times C. The references listed in Table 1 are mostly 

sources of vapor pressure and/or boiling point data. 

 The rate of loss of mass from the meteor due to evaporation, is 

 (dm/dt)evap = -4r

2 (i=1,N) (!vap(i) Fevap(i)) . (10) 

There will also be some mass loss due to sputtering, given by (dm/dt)sputt = r

2

v

3

'sputt , where 'sputt is 

the ablation coefficient associated with sputtering (units of s2/cm2). The meteor radius r is related to the 

mass m by r = (3m/4s)

1/3 , where s is the mass density of the solid meteor. 

 Finally, the rate of deceleration of the meteor is given by Eq 3. 

 dv/dt = - r

2

v

2

/m . (3) 

 We have developed our own computer model that incorporates the above processes in the form 

of a set of ordinary differential equations expressing the rates of change of meteor mass, velocity, radius, 

temperature, etc. as functions of time. The input meteor composition can be either a pure compound or 

a mixture of compounds. The differential equations are detailed in Appendix A. This model appears to 

be very similar to the one described by Vondrak et al, 2008. 

 Some key questions are, of course: (1) What is the meteor composition? (2) What is its mass 

density? (3) Does the meteor actually remain intact after it melts? and (4) What is the contribution of 

sputtering to the total ablation coefficient? 

 Figures 3a-3f show comparisons, for a set of six traces, of computed vs measured decelerations 

vs altitude. For inputs to the computations for each trace we take (1) the measured initial velocity; (2) 

the measured trajectory inclination angle; (3) an assumed initial value of ms

2

, which is shown on the 

plot; (4) an assumed initial composition -- namely an equimolar mixture of SiO2, FeO and MgO (which 

corresponds roughly to the expected decomposition products of olivine, a mineral that is commonly 

found in stony meteorites); (5) an assumed energy for sputtering, E* = 15 eV per molecule, giving a 

constant sputtering contribution of 2.1×10-12 s2

/cm2 to the total ablation coefficients; (6) a mass density 


s of 1.0 g/cm3

. With these assumptions Figures 3a-3f show good agreement between the computed 

results and the data. In all, we found satisfactory agreement in 20 of the 32 cases. 

(a) 

 

 Figures 3a-3f. In each of these plots the solid curve is the acceleration derived from the data fit, and the dotted 

curve is the one computed with the model (with inputs described in the text). 

 We also ran computations with other assumed mass densities (s) and sputtering energies (E*), 

although the results will not be shown here. From comparisons of the results with Figs 3a-3f we found 

that the computed deceleration rates did not depend at all on the assumed density s . This is to be 

(b)

(c) (d) 

(e) (f) 


expected, since the initial meteor mass is equal to the input ms

2

 divided by s

2

, and the separate 

dependencies of the acceleration rates on m and s are always connected through the ms

2

. 

 We also found that without the assumed relatively large sputtering contribution to the ablation 

coefficients the agreement with the data was less good than the extent of agreement shown in Figs 3a-3f. 

 Although the computed deceleration values are independent of the separate values of m and s

(once the value of the product ms

2

 is prescribed), the mass m is of course equal to ms

2

/s

2

. Because of 

this it is possible to arrive at rough estimates of both m and s separately, using the measured values of 

decelerations and radar cross sections in combination, and using the Close et al electrostatic scattering 

model (Close et al, 2004) together with our present ablation and deceleration model. Figures 4a and 4b 

show two examples of such attempts to determine both m and s from the experimentally determined 

ms

2

 and “mass1” (mass from the radar cross sections). In Figure 4a, representing trace #8, the four 

solid curves are the computed inertial mass values vs altitude derived from the best-fit ms

2

 (from Fig 

3b) assuming four different values of s, namely 0.1, 0.316, 1.0 and 3.16 g/cm3 , while the dashed curve 

is mass1. In this case it appears that the best-fit density s is about 1 g/cm3

 , and the initial pre-ablation 

mass is about 1×10-4 g. Figure 4b is a similar set of plots, but representing trace #9 (from Fig 3c). In 

this case the best-fit s is about 0.3 and the initial mass is again about 1×10-4 g. We have made similar 

plots (not shown here) for each of the other measured traces, and we find that the average best-fit s is 

about 0.5, but with a spread of values between about 0.1 and 1.

 Figures 4. (a) Here the solid curves are the inertial masses (for trace #8) computed with the numerical model, using 

the best-fit value of ms

2 together with four different assumed values of the meteor density s, namely (from top to 

bottom) 0.1, 0.316, 1.0 and 3.16 g/cm3

 . The dashed curve is the “mass1” (mass determined from the measured 

cross sections together with the electrostatic scattering model. (b) Same as for (a), but representing trace #9. 

(a) (b) 

 To elaborate on some further details of the model computations: Figures 5a and 5b show more 

results from one of the runs, namely the one representing trace #8. Figure 5a shows the computed 

meteor temperatures vs altitude, showing the successive evaporation of MgO, FeO and SiO2; and Figure 

5b shows the computed variations of the effective ablation coefficient ' with altitude, including the total 

' and the separate evaporative contribution. 

 For meteors composed of mixtures of materials the total vapor pressure at any point is the sum of 

the vapor pressures of the individual constituents, irrespective of their relative amounts. Then the 

evaporation rate for each component should be given by the Langmuir equation (Eq 7), irrespective of 

the fraction of that component in the mixture. Then at each instant all of the constituents will be 


evaporating simultaneously at rates proportional to their individual vapor pressures – until such times as 

each successive constituent disappears by evaporation. One result of this is that the meteor temperature 

rises in a series of discrete steps, where the steps correspond to the disappearances of successive 

components. This is illustrated in Figure 5a. The ablation coefficients also exhibit a stepwise character, 

but with sharp decreases between successive steps, as is shown in Figure 5b. It is notable of course that 

the ablation coefficients are by no means constant, in contradiction to the assumption in Eq 5. 

 Our assumed constant sputtering contribution to the ablation coefficient produces a substantial 

difference in the computed ablation and deceleration rates. Figure 5c shows the computed ablation 

coefficient vs altitude for the same case as that shown in Figures 5a and 5b, where in the computation 

the sputtering energy E* was raised to 1000 eV per molecule, so that the sputtering contribution to 

sigma was reduced to 3.1×10-14 s2/cm2 , which would be in better agreement with the laboratory data. 

The result was a considerable reduction in the effective average ablation coefficients and a reduction in 

the meteor deceleration rates. 

 

(a) (b) 

(c) 

Figures 5. (a) Computed temperature history for the same meteor as in 3a. (b) Computed ablation coefficient vs altitude for 

the same meteor as in 3a, and 5a. The dashed curve is the evaporative contribution, and the solid curve is the total. (c)

Computed ablation coefficient vs altitude for the same case as in Figures 5a,b, when in the computation the assumed 

sputtering energy E* is raised to 1000 eV. 


5 Direct Determination of ms

2 from the Deceleration Data

The quantity ms

2

 can be determined directly from the fitted velocity and deceleration rate data without 

the need to use the computer model, but assuming only that the meteor is a sphere. Then the rate of 

deceleration is as given by Eq 3. For a sphere of density s the quantity r

2

 is r

2

 = 1.209 (m/s)

2/3 . 

Then, combining these two equations we obtain 

 ms

2

 = [-1.209  v

2

/ (dv/dt)]3 (11) 

 The values of ms

2

 thus determined are of course very sensitive to errors in the measured/fitted 

deceleration rates. If we nevertheless proceed to evaluate the ms

2

 from the data fits for 27 of the 

measured traces, and plot them as functions of altitude, the result is Figure 6. Only about twenty of 

these curves seem to be believable, namely those that slope upward to the right and are concave 

downward. This set of twenty is the same as the twenty for which we found agreement between the 

computed and measured deceleration rates as described in the previous section. 

 Despite the expected inaccuracies in these ms

2

 values, it is of interest to compare them with the 

corresponding values that we determined in the previous section from fitting the model-computed 

decelerations to the data. Table 2 shows, for each of the twenty chosen traces, (1) the initial (uppermost) 

altitude, (2) the initial value of ms

2

 at that altitude, as determined directly from the data using Eq 11, 

(3) the ms

2

 value at the same altitude as computed with the model, and (4) the value extrapolated to the 

top of the atmosphere using the model. As expected, the agreement between the values in columns 3 

and 4 is not very good, but nor is it extremely bad in most cases. The worst disagreement is for traces 4 

and 27, which are also exceptional in that their altitudes are more than fifteen kilometers higher than the 

rest. 

Figure 6. A composite plot of the combined variable ms

2 for 27 traces. 


Table 2. Comparisons between values of ms

2

 determined directly from the data via Eq 11 and values determined 

by the method described in Section III. 

Trace # Initial altitude 

(z1) (kilometers) 

ms

2 at z1 

from Eq 11 

ms

2

 at z1 

from model 

ms

2

 (z = õ) 

from model 

 1 104 2.e-6 1.6e-6 8.4e-6 

 4 124 2.e-7 3.0e-8 4.6e-8 

 8 105 3.e-5 8.5e-5 1.5e-4 

 9 108 1.e-4 1.4e-5 2.0e-5 

 10 107 3.e-5 6.e-6 1.0e-5 

 11 102 1.5e-6 4.5e-6 7.e-5 

 12 104 2.e-5 2.1e-5 3.2e-5 

 13 104 1.e-6 4.0e-6 1.2e-5 

 15 105 3.e-6 4.1e-6 1.2e-5 

 16 103 4.e-7 1.4e-6 1.6e-5 

 17 105 2.e-5 6.e-6 1.4e-5 

 20 104 3.e-7 4.3e-7 4.1e-6 

 23 105 2.e-7 3.e-7 3.e-6 

 24 106 3.e-6 1.0e-6 4.2e-6 

 25 107 1.e-5 2.1e-5 3.4e-5 

 27 123.5 3.e-5 2.0e-7 2.7e-7 

 28 106 4.e-6 7.e-6 1.5e-5 

 29 106 4.e-7 1.1e-6 3.1e-6 

 30 105 4.e-6 2.7e-6 6.8e-6 

 32 99.5 4.e-6 1.3e-5 8.2e-5 

 This procedure (i.e. using Eq 11) has the obvious advantage that it does not use any assumptions 

about the meteor composition, whereas in using the model a composition must be assumed. In both 

cases we assume a spherical meteor shape. Using the model has the advantage that it allows us to 

extrapolate the ms

2

 to the top of the atmosphere. 

6 Discussion 

With the present 32-trace data set the velocities and trajectory inclinations were arrived at by 

differencing the measured 3D position vs time data. In view of the expected errors inherent to 

numerical differencing procedures, it has been encouraging to find that these 3D velocity data can be 

fitted so well as quadratic functions of Q. However, it is also not surprising to find that when we try to 

infer the ms

2

 quantities directly from these data, as in the previous section, that many of the ms

2

 vs 

altitude curves look crazy. We are currently in the process of analyzing a much larger set of ALTAIR 

meteor data from 2007-2008, where it appears to be possible to obtain more accurate velocities from 

range Doppler measurements. We are hopeful that when these data are available we can go through 

these same procedures to obtain a larger set of more reliable ms

2

 values. With such a data set we will 

be able to extract more detailed information about the evaporation rates, ablation coefficients etc. 

 For purposes of evaluating the initial values of ms

2

 we have chosen to use the computer model 

to find the values that produce the best fits to the deceleration rate data. However, a serious problem 


with that is that the model results are sensitive to the assumed chemical compositions of the meteors, 

which are of course not known. Our assumption of the olivine-like composition was convenient because 

the necessary data on vapor pressures and heats of sublimation of the decomposition products were 

available in the literature. 

 In the process of comparing the model results to the deceleration data we found that the fits were 

improved when we assumed a rather large sputtering contribution to the effective ablation coefficients, 

namely 2×10-12 s2

/cm2. This value is significantly larger than values that have been determined in 

laboratory measurements of sputtering from energetic ion bombardment of solid target materials 

(Behrisch 1981, Bodhansky et al 1980, Lebedinets and Shushkova 1970, Ratcliff et al 1997, Tielens et al 

1994)). However, with meteors entering the atmosphere the collision fluxes are much larger than in the 

laboratory experiments, and for most of the time the meteors are molten. Then the laboratory results 

may not be directly comparable 

 The model results show that the meteor temperatures almost invariably exceed the melting points 

before very much ablation occurs. Nevertheless, in our twenty selected cases the ablation and 

deceleration rates appear to vary smoothly, without obvious evidence of fragmentation. This seems 

quite surprising. However, in the remaining twelve cases the failure to fit our model could be an 

indication of fragmentation. 

 In our computer model we have assumed that the vapors emitted by the meteors are molecular 

rather than atomic. This seems to differ from the assumptions in the model described by Vondrak et al 

2008, and Janches et al 2009. In view of the fact that the dissociation energies of, for instance, SiO2, 

MgO and FeO are very much larger than their sublimation energies, it seems unlikely that the 

evaporation products would be atomic. On the other hand, subsequent collisions of the evaporated 

molecules with background air molecules would certainly lead to dissociation and/or ionization. 

7 Summary 

It appears that with most of these 32 radar traces the range and altitude vs time measurements are of 

sufficient quality to allow us to extract reliable velocities, trajectory inclinations and deceleration rates. 

In about 80% of the cases the velocities can be fitted with good accuracy as quadratic functions of the 

integrals of the air densities along the measured trajectories, and the time derivatives of these functions 

provide reasonable values of deceleration rates. We have used these fitted velocities and deceleration 

rates together with a computer model to determine best-fit values of the quantity ms

2

, the product of the 

initial meteor mass times its mass density squared, successfully in 20 of the 32 cases. The model, which 

we have described, treats the coupled processes of meteor deceleration through air molecule collisions 

and the associated heating of the meteor, together with cooling by blackbody emission and by 

evaporation of its constituents, and the rate of loss of mass through evaporation and by sputtering. This 

procedure does not provide information about the separate quantities m and s. However, separate 

estimates of the masses m have been obtained from the measured radar scattering cross sections, using 

an electrostatic scattering model. By combining these m values with the ms

2

 we have obtained values 

of s , almost all of which fall in the range between 0.1 to 1 g/cm3. We have also described a process by 

which we can obtain ms

2

 values directly from the velocity and deceleration data without using the 

computer model, although the results are very sensitive to errors in the decelerations. 


APPENDIX A - The Mathematical Model

Definitions of variables:

t = time (s) 

z = altitude (cm) 

s = meteor mass density (g/cm3

) 

r = meteor radius (assumed spherical) 

M = meteor mass = (4/3)sr

3 

mi = mass of the ith meteor constituent (g) 

fi = mass fraction of the ith constituent 

v = meteor velocity (cm/s) 

T = meteor temperature (assumed isothermal) 

G = trajectory zenith angle 

(z) = local air density (g/cm3

) 

H = meteor total enthalpy (ergs) 

9Hvap(i) = heat of vaporization (erg/g) of the ith constituent 

9Hsput = enthalpy loss by sputtering (ergs) 

E*sput = energy required for sputtering of one gram (erg/g) 

!m(i) = molecular weight of the ith constituent (g/molec)) 

!vap(i) = molecular weight of the ith vapor constituent (g/molec) 

'SB = Stephan-Boltzmann constant (erg cm-2 deg-4 s-1) 

Cp = specific heat of meteor material (erg/g) 

Pvap(i) = vapor pressure of the ith constituent (d/cm2) 

Avap(i) and Cvap(i) = constants for the ith meteor constituent 

 Index i refers to the ith chemical constituent. 


 Differential (and other) equations:

M = i mi 

fi = mi /M 

dz/dt = -v cosG dt 

dv/dt = -r

2

v

2

/m 

(dH/dt)coll = 0.5 r

2

v

3

 

dmi/dt = (dmi /dt)sput + (dmi /dt)evap 

(dmi/dt)evap = -4r

2 

!vap(i) {3.51×10+19 Pvap(i) /(!vap(i)T)1/2} (if mi > 0. otherwise zero) 

(dmi/dt)sput = -fi!m(i)(dH/dt)coll/E*sput 

dH/dt = (dH/dt)coll + (dH/dt)rad + (dH/dt)evap 

(dH/dt)rad = -4r

2

'SBT4 

(dH/dt) evap = i 9Hvap(i) (dmi/dt) evap 

T = H/(Cp M) 

Pvap(i) = Avap(i)exp(-Cvap(i)/T) 


APPENDIX B – Meteor Temperatures and Evaporative Ablation—Quasi-Analytic Solutions of 

the Steady-State Equations – for a Single-Component Meteor

Simple calculations show that an incoming meteor must be heated by air molecule collisions to quite 

high temperatures, which are mitigated by the emission of blackbody radiation and by evaporative 

cooling associated with Langmuir evaporation of the meteor constituents. In the present case the 

meteors are quite small, so that heat conduction is fast enough to assure that their internal temperature 

profiles are isothermal. The collisional energy input rate is r

2

v

3

/2 . The radiative energy loss rate is 

4r

2

'SBT4 , where T is the meteor temperature and 'SB is the Stephan-Boltzmann constant. The vapor 

pressure for a single molecular constituent is approximated by the Clapeyron-Claussius relation 

 Pvap = A exp(-C/T) , (B-1) 

where A and C are constants characteristic of the particular evaporating meteor constituent. And the 

evaporative flux from the surface is given by the Langmuir relation 

 Fevap = Cflx Pvap / (!vap T)1/2 cm-2s

-1 , (B-2) 

(Taylor and Langmuir 1933), where !vap is the molecular weight of the vapor. If Pvap is in dynes/cm2 

and !vap is in grams, then the constant Cflx is equal to 3.40×107. Then the rate of energy loss from the 

meteor surface due to evaporation is 4r

2 9Hsblm Fevap , where 9Hsblm is the heat of sublimation 

(erg/molecule). We expect that the collisional heating and the radiative and evaporative cooling will 

balance each other, so that at each point in the meteor trajectory the temperature should be given by the 

steady-state relation 

r

2 v3

/2 - 4r

2

'SBT4 -

 4r2 9Hsblm Fevap = 0 . (B-3) 

(This equation is equivalent to Eq 3 of Hunt et al, 2004, or Eq 2 of Vondrak et al, 2008, although we 

assume the steady-state condition dT/dt = 0 (or negligible).) 

This equation can be solved for T by Newton-Raphson iteration, and when T is determined we can 

calculate the evaporative mass loss rate 

 dm/dt = - 4r

2

!vap Fevap (B-4) 

at each point along the trajectory. Then using this equation together with Eq 2 we can solve for the 

evaporative contribution to the effective ablation coefficient ', which is now a function of altitude. 

From Eqs B-3 and B-4 we can see that this effective ' is a function of the air density , the velocity v 

and the thermodynamic properties of the meteor material (or individual meteor constituents), but it is not 

directly dependent on the meteor mass or the mass density or the trajectory inclination angle. 

 Figures B-1(a,b), B-2(a,b) and B-3(a,b) show computed temperatures and effective ablation 

coefficients as functions of altitude for meteors composed of pure SiO2, or MgO, or FeO, respectively. 

These three compounds are expected to be the decomposition products of the mineral olivine, which is 

commonly found to be a dominant constituent in stony meteorites (Korotev, 2006). 


Figure B1a. Composite plots of steady-state temperatures vs altitude for SiO2 meteors with velocities of 30, 40, 50, 

60, 70 and 80 km/s (in that order from bottom to top). 

Figure B1b. Composite plots of effective ablation coefficients vs altitude for the same set of cases, and in the same 

order. 


Figures B2a,b. Same as in Figures B1a,b, but for magnesium oxide meteors. 


Figures B3a,b. Same as in Figures B1a,b, but for ferrous oxide meteors. 


 It is interesting to note that in figures B-1b, B-2b and B-3b in each case the effective sigma’s 

tend to converge to a common value at the lowest altitudes. This is due to the fact that at the lowest 

altitudes the temperatures are so high that the evaporative cooling rate dominates over the radiative 

cooling rate. Then the second term in Eq B-3 can be ignored in comparison with the third, and 

combining Eqs B-3, B-4 and 2 gives 

' = !vap /(2 9Hsblm) (limit for low altitudes and high temperatures). (B-5) 

 It is also interesting that the limiting low-altitude values of the effective sigma’s are not very 

different from the average ' values that we determined from our data using the constant-' assumption 

and Eq 5 (although the details of that analysis will not be shown). 

 In writing Eqs B-3 and B-4 we have not mentioned the fact that the meteors can be expected to 

melt before they vaporize to an appreciable extent. The present radar data seem to indicate that the 

meteors do not immediately disintegrate upon melting – i.e. the traces seem to be continuous when the 

temperatures are expected to exceed the melting points. Apparently the molten meteors are held 

together by surface tension. In writing Eq B-3 we have not specifically included the solid-liquid 

transition, and we have used the heat of sublimation 9Hsblm as if the meteor evaporated directly from the 

solid phase. 

 The calculations in this section have been for hypothetical meteors composed of a single 

vaporizable material. Of course actual meteors are expected to be made of a mixture of materials, each 

of which would vaporize at its own rate. More detailed computations including mixtures of materials 

have been described in section IV . In the present section we have also ignored the effect of sputtering. 

It is to be expected that at the highest altitudes, where the meteor temperatures are relatively low, the 

meteor mass loss rate will be dominated by sputtering, so the effective ' should include an added 

constant term for the sputtering contribution. On the basis of laboratory experimental results and 

theoretical studies (Behrisch 1981, Bodhansky et al 1980, Lebedinets and Shushkova 1980, Ratcliff et al 

1997, Rogers et al 2005, Tielens et al 1994), we would expect that the sputtering term should be of the 

order of 4×10-14 s2

/cm2. However, our deceleration data suggest a much larger value, of order 2×10-12 . 

The laboratory sputtering measurements of course involved much lower collisional fluxes than those 

expected for an incoming meteor, and much lower temperatures, and solid rather than molten targets. 

 The physico-chemical parameters used in these calculation have been shown in Table 1 of 

Section IV. 

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Meteoroid Fragmentation as Revealed in Head- and Trail-echoes Observed with the 

Arecibo UHF and VHF Radars 

J. D. Mathews1• A. Malhotra 

Abstract We report recent 46.8/430 MHz (VHF/UHF) radar meteor observations at Arecibo 

Observatory (AO) that reveal many previously unreported features in the radar meteor return–including 

flare-trails at both UHF and VHF– that are consistent with meteoroid fragmentation. Signature features 

of fragmentation include strong intra-pulse and pulse-to-pulse fading as the result of interference 

between or among multiple meteor head-echo returns and between head-echo and impulsive flare or 

“point” trail-echoes. That strong interference fading occurs implies that these scatterers exhibit well 

defined phase centers and are thus small compared with the wavelength. These results are consistent 

with and offer advances beyond a long history of optical and radar meteoroid fragmentation studies. 

Further, at AO, fragmenting and flare events are found to be a large fraction of the total events even 

though these meteoroids are likely the smallest observed by the major radars. Fragmentation is found to 

be a major though not dominate component of the meteors observed at other HPLA radars that are 

sensitive to larger meteoroids. 

Keywords meteor radar · meteoroid fragmentation · meteor flare 

1 Introduction 

Here we provide an update to Mathews et al. (2010) who present Arecibo Observatory (AO) radar 

meteor results that are consistent with meteoroid fragmentation. While this conclusion has proven to be 

controversial; the finding that fragmenting meteoroids are observed both optically and with radar has a 

long history. In reference to fragmentation, Verniani (1969) notes that “At present, the structure and 

composition of meteoroids is a matter of controversy, with contrasting views put forward by different 

investigators.” In fact, Mathews (2004) notes evidence of meteoroid fragmentation and terminal flares 

dating to the first known radar meteor Range-Time-Intensity (RTI) image given in Hey et al. (1947) and 

in Hey & Stewart (1947). Additionally, there is much evidence and many papers on “gross 

fragmentation” in optical bolides – e.g., see Ceplecha et al. (1993) and references therein. 

 At the Meteoroids 2001 conference Elford & Campbell (2001) noted that “Radar reflections 

from meteor trails often differ from the predictions of simple models. There is a general consensus that 

these differences are probably the result of fragmentation of the meteoroid.” Elford (2004) concluded 

that approximately 90% of all specular trail events are accessible to his Fresnel holography approach 

while only about 10% of these events can be analyzed via the classical approach and thus that 

fragmentation is a dominant process for 80% of the specular trail events. 

 “Terminal” radar meteor events–referred to here as terminal flares–are reported in the Arecibo 

UHF/VHF results by Mathews (2004). Kero et al. (2008) report smooth to complex meteor light-curves 

 

J. D. Mathews ( ) • A. Malhotra 

Radar Space Sciences Lab, The Pennsylvania State University, University Park, PA USA 16802. Email: JDMathews@psu.edu


(their Figures 1-3) that they interpret as simple ablation, two-fragment, & multiple-fragment events with 

interference of the various head-echo signals. Roy et al. (2009) use genetic algorithm techniques to 

explore details of fragmenting meteors observed at the Poker Flat Incoherent Scatter Radar (PFISR). 

They employ multiple model point scatterers as we will outline below and a genetic algorithm to find 

via the evolution of three multi-fragment meteor events in a piece-wise fashion over groups of five radar 

pulse voltage (as opposed to power and thus lost phase information) returns finding the speed, 

deceleration, and amplitude of each particle in the ensemble. Their fitting procedure yields relative 

speed resolutions of as little at 1 m/s. Briczinski et al. (2009) utilize statistical techniques to estimate the 

role of fragmentation and terminal flares in Arecibo UHF radar meteor data. They find that terminal 

flares constitute up to ~15% of all events and that low-SNR, short duration, and/or fragmentation 

explain the ~67% of all events for which deceleration cannot be determined. 

2 Observational Technique 

The observations reported here utilize both the AO 430 MHz and 46.8 MHz radar systems. It is 

important to emphasize that these radars are frequency and time coherent and thus phase coherent over 

very long periods – years – and so in principle offer the ability to resolve features or motions on the 

scale of a fraction of a wavelength and centimeters/sec, respectively. These properties are utilized in the 

observations reported here. These two radars employ co-axial feeds yielding an overlapping central 

illuminated volume thus yielding a sizeable fraction of events that are seen in both radars. Table 1 lists 

the relevant parameters of both radars while Figure 1 shows the 430 MHz linefeed that illuminates the 

spherical-cap surface along with the four Yagi feeds arranged co-axially around the linefeed. At 46.8 

MHz the dish is effectively parabolic allow this “point” feed arrangement. In Table 1 the quality factor 

is transmitter power (MW) time the effective area of the antenna (m2

) divided by the system temperature 

(Kelvins). Clearly the UHF system is much more sensitive – by a factor of ~600 – than the VHF system. 

Table 1. Arecibo V/UHF Radar Properties 

Radar Beamwidth Gain (dBi) Power System Temp Quality Factor 

46.8 MHz 1.4o 40 ~40 kW 3000 K ~3 

430 MHz 0.17o 61 ~2 MW 100 K ~1825 

Figure 1. The VHF & UHF antenna feed layout of the AO carriage-house radars. 


For the results given here a 20 μsec uncoded pulse was used at UHF while – due to system duty 

cycle limitation – a 10 μsec uncoded pulse delayed by 12 μsec relative to the UHF pulse start was 

employed at VHF. In both cases the receive system bandwidth was 1 MHz while in-phase and 

quadrature samples were taken at baseband with 1 μsec sampling intervals yielding 150 m range 

resolution. A 1 ms InterPulse Period (IPP) was utilized with the overall technique based on early AO Dregion observations (Mathews 1984). The first dedicated AO meteor observations are reported by 

Mathews et al. (1997). 

3 Observational Results 

The results presented here were obtained during two ~12 hr observing sessions beginning at 2000 hr 

AST (Atlantic Standard Time) on 5 and 6 June 2008. Approximately 17,000 meteors were detected at 

UHF using automated detection software (Briczinski et al. 2009, Mathews et al. 2003, Wen et al. 2005, 

Wen et al. 2004). This approach was not separately applied at VHF due to the relatively short pulse and 

the high level of interference in the VHF band. The VHF results have been manually searched for large 

events that include some of the flare-trail results reported here. 

Figure 2 displays Range-Time-Intensity (RTI) images of three meteor events that together 

characterize many of the ~17,000 UHF events we report here. Event 1, seen at 430 MHz, shows strong 

interference fading consistent with two slowly separating meteoroid fragments each of which has an 

individual head-echo. This interpretation builds on the results of Mathews et al. (2010) and Roy et al. 

(2009) and will be addressed further in the discussion section. 

 Event 2a, seen at VHF, shows several features including an underlying interference or fading 

pattern similar to event 1 but also an altitude-narrow trail that we attribute to an impulsive fragmentation 

“flare” occurring at about 40 ms and that results in a relatively small “blob” of plasma embedded in the 

background atmosphere. The term “flare” is adopted from optical meteor observations that often reveal 

impulsive brightening events. Event 2b shows the UHF return which defines the center of both beams. 

Note the strong intra-pulse fading that is due to the rapidly evolving particle distribution relative to the 

69.7 cm wavelength. Figure 2, Event 3, shown only at VHF as the corresponding UHF event was very 

weak, shows mild fragmentation prior to 60 ms when a strong fragmentation flare occurs followed by a 

second flare at 110 ms. Of special interest in Event 3 is the strong interference fading – similar in effect 

to the Event 1 interference pattern – between the head-echo and trail-echoes. The implications of these 

various two-scatterer interference patterns will be explored in the discussion section and additional 

example events including those resembling differential ablation (Janches et al. 2009) and those opposite 

to differential ablation signature (intensity rises rapidly and falls slowly) are given in Mathews et al. 

(2010). 

Next we consider some of the more subtle and perhaps surprising results from this dataset. Figure 

3 displays a short UHF meteor head-echo that shows the beam pattern with a stronger central return and 

two side-lobe returns as the meteor moves across the beam. This event also displays a complex intrapulse fading consistent with multiple, closely-spaced but rapidly dispersing, meteoroid “fragments” 

similar to those seen in Figure 2 event 2b. which is more slowly evolving (Roy et al. 2009). We are able 

to resolve these features of the meteoroid multi-head-echo evolution at the microsecond level due to the 

phase coherent nature of these radars. The Figure 3 VHF return is much longer than at UHF because – 

per Table 1 – the VHF beam is much wider. The combined U/VHF event is in common volume only 

over the span of the UHF return. The VHF meteor interference feature is simple like that of Figure 2, 

event 1 but fades more slowly than the Figure 3 UHF return as the wavelength is more than a factor of 


nine longer. The VHF return displays a clear terminal flare that is consistent with the LATE (LowAltitude Trail-Echo) reported at Jicamarca (Malhotra & Mathews 2009). This type of event is relatively 

common. 

Figure 2. RTI images of three archetypal AO meteor events. Event 1, seen at UHF, shows a strong fading pattern 

consistent with two slowly separating meteoroid fragments each of which has an individual head-echo. The event 2 

panels demonstrate the value of viewing the same event at two widely separated frequencies. Event 2a, seen at 

VHF, shows several features including an underlying interference pattern similar to event 1 but also an altitudenarrow trail that we attribute to a fragmentation “flare”. Event 3 shows some Event 1 like fragmentation and two 

flare-trails. (Fig. 1 from Mathews et al. (2010)) 

Figure 3. RTI images of a meteor event seen at both UHF and VHF. The UHF head-echo shows the beam-pattern 

as strong intra-pulse fading. The VHF echo has a terminal flare. 


 Figure 4 shows two UHF meteor events that are ambiguous and thus point to the wide range of 

knowledge potentially available via radar meteor studies. Event 1 is likely due to two or more particles 

that cause the strong intra-pulse interference fading visible in the ~60-70 IPP and ~82-95 IPP. It is 

unclear if the early event results in a trail and is then followed by a separate event that clearly results in 

the UHF trail. In any case, we might deem this total event a nano-shower in that almost certainly all 

particles were associated with a parent body at or just above atmospheric entry. Figure 4 event 2 is likely 

a terminal flare trail event similar to those reported at the 1280 MHz Sondrestrom Research Facility 

(SRF) terminal events (Mathews et al. 2008). It is also possible that this event is a “classical” trail event 

where the trajectory of the meteoroid is perpendicular to the zenith-pointing beam. 

Figure 4. RTI images of two complex UHF head- and/or trail-echo events. Event 1 shows strong intra-pulse fading 

due to two or more individual head-echo producing meteoroids in close proximity. Event 1 displays a clear trailecho after IPP 95. Event 2 is likely a terminal-flare trail but may be a classical trail-echo where the trajectory of the 

meteoroid is perpendicular to the zenith-pointing beam. 

Figure 5 points to a new – previously unreported – class of radar meteor event. These longlasting – for k B ä 45A – trail events appear to be the “fossil” remnants of a radar bolide event. That is, 

while the head-echo of the progenitor event is not always identifiable, the event generated sufficient 

(flare?) trail-producing plasma that the resultant trail-echo lasts a few seconds and may in fact drift into 

the VHF beam at the normal D-region wind speeds of order 100 m/s (Mathews 1976). Note the complex 

interference fading of the several regions of the trail-plasma. 

Figure 5. A likely “fossil” radar bolide event that has an ~3 sec lifetime. The progenitor event was not observed. 


4 Discussion 

We report several classes of V/UHF “common volume” radar meteor events that are, we argue, 

consistent with fragmenting meteoroids that produce multiple, interfering, head-echo events as well as 

“flare” and “terminal flare” trails that often display interference fading between/among the head- and 

trail-echo components. That fading occurs in a simple pattern (e.g., similar to the classic Young’s pointsource optics experiment) suggests a simple model of the meteor scattering process that, as we show 

below, appears both necessary and sufficient to explain what we observe. It is important to stress in 

introducing this model that it is successful in part due to the time and frequency and thus phase 

coherence of both the VHF and UHF radars that permit full use of the model we present. We also note 

that this capability has been intrinsic to most radars for many years but that full advantage of this 

“holographic” capability is just beginning for the modern geophysical radars. 

In the model scenario we propose, each head- or trail-echo signal is consistent with a point target 

– i.e., each has a well-defined phase center – that is readily modeled at the receiver baseband as

xn (t) 
 An exp j4Rn (t)



 



 



 (1)

where Rn(t) = Rn(t0) – vn(t – t0) + dn(t – t0)

2

 / 2 – the subscript n refers to the nth meteoroid fragment. In 

(1), j = -1 and the multiple meteoroid fragments are taken to be traveling on the same trajectory at 

range Rn(t) time t with t0 the initial time and with constant speed and deceleration vn, dn, respectively. It 

is important to note that equation (1) is accurate only if all the meteor energy is contained in the received 

bandwidth at baseband – otherwise filter features such as ringing may occur. To this end we employ a 1 

MHz bandwidth (actually 0.5 MHz at baseband for both the in-phase and quadrature channels thus 

satisfying the Nyquist sampling condition), 1 !s sample intervals, and a transmitter pulse of 10/20 !s at 

VHF/UHF, respectively. Thus the pulse spectrum is very narrow with respect to the sampled bandwidth 

so that the meteor Doppler shift (~22 kHz at VHF and ~200 kHz at UHF for a 72 km/s meteor) does not 

result in signal energy being lost outside the filter bandpass. Also note that eqn. (1) embodies the 

Doppler shift of the spectrum via the time rate of change of R(t) within a given pulse. 

 In an example of the successful use of equation (1), it can be seen that the signals from two 

slowly separating fragments alternately appear in- and out-of-phase as the net path from the two 

particles to the receiver varies over half a wavelength, /2. This results in a Young’s experiment-like 

outcome as we demonstrate below. Use of (1) to successfully characterize meteor head-echo returns and 

extract Doppler information dates to the earliest meteor observations at Arecibo Observatory (Janches et 

al. 2003, Mathews et al. 2003, Mathews et al. 1997). Radio science implications are discussed by 

Mathews (2004). 

 Figure 6 bottom panel shows Figure 2, event 1 along with modeling results that employ eqn. (1) 

for two particles (head-echoes) at both AO radar frequencies. The model results include Gaussian 

distributed random noise in both the in-phase and quadrature channels. As noted in the caption, the two 

particles are taken to start together but then separate at speeds of 50.4 km/s and 50.3 km/s, respectively, 

with no deceleration. The particle head-echoes have equal scattering cross-sections. The model beampattern at UHF is modeled as a double Gaussian yielding main- and side-lobes that closely match the 

observed meteor return. The VHF beam-pattern is a single very wide Gaussian that causes slight 

intensity decrease at the model event edges. 

 The Figure 6 model results at 430 MHz are completely consistent with the observations. The 

matching could be “tuned” by adjusting the speeds, adding a slight deceleration, and adjusting the initial 


phase separations of the two particles. However, this complexity is unnecessary and will be left to actual 

multi-particle fitting algorithms (Briczinski et al. 2006) that are currently under development for the 

multi-particle case. Mathews et al. (2010) gives a similar modeling/data comparison but for head-echo 

fading with a stationary flare-trail while Roy et al. (2009) give details on using equation (1) fitting via 

genetic algorithms. The VHF model result in Figure 6 shows the slower fading rate at VHF relative to 

UHF. This model result is similar to the observational results given in Figure 3 where the UHF fading 

rate is very rapid while the VHF fading rate is quite similar to the Figure 6 VHF model result. 

Figure 6. RTI images of an observed and modeled two-particle meteor event. The bottom panel event is just Figure 

2, event 1. The model is eqn. (1) applied separately to two particles of equal scattering cross-section that start at the 

same location but separate as the speeds are taken to be 50.3 km/s and 50.4 km/s with no deceleration. The VHF and 

UHF fading rates are different due to the much longer wavelength (6.4 m vs. 0.697 m) at VHF. See text for details 

on the beam-patterns. 

5 Conclusions 

We have reported on common volume V/UHF radar meteor observations at Arecibo Observatory. These 

observations have revealed meteor head- and trail-echo features that are consistent with meteoroid 

fragmentation. Further, the VHF observations have revealed flare-related trail-echoes that, due to the 

interference fading between the head- and trail-echoes, are found to be “small” compared with a 

wavelength in that a well defined phase center exists. We additionally find that both a necessary and 

sufficient description of the head- and trail-echoes is given by eqn. (1) which simply models point-target 

scattering at receiver baseband with no Doppler spreading of the spectrum as this has not proven 

necessary. We give modeling results supporting this conclusion. These results go beyond those given by 

Mathews et al. (2010) and Roy et al. (2009) and provide necessary insight into the radio science aspects 

of radar meteor observations (Mathews 2004). 

 We additionally report observations of UHF trail-echoes and UHF meteor echoes that are 

consistent with meteoroid terminal “flare” events and/or “classical” meteor echoes from a meteor 

traveling perpendicular to the radar pointing direction that is at zenith for these results. Also, we report 


what may be a new class of radar meteor events that we term “radar bolides”. Thus far, radar bolides 

appear only as large (i.e., intense, distributed in altitude, and long-lived) trail-events in that the 

progenitor meteoroid head-echo has not been convincingly identified as it apparently falls outside the 

radar beam. The radar bolides last 100’s of milliseconds through, thus far, to about 10 seconds and 

consist of multiple scattering centers distributed over several kilometers in range. Apparently these 

“trails” drift into the radar beam due to the ~100 m/s winds in the upper mesosphere (Mathews 1976). It 

seems likely that this pattern of scatterers is formed when a large meteoroid breaks into a pattern of still 

large meteoroids with significant horizontal dispersion at 90 km altitude where we observe the “radar 

bolide” event. In any case, the “radar bolide” is quite intensive relative to the usual meteor events. 

 While Mathews et al. (2010) reports ~90% fragmentation signatures for this set of observations, 

a companion paper (Malhotra and Mathews, these proceedings), report a different distribution of meteor 

events from the Resolute Bay Incoherent Scatter Radar (RISR). At RISR they find an event type 

distribution of fragmentation (48%), simple ablation (32%), and differential ablation (20%). We suggest 

that this contrast is likely caused by AO “seeing” significantly smaller meteoroids than RISR – this due 

to the much higher sensitivity of AO relative to RISR. 

 Finally we note that the simultaneous presence of close meteoroid fragments renders a clear 

definition of dynamic mass (Fentzke et al. 2009, Janches & Chau 2005, Mathews et al. 2001), absolute 

scattering-cross section mass (Close et al. 2005), and meteoroid mass density (Briczinski et al. 2009, 

Novikov & Pecina 1990) difficult at best. Additionally, interpretation of details such as differential 

ablation (Janches et al. 2009) also becomes difficult as the ensemble of evolving particles appears to be 

capable of producing not only the lightcurves we expect for a differential ablation event but also the 

exact opposite (Mathews et al. 2010; Malhotra and Mathews, these proceedings). Put concisely, our 

results indicate that many meteoroids arrive at the top of the atmosphere as a “dustball” or an otherwise 

loosely-attached configuration of particles (Verniani 1969) that begin to separate immediately on 

encountering the atmosphere and/or as the system proceeds into the atmosphere and becomes visible as 

a radar meteor. These particles also undergo occasional instantaneous “flaring” whereby one of the 

ensemble of particles or a newly created particle is apparently terminally destroyed thus creating the 

plasma “blob” that we observe as the flare. 

 To paraphrase (Verniani 1969), the authors wish to conclude this section by quoting the thoughts 

of one of the historically-most-established leaders in meteor research: “I regard the process of 

fragmentation of meteor bodies as even more important than is recognized now. Therefore further 

studies of this process seem to be necessary. It is impossible to predict the course of fragmentation for 

an individual meteor particle but statistical regularities of the fragmentation process must exist and they 

should be studied. These statistical regularities are probably somewhat different for different meteor 

streams and also probably vary with the mass of the meteor particles.” (Levin 1968) 

Acknowledgements

The Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated 

by Cornell University under a cooperative agreement with the National Science Foundation. This effort 

was supported under NSF grant ATM 07-21613 to The Pennsylvania State University.


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References 

S.J. Briczinski, J.D. Mathews, & D.D. Meisel, J. Geophys. Res., 114 A04311 (2009) 
A Study on Various Meteoroid Disintegration Mechanisms as Observed from the 

Resolute Bay Incoherent Scatter Radar (RISR) 

)

A. Malhotra1

• J. D. Mathews 

Abstract There has been much interest in the meteor physics community recently regarding the form 

that meteoroid mass flux arrives in the upper atmosphere. Of particular interest are the relative roles of 

simple ablation, differential ablation, and fragmentation in the meteoroid mass flux observed by the 

Incoherent Scatter Radars (ISR). We present here the first-ever statistical study showing the relative 

contribution of the above-mentioned three mechanisms. These are also one of the first meteor results 

from the newly-operational Resolute Bay ISR. These initial results emphasize that meteoroid 

disintegration into the upper atmosphere is a complex process in which all the three above-mentioned 

mechanisms play an important role though fragmentation seems to be the dominant mechanism. These 

results prove vital in studying how meteoroid mass is deposited in the upper atmosphere which has 

important implications to the aeronomy of the region and will also contribute in improving current 

meteoroid disintegration/ablation models. 

Keywords meteor radar · meteoroid disintegration · meteoroid fragmentation · ablation 

1 Introduction 

Meteoroids are responsible for thousands of kilograms of mass flux into the earth’s upper atmosphere 

annually (Mathews et al. 2001).These meteoroids are not only the only source of metallic ions in the 

upper atmosphere (Kelley 1989) but also, as a result of this very high mass flux, pose a threat to our 

space infrastructure (Caswell and McBride 1995) and are responsible for a variety of ionospheric 

phenomenon such as the Sporadic-E (Malhotra et al. 2008) and Polar Mesospheric Summer Echoes 

(Bellan 2008). This makes it imperative that we know and understand the form in which meteoroids 

disintegrate into the upper atmosphere in order to understand the aeronomy of the region. 

 As the meteoroid enters the earth’s atmosphere, it collides with the air molecules and heats up. 

When the temperature reaches around 2000K – usually between 80-120km – surface particles start 

evaporating from the body. These particles quickly ionize, also ionizing the air molecules around them, 

forming a ball of plasma around the meteoroid. Radar scattering from this ball of plasma surrounding 

the meteoroid is called the head echo. Although meteor head echoes were first observed in the 1940s 

(Hey et al. 1947), their study gained momentum only in the 1990s when they were observed using the 

High Power Large Aperture [HPLA] radars (Mathews et al. 1997). Since then, these head echo 

observations have proved invaluable in determining meteoroid velocities (Janches et al. 2000), mass flux 

(Mathews et al. 2001) and radiants (Chau and Woodman 2004). More recently, these head echo 

observations are being studied to determine the form that meteoroid mass flux takes when it enters into 

 

A. Malhotra • J.D. Mathews ( ) 

Radar Space Sciences Lab, The Pennsylvania State University, University Park, PA USA 16802. Phone: 814-865-2354, Email: 

JDMathews@psu.edu 


the earth’s upper atmosphere. As outlined below, these initial studies on meteoroid disintegration using 

various HPLA radars have produced contrasting results, generating much interest and even controversy 

in the meteor community. 

 Kero et al. (2008), using the EISCAT 930 MHz UHF radar, provide “the first strong 

observational evidence of a submillimeter-sized meteoroid breaking apart into two distinct fragments” 

i.e. fragmentation. Fragmentation can take place either due to thermally induced stresses (Jones and 

Kaiser 1966) or due to the separation of a molten metal droplet from the lower density chondritic 

compounds of a heated meteoroid (Genge 2008). Kero et al. (2008) provide an example of a “beat 

pattern” light curve event [the light curve is defined as the pulse-integrated Signal-to-Noise Ratio 

(SNR)], their Figure 2, and interpret it as being due to interference from two distinct scattering centers. 

They show that the result is consistent with interference from two fragments of unequal cross-sectional 

area over mass ratio, separating from each other due to different deceleration along the trajectory of the 

parent meteoroid. They also provide examples of a “smooth” light curve where the measured SNR 

follows the antenna beam pattern (their Figure 1) i.e. simple ablation and a quasi-continuous 

disintegration event (their Figure 3). 

 Mathews at al. (2008), carrying out a similar analysis for the meteor echoes observed by the 

Sondrestorm Radar Facility (SRF) 1290 MHz radar, conclude that almost all the meteors observed by 

the SRF radar are fragmenting large meteoroids that are observed only in the terminal phase of their 

encounter with the upper atmosphere. 

 Roy et al. (2009) use a genetic-algorithm based search and fitting procedure to solve for the 

number of scatterers and their differential speeds in estimating the properties of complex light curves 

observed by the Poker Flat ISR radar. Based on the above-mentioned analysis, they conclude that 

fragmentation is the cause of complex light curves. 

 Dyrud and Janches (2008) determine meteoroid properties by comparing expected results from a 

theory based ablation model of the meteor head echo and observed meteor properties using the Arecibo 

430 MHz UHF radar. They do not include the effects of fragmentation in their model as they “find no 

evidence that meteoroid fragmentation plays a role in the vast majority of head-echo observations at 

Arecibo”. However, they also conclude that a simple ablation model cannot account for the non-smooth 

light curves observed by the radar. 

 Janches et al. (2009), using the Arecibo 430 MHz UHF radar, provide the first observations of 

differential observations in micrometeoroids. In the differential ablation process, the particle’s more 

volatile components (Na and K) are released first when the temperature is still relatively low followed 

by the evaporation of less volatile components (Si, Fe and Mg) as the particle descends through the 

atmosphere, increasing its temperature. Events undergoing differential ablation are characterized by a 

sudden decrease or increase in the light curve. Though they observed features of the differential ablation 

process only in small percentage of the detected events, they still conclude that differential ablation is 

the main mechanism by which micron-sized particles deposit their mass in the upper atmosphere. 

 Mathews et al. (2010), using data collected from simultaneous observations using the same 

Arecibo 430 MHz UHF radar and the Arecibo 46.8 MHz common-volume VHF radar, present many 

unreported features in the radar meteor return that are consistent with meteoroid fragmentation. Based 

on modeling studies and statistical analysis, they conclude that fragmentation is the dominant process by 

which micrometeoroids deposit their mass in the upper atmosphere H a conclusion at direct odds with 

the one reached by Janches et al. (2009), though both the studies use the same radar. 

 It is clear from the above introduction that the process by which micrometeoroids deposit their 

mass in the upper atmosphere remains is a topic of much interest in the community and the relative roles 

of fragmentation, differential ablation and simple ablation is a subject of much debate and speculation. 


However, to-date there has been no statistical study studying the relative contribution of the three 

mechanisms. In this paper, we present the results from first-ever such study. In Section 2, we present 

details of the observational set-up and radar parameters. The results are presented in Section 3, followed 

by the discussion in Section 4. We end with the conclusions of our study and the scope for future work

in Section 5. 

2 Observational Set Up 

The results presented herein happen to be one of the first published results from the newly-operational 

442.9 MHz Resolute Bay Incoherent Scatter Radar (RISR) located in Resolute Bay, Nunavut, Canada 

(74.72950° N, 94.90539° W). For these observations carried out on 24-25 and 26 August 2009 from 

2140 to 0040 hours (UT) and 1120 to 1455 hours (UT) respectively (totally ~ 6.3 hours of data), the 

radar beam was pointed in a direction parallel to the Earth's rotation axis and the maximum power 

transmitted was ~ 1.7 MW. Transmission and reception was done using all the 128 panels of the radar. 

A pulse width of 90 !s with an IPP (Inter Pulse Period) of 2 ms was used for transmission. 

3 Observational Results 

We observe meteor signatures of all three micrometeoroid disintegration mechanisms, i.e. 

fragmentation, differential ablation and simple ablation using the Resolute Bay Incoherent Scatter Radar 

(RISR), enabling us to conduct a statistical analysis of the relative role of these mechanisms. We begin 

by presenting representative examples of all the three mechanisms as observed by RISR. These events 

will also serve to facilitate future similar studies using RISR and the other HPLA radars. 

Figure 1a is a RTI (Range-Time-Intensity) plot of a typical fragmenting meteor event. Note the 

structure present in the meteor return. The beat pattern can be noticed even without the aid of the light 

curve. Figure 1b shows the light curve (pulse integrated SNR for each IPP) for the event shown in 

Figure 1a. As expected from the RTI plot, the beat pattern associated with fragmentation is observed. An 

explanation on the cause of this observed beat pattern is given in a companion paper by Mathews and 

Malhotra in this issue. 

Figure 2a is a RTI plot of a typical meteor event undergoing differential ablation and the 

corresponding light curve is shown in Figure 2b. Notice the abrupt decrease in SNR received at ~ 32 ms; 

a possible signature of differential ablation [Figure 2 of Janches et al. (2009)]. Janches et al. (2009) 

attribute this sudden decrease in received power to the complete ablation of the main meteoroid 

constituents (Si, Fe and Mg). The reduced power received after the sudden decrease is due to the plasma 

created in ablation of the refractory metals (Ca, Al and Ti). 

 Figure 3a is a RTI plot of a typical meteor event undergoing simple ablation and Figure 3b is the 

corresponding light curve for this event. Notice the relatively smooth pattern (compare to the cases 

presented in Figure 1b and 2b) obtained for this event in Figure 3b. We assume simple ablation occurs 

due to the homogeneous composition of the meteoroids.


 

Figure 1. (a) Range Time Intensity (RTI) plot of a fragmenting meteor event. Notice the structure within the meteor 

return. (b) The light curve for this event. The “beat pattern” observed is obtained due to alternate in-phase and outof-phase scattering due to change in separation between multiple particles. 

Figure 2. (a) RTI plot of a meteor event undergoing differential ablation. (b) The light curve for this event. The 

sudden drop in SNR is attributed to the complete ablation of the more volatile meteoroid constituents. 


 

 

Figure 3. (a) RTI plot of a meteor event undergoing simple ablation. (b) The light curve for this event. Notice the 

relatively smooth profile compared to the events shown in Figure 1 and 2. 

4 Discussion 

Figures 1-3 show typical meteor events observed by RISR exhibiting fragmentation, differential ablation 

and simple ablation respectively. Note that we use Figures 1-3 to define what we interpret as these 

processes. We present the results from the statistical analysis determining the relative contributions of 

the three meteoroid disintegrating mechanisms. For the purpose of this analysis, we ignored low SNR 

events (SNR less than 2dB) as in these cases, even small changes in received power might result in 

giving an impression of a beat pattern, which might be wrongly interpreted as fragmentation. The events 

that exhibited two or more of the mechanisms were classified in all the relevant categories. 

 Following the above-mentioned criteria, we were able to classify 318 events in our data sets. 153 

or ~48% of these events exhibited signatures of fragmentation, 62 or ~20% of the events exhibited 

signatures associated with differential ablation while 103 or ~32% of the events showed signatures of 

simple ablation. Fourteen events showed signatures of both fragmentation and differential ablation. 

Though we also observe events exhibiting both simple ablation and fragmentation, they are all low SNR 

cases and thus not included in the final count for the reasons mentioned above. 

 From these results, it is obvious that meteoroid disintegration in the upper atmosphere is a 

complex process in which all the three disintegration mechanisms play an important role, though from 

these results it seems that fragmentation is the dominant disintegration mechanism. This result has 

important implications on the aeronomy of the MLT (Mesosphere-Lower Thermosphere) region as it 

implies that majority of the mass flux from the micrometeoroids is deposited in form of dust rather than 

atomic metal form obtained due to ablation. The abundance of this meteoroic dust could also provide 

valuable insights into the formation of PMSEs. The fact that all the three mechanisms play a vital role in 

meteoroid disintegration is an equally important conclusion as it differs from the conclusions arrived at 

by Janches et al. (2009) and Mathews et al. (2010), which lay emphasis on differential ablation and 

fragmentation only, respectively. This result stresses the need for all the three disintegration mechanisms 

to be taken into account while coming up with any model for meteoroid ablation. The models currently 

in use to estimate radar meteor head echo properties consider only simple ablation and the above 

analysis shows that there clearly is a lot of scope for improvement in these models. 


5 Conclusions 

We have presented results from the first-ever study determining the relative importance of the three 

meteoroid disintegration mechanisms, namely fragmentation, differential ablation and simple ablation – 

a topic of much discussion and debate presently in the meteor community. We present “type specimen” 

meteor events that serve to define the presence of the three disintegration processes. Additionally, these 

results also constitute the one of the first reported observations from the newly-operational Resolute Bay 

Incoherent Scatter Radar. Our results suggest that meteoroid arrival and disintegration in the upper 

atmosphere observed by the UHF is a complex process in which all the three mechanisms play an 

important role though it seems that fragmentation is the dominant mechanism – an important result as it 

implies that majority of meteoroid mass flux is deposited in the upper atmosphere in dust rather than 

atomic form. The meteoroid disintegration process is further complicated by presence of events 

exhibiting signatures of more than one disintegration mechanism. Our results strongly suggest that any 

theoretical model explaining meteoroid disintegration should consider all the three disintegration 

mechanisms. Finally, we recommend that a similar classification study should be conducted not only at 

RISR with a larger data set but also at other radars such as the Arecibo, PFISR, SRF, ALTAIR and 

Jicamarca radars. Such a study would help in understanding the difference in the type of meteoroid flux 

observed by these radars at different locations operating at different frequencies and also lend further 

insights into the aeronomy of their respective MLT regions. 

Acknowledgements 

This effort was supported under NSF grants ATM 07-21613 and ITR/AP 04-27029 to The Pennsylvania 

State University. 

References 

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M.J. Genge, Earth, Moon and Planets 102, 525 (2008). 

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D. Janches, L. Dyrud, S.L. Broadley, J.M.C. Plane, Geophysical Research Letters (2009) doi:10.1029/2009GL037389. 

D. Janches, J.D. Mathews, D.D. Meisel, Q.H. Zhou, Icarus 145, 53 (2000). 

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doi:10.1029/2007GL032733. 

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A. Roy, S.J. Briczinski, J. Doherty, J.D. Mathews, IEEE Geoscience and Remote Sensing Letters 6, 27 (2009)


CHAPTER 9: 

VIDEO AND OPTICAL OBSERVATIONS 


Video Meteor Fluxes 

M. D. Campbell-Brown1• D. Braid 

Keywords meteor · Eta Aquariid · sporadic · flux · video 

1 Introduction 

The flux of meteoroids, or number of meteoroids per unit area per unit time, is critical for calibrating 

models of meteoroid stream formation and for estimating the hazard to spacecraft from shower and 

sporadic meteors. Although observations of meteors in the millimetre to centimetre size range are 

common, flux measurements (particularly for sporadic meteors, which make up the majority of 

meteoroid flux) are less so. It is necessary to know the collecting area and collection time for a given set 

of observations, and to correct for observing biases and the sensitivity of the system. 

 Previous measurements of sporadic fluxes are summarized in Figure 1; the values are given as a 

total number of meteoroids striking the earth in one year to a given limiting mass. The Grün et al. (1985) 

flux model is included in the figure for reference. Fluxes for sporadic meteoroids impacting the Earth 

have been calculated for objects in the centimeter size range using Super-Schmidt observations 

(Hawkins & Upton, 1958); this study used about 300 meteors, and used only the physical area of overlap 

of the cameras at 90 km to calculate the flux, corrected for angular speed of meteors, since a large 

angular speed reduces the maximum brightness of the meteor on the film, and radiant elevation, which 

takes into account the geometric reduction in flux when the meteors are not perpendicular to the 

horizontal. They bring up corrections for both partial trails (which tends to increase the collecting area) 

and incomplete overlap at heights other than 90 km (which tends to decrease it) as effects that will affect 

the flux, but estimated that the two effects cancelled one another. Halliday et al. (1984) calculated the 

flux of meteorite-dropping fireballs with fragment masses greater than 50 g, over the physical area of 

sky accessible to the MORP fireball cameras, counting only observations in clear weather. In the micron 

size range, LDEF measurements of small craters on spacecraft have been used to estimate the flux (Love 

& Brownlee, 1993); here the physical area of the detector is well known, but the masses depend strongly 

on the unknown velocity distribution. In the same size range, Thomas & Netherway (1989) used the 

narrow-beam radar at Jindalee to calculate the flux of sporadics. In between these very large and very 

small sizes, a number of video and photographic observations were reduced by Ceplecha (2001). These 

fluxes were calculated (details are given in Ceplecha, 1988) taking the Halliday et al. (1984) MORP 

fireball fluxes, slightly corrected in mass, as a calibration, and adjusting the flux of small cameras to 

overlap with the number/mass relation from that work. Then faint video observations, which overlap 

with small cameras at their largest sizes, were similarly calibrated using the small camera data. The flux 

data from Ceplecha's study between 10-6 and 10-4 kg does not fit the slope between the LDEF and SuperSchmidt data (Figure 1), so uncertainty remains in this region. The flux in this size range is of particular 

importance, since much of the mass lost by comets is in particles of this size; also, the greatest danger to 



M. D. Campbell-Brown ( ) 

University of Western Ontario, London ON N6A 3K7 Canada. E-mail: margaret.campbell@uwo.ca 


Figure. 1. Plot of meteoroid fluxes on the Earth from previous studies. 

spacecraft comes from particles common enough to pose a real threat, and large enough to cause 

damage. 

 Shower fluxes have been estimated from visual observations (Brown & Rendtel, 1996), and from 

photographic and video observations. The usual method (employed in calculating Leonid fluxes by 

Koten et al. (2007), for example), uses the physical area observed by a pair of cameras at 100 km and 

applies a correction for radiant elevation. The most rigorous optical fluxes have been calculated for 

Leonids, Orionids and some minor showers (e.g. Gural et al., 2004; Trigo-Rodriguez et al., 2007, 2008) 

using a thorough simulation of the observing systems, including the camera sensitivity, range biases, and 

angular speed of the meteors on each camera. Details of the simulation are given in Molau et al. (2002). 

 In this work, we rigorously calculate the collecting area for a set of two intensified video 

cameras deployed in Arizona in 2006. The collecting area calculation was tested on the Eta Aquariid 

meteor shower and then applied to the antihelion, apex and north toroidal sporadic sources to obtain a 

sporadic flux. 

2 Observations & Data Analysis 

The data used in this study were taken from two sites in Arizona: the Fred Lawrence Whipple 

Observatory (31.675°N, 110.953°W) and Kitt Peak National Observatory (31.962°N, 111.60°W),using 

identical cameras, during a nine-night campaign in 2006. The baseline between the two sites was 


approximately 75 km. Both systems had 25 mm, f/0.85 objective lenses, Gen III ITT image intensifiers, 

and Cohu 4910 video cameras. Each system produces 30 interlaced frames per second, with standard 

video resolution of 640×480 pixels and 8 bits per pixel. The data were recorded on digital tapes for later 

analysis. Two nights of data were analyzed for this project: April 27 and May 6, 2006. The latter is the 

peak of the eta Aquariid meteor shower. 

 The MeteorScan software package (Gural, 1997) was used to identify meteors in the data. A total 

of 235 meteors simultaneously observed with both cameras were identified. The astrometry and 

photometry were measured using an in-house software package called PhotoM. Trajectories of the twostation meteors were calculated using MILIG, developed by J. Borovika (Borovika, 1990). 

Photometric masses were calculated for each of the meteors, and the distribution of these masses was 

used to find the sporadic mass index, s = 2.02 ± 0.02, and the limiting mass, 2.06×10-6 kg. 

 In order to calculate the flux of meteoroids from a particular radiant, the number of meteoroids 

must be counted. Rather than calculate a partial trail correction, we accept only meteors for which the 

maximum of the light curve occurred in the common volume of the two cameras. There is some 

uncertainty even in this strict criterion: many meteor light curves are nearly flat at the peak, so judging 

whether the maximum was just inside or just outside the volume can be difficult. Some meteors were 

growing fainter when they entered the field of view of both cameras, and some growing brighter as they 

left both cameras: while the first or last observed frame might have been the maximum, these meteors 

were excluded. This left 121 meteors in the sample. 

 Figure 2 shows the radiant distribution in ecliptic coordinates. The apex of the Earth's way is in 

the centre of the plot, and the antihelion source to the right, near the antihelion point at 180° ecliptic 

longitude. The antihelion source is the clearest feature: the north apex source is also identifiable. 

Although there are meteors in the region of the north toroidal source, its borders are not clearly defined. 

The Eta Aquariids are visible as a small cluster of radiants to the left of the apex source, just above the 

ecliptic around longitude 295°. There are virtually no meteors in the region of the south apex source, and 

only one close to the helion source. There are a large number of meteors which are not within the 15 

degree radius of any of the sporadic sources. 

Figure 2. Radiants of meteors used in the flux study. The horizontal axis is the ecliptic plane; the apex of the 

Earth's way is in the centre (270° longitude) and the sun is at (0,0). The darkest dot represents six meteors with very 

close radiants; the lightest dots have only one meteor per 1 degree bin. 


3 Collecting Area 

If meteoroids all ablated at the same height, and detectors were uniformly sensitive, calculating the 

collecting area would be straightforward: the physical area covered by the detector at that height could 

be found quite simply. Even at a single height, the problem is more complicated: the sensitivity of a 

camera is generally a function of the position on the detector (with the most sensitivity generally 

occurring in the center of the field of view, and the least at the edges, mainly due to vignetting from the 

objective lens). The area in the sky is not at a uniform distance from the camera, so the limiting 

sensitivity will vary according to the range. Finally, the angular speed of the meteor as seen at the 

detector will influence whether or not it will be detected: a meteor coming straight at the camera may 

not be identified as a meteor at all, since it does not trace out a line, while one which is moving 

perpendicular to the line of sight will have its light in each frame spread over more pixels, which may 

reduce the signal until it is lost in the noise. All of these effects should properly be taken into account 

when calculating flux. 

 Even for shower meteors, the heights of meteors vary significantly from one to another, and 

meteors may not all cross one particular surface of constant height. In that case, the collecting area must 

be calculated at different heights, with a weighting for the probability of observing a meteor at that 

height. 

 The sensitivity of each camera was calculated from flatfields for each system. The optical centre 

of the image was found, using the highest pixel values in the flatfield to find the region of maximum 

sensitivity. The distance of each pixel in degrees from this optical centre was determined, and a fit 

performed to find the sensitivity as a fraction of the maximum as a function of angle from the centre. 

 For a particular radiant, the collecting area was calculated for half hour intervals throughout the 

night. For each time interval, slices from 80 to 120 km, with a spacing of 2 km, were taken; the 

corrected area of each slice was calculated, and a weighting factor was applied according to the height 

distribution of maximum luminosities of the meteors in the dataset. The weights, found using the 

distribution of maximum heights in the data set, were distributed as a Gaussian, with a maximum at 98 

km and a standard deviation of 13 km; the final collecting area was normalized by dividing by the sum 

of the weights. Each slice was divided into squares 4 km × 4 km; the area of each square was weighted 

by the sensitivity of each camera, compared to the maximum sensitivity, the range to each camera 

squared, and the angular speed of a meteor from the given radiant at that position on each camera. If the 

trails at that point would be less than 3 pixels long, the area of that square was set to zero, assuming the 

meteor would not have been detected. The area was also weighted for the cosine of the zenith angle of 

the radiant, since the rate depends geometrically on the angle between the radiant and the surface. The 

total weighting factor was taken to the power of s 1; if the mass index is large, there are many faint 

meteors, and more meteors will be missed in the less sensitive areas. If s is small, there are many bright 

meteors and fewer will be missed, so the collecting area is larger. 

 The integrated nightly collecting area for all heliocentric radiants is shown in Figure 3. It can be 

seen that the maximum collecting area occurs outside the sporadic sources, and partly explains the large 

number of meteors observed outside the sources. The collecting area for the north apex and antihelion 

sources are actually low compared to other parts of the sky. The region where the radiants pass through 

the fields of view of the cameras is also clearly visible as a cuved line of lower collecting areas in the 

middle of the maximum area. 


Figure 3. Integrated daily collecting area of the video system in heliocentric coordinates (as in Figure 2). 

4 Eta Aquariid Fluxes 

May 6, 2006 was the peak of the Eta Aquariid meteor shower. Although the radiant rose only about two 

hours before dawn at the observing site, and only 8 two-station Eta Aquariids had their light curve 

maximum in the common volume, we calculated the shower flux as a test of the method. The IMO value 

of the mass index, 1.95, was used (Dubietis, 2003), even though this is for larger visual meteoroids, 

since there were not enough Eta Aquariid meteors in our sample to calculate the mass index. The 

collecting area of the system for the Eta Aquariid radiant is shown in Figure 4. 

Figure 4. Collecting area for the Eta Aquariid radiant at half-hour intervals. The shaded regions 

indicate times when the sky was too bright to observe, starting and ending at nautical twilight. 


 The non-zero collecting areas were summed and the flux obtained for the two hour period was 

0.0028 ± 0.0009 meteoroids km-2 hr-1. This corresponds to a zenithal hourly rate of 65 (see Brown & 

Rendtel, 1996, for the formula to convert between ZHR and flux), which is very close to the value 

recorded for visual observations that year by the IMO (imo.net). This is certainly due partly to chance; 

since the number of meteors used in the flux calculation was so small, there are significant uncertainties 

in the estimate, but it gives us confidence that the collecting area calculation is correct. 

5 Sporadic Fluxes 

Sporadic fluxes are slightly more complicated than shower fluxes. The sources are diffuse, so the radius 

chosen will strongly affect the number of echoes included and therefore the flux. The collecting area 

also varies significantly across the source: the leading edge of the source can rise more than an hour 

before the trailing edge. When calculating the angular speed, there are uncertainties not only because of 

the large radiant area, but also because the speeds of the meteors have a broad distribution around the 

average, instead of being tightly confined as shower speeds are. For this study, we take a simple 

approach. Each source is divided into four quadrants, and the collecting area for each quadrant is 

calculated in half hour intervals. The average of these four values is used as the true collecting area. This 

approach is more efficient than the more rigorous version, which would involve calculating the 

collecting area for dozens of points around the source and then performing a weighted average reflecting 

the differing activity of each small point around the source, and it correctly reproduces the slow rise in 

collecting area as the radiant moves above the horizon. In calculating angular velocity, the average 

speed for each source (30 km/s for the antihelion, 35 km/s for the north toroidal, and 60 km/s for the 

north toroidal) was used rather than a distribution. The collecting area should be slightly lower for 

meteors moving faster than the average, and slightly higher for slower meteors, but the total collecting 

area should be the same if the velocity distributions are Gaussian. 

 Fluxes were calculated separately for the two nights of data, since the collecting areas for each 

source vary very slightly in that time period. Since the number of observed meteors was low, hourly 

fluxes were not calculated; the total number of meteors from each source was divided by the average 

collecting area. It was not possible to calculate a mass index for each source individually from the small 

numbers, so a mass index of 2.0 was assumed for each source, consistent with the s measured for all the 

sporadics observed in the dataset. 

 A total of 24 antihelion, 21 north apex, and 15 north toroidal meteors were recorded on the two 

nights. When divided by collecting area (pictured in Figures 5-7), this produced fluxes of 0.039 ± 0.006 

meteoroids km-2 hr-1 for the antihelion source, 0.041 ± 0.006 meteoroids km-2 hr-1 for the north apex, and 

0.012 ± 0.002 meteoroids km-2 hr-1 for the north toroidal. The errors were calculated using Poisson 

statistics for the small numbers, plus estimates of the error due to assuming a mass index and height 

distribution based on small numbers. The collecting area was varied to look at a reasonable range of 

mass indices for each source, and was found to vary by about 10%. The change in the weighted area of a 

slice from 90 km to 110 km was also found to be close to 10%. 

 To find the total sporadic flux, the flux from each of the three observed sources was doubled to 

account for its unobserved pair: the helion, south apex and south toroidal sources. This ignores the fact 

that the flux of the helion and antihelion sources vary through the year and the maxima and minima do 

not coincide (Campbell-Brown & Jones, 2006). It is believed that the pairs of sources have very close to 

symmetrical flux values when summed over the year, so this method should give a good annual value if 

there was more data. We proceed with this value, knowing that it is based on too little data, to see how it 

compares to previous studies. 


Figure 5. Collecting area for the antihelion source. The shaded regions indicate daytime until nautical twilight, when the sky was too bright to observe. 

Figure 6. Collecting area for the north apex source. 

Figure 7. Collecting area for the north toroidal source. 


 The total sporadic flux from all the sources is 0.18 ± 0.04 meteoroids km-2 hr-1. To compare this 

to the studies mentioned in the introduction, we convert this to a fluence over the whole Earth over a 

year, by multiplying by the cross-sectional area of the Earth and the number of hours in a year. The total 

is (2.0 ± 0.4) × 1011 meteoroids. 

 The error bars include only errors in our measured value: they do not reflect the fact that the 

sporadic flux changes over the course of a year and that figures for part of two days are being used to 

estimate the flux over a full year. Figure 8 shows this result with previous studies. Note that the error 

bars are smaller than the symbol, because of the logarithmic scale. 

Figure 8. Plot of meteoroid fluxes on the Earth from previous studies, with the data point from the current study. 

6 Discussion 

The flux results for the Eta Aquariid meteor shower, though based on few meteors, are very promising, 

and give confidence that our method of calculating collecting area for particular radiants gives 

reasonable results. Shower fluxes are easier to calculate than sporadic fluxes, because of the higher 

numbers and narrow range of radiants and velocities, and more measurements with other systems are 

available for comparison, so future studies will examine more showers to further validate the method. 

 The total sporadic flux measured in this study fits surprisingly well on a line joining the fireball 

camera data to the Grün model, and is well above the flux from video studies by Ceplecha (2001). The 

fit is more surprising considering that it is based on only two nights of data from one part of the year, 

and a total of only 60 meteors. 


 The flux reported here reflects only meteoroids with radiants in one of three sporadic sources. An 

additional 61 meteors with maximum luminosity in the common volume were not included in the flux 

calculations because their radiants lay outside the sources. While this would seem to introduce a factor 

of two error in our measurement, we believe that the actual change in flux would be small if these other 

meteors were included. Inspection of Figures 2 and 3 shows that most of the meteors from radiants 

outside the sources occur in regions of the sky with very large collecting areas, meaning that the flux 

from those areas will be low. 

 For the past year, we have been running an automated two-station video system at the University 

of Western Ontario, and have collected over 1500 two-station meteor observations, mostly sporadic 

meteors. This dataset will be the subject of the next flux study, which will use a much larger dataset 

collected over a much more extensive range of solar longitudes to calculate the flux of sporadic meteors. 

In addition to the flux from the sporadic sources, this new study will calculate the fluxes from the whole 

visible sky, something which will be possible with much larger numbers. This new flux value, and the 

mass index which will accompany it, will better fill in the gap in our understanding of meteoroids in the 

millimetre to centimetre size range. 

Acknowledgements 

Thanks to Jean-Baptiste Kikwaya and Shannon Nudds, who collected the video data, and to the NASA 

Meteoroid Environment Office for funding. 

References 

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Brown P., Rendtel J., “The Perseid Meteoroid Stream: Characterization of recent activity from visual observations”, Icarus, 

124, 414-428 (1996) 

Campbell-Brown M., Jones J., “Annual Variation of Sporadic Radar Meteor Rates”, MNRAS 367, 709-716 (2006) 

Ceplecha Z., “Earth's Influx of Different Populations of Sporadic Meteoroids from Photographic and Television Data”, 

BAICz 39, 221-236 (1988) 

Ceplecha Z., “The Meteoroidal Influx to the Earth”, in Collisional Processes in the Solar System, 35-50. Kluwer, Dordrecht 

(2001) 

Dubietis A., “Long-term Activity of Meteor Showers from Comet 1P/Halley”, JIMO 31, 43-48 (2003) 

Halliday I., Blackewell A.T., Griffin A.A., “The frequency of meteorite falls on the earth”, Science 223, 1405-1407 (1984) 

Hawkins G., Upton E., “The Influx Rate of Meteors in the Earth's Atmosphere”, ApJ, 128, 727-735 (1958) 

Grün E., Zook H.A., Fechtig H., Geise R.H., “Collisional Balance of the Meteoritic Complex”, Icarus 62, 244-272 (1985) 

Gural P., “An Operational Autonomous Meteor Detector: Development Issues and Early Results”, JIMO 25, 136-140 (1997) 

Gural P., Jenniskens P., Koop M., Jones M., Houston-Jones J., Holman D., Richardson J. “The Relative Activity of the 2001 

Leonid Storm Peaks and Implications for the 2002 Return”, AdSpR 33, 1501-1506 (2004) 

Koten P., Borovika J., Spurny P., Evans S., Štork R., Elliott A., “Video Observations of the 2006 Leonid Outburst”, EM&P 

102, 151-156 (2007) 

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553 (1993) 

Molau S., Gural P., Okamura O., “Comparison of the `American' and the `Asian' 2001 Leonid Meteor Storm”, JIMO 30, 3-21 

(2002) 

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Trigo-Rodriguez J., Madiedo J., Llorca J., Gural P., Pujols P., Tezel T., “The 2006 Orionid Outburst Imaged by All-sky CCD 

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Searching for Serendipitous Meteoroid Images in Sky Surveys 

D. L. Clark1• P. Wiegert 

Abstract The Fireball Retrieval on Survey Telescopic Image (FROSTI) project seeks to locate 

meteoroids on pre-existing sky survey images. Fireball detection systems, such as the University of 

Western Ontario’s ASGARD system, provide fireball state vector information used to determine a precontact trajectory. This trajectory is utilized to search databases of sky survey image descriptions to 

identify serendipitous observations of the impactor within the hours prior to atmospheric contact. 

Commonly used analytic methods for meteoroid orbit determination proved insufficient in modeling 

meteoroid approach, so a RADAU based gravitational integrator was developed. Code was also written 

to represent the description of an arbitrary survey image in a survey independent fashion, with survey 

specific plug-ins periodically updating a centralized image description catalogue. Pre-processing of 

image descriptions supports an innovative image search strategy that easily accounts for arbitrary object 

and observer position and motion. 

Keywords meteor · meteoroid · pre-detection · sky survey · frustum · image search 

1 Introduction 

The association of in-space and in-atmosphere images provides a unique opportunity to correlate results 

from differing observation and modelling techniques. In-space and in-atmosphere observations both 

directly and indirectly yield conclusions as to object size, composition and dynamics. With the two 

observations of the same object, one is able confirm consistency, or highlight discrepancies, in existing 

methods. One would hope as well that the discovery of a pre-fireball meteoroid (PFM) would add to the 

understanding of the visual properties of Earth-impacting objects. The discovery of a PFM in space 

would serve to confirm or suggest refinements to methods used to calculate heliocentric orbits from 

fireball observations. 

When work began on the FROSTI project in the summer of 2007, there had not been a single 

fireball object which had both been recorded in space on its approach to Earth, and recorded in the 

atmosphere as a fireball. The goal of FROSTI is to discover such dual observations through a systematic 

search of historical sky survey images for objects detected in all-sky camera systems. The initial data 

image survey targeted was the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) image 

catalogue (CFHT, 2009). A lofty goal of FROSTI was to be the first to relate in-space and inatmosphere observations of a common object. However, that accomplishment was met with the precontact discovery of object 2008 TC3 by the Catalina Sky Survey (Jenniskens, et al., 2009) prior to the 

object’s atmospheric entry over Liberia, and its subsequent meteorite deposit. Regardless, the FROSTI 

project continues with the intent to systematically arrive at further like observations. 

 

DL. Clark ( • PWiegert 

Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada. Phone: +1-519- 657-6825; E- mail: 

dclark56@uwo.ca 


The software used in this project is a pre-existing astronomical simulation package (ClearSky) 

developed by the author. Figure 1 depicts the flow of processing involved in searching for serendipitous 

images of PFMs using this software. (1) The atmospheric contact position and velocity state of the 

object, with error bars, are made available to ClearSky. This may involve the simple keying of an 

individual event or the development of custom plug-ins for event collections. The contact state 

information required is contact longitude, latitude and elevation, apparent radiant right ascension and 

declination, and the contact velocity, all with error bars. The software handles a variety of coordinate 

systems and reference frames. (2) A probability cloud of positional probability members is sampled 

from the input data and error bars. Each of these members is gravitationally integrated back in time for 

48 hours, resulting in an ephemeris over time for each member. An orbit at infinity is calculated at the 

end of the integration of each member. The entire cloud of probability members is used to report a 

statistical orbit at infinity estimate with error bars. This orbit may be used as verification against 

published orbit elements, typically arrived at by analytic methods. (3) In preparation for image 

searching, sky survey updates are periodically downloaded to maintain a local generic image description 

catalogue. (4) The image catalogue is searched for candidate images using the generated ephemerides, 

and a simulated image is created for each candidate. (5) Using the simulated image as a guide, the 

actual sky survey image is manually searched for the PFM. 

2 Modelling PFM Visibility 

2.1 Primitive Modelling 

The initial goal of modelling PFM visibility was to determine whether these objects are in fact visible 

for any significant duration of time prior to contact. Frequency distributions were not initially 

considered. PFM characteristics affecting visibility are size, distance from Earth and the Sun, phase 

angle, and albedo. Wiegert et al. (2007), extending on Bowell et al. (1989), document a relationship of 

asteroid diameter D in kilometers to absolute magnitude Hk and albedo Ak for colour filter k as: 

F  !C¡!V¢£¤D¥

¦¤

2 1D (1) 

Disregarding colour filters, rearranging and combining with (7) and (8), and assuming a constant 

approach speed v such §  g_ that for a time t prior to contact, we derive a formula for apparent 

magnitude m: follows: 

f  i`]b!V

¦2 1D

!C¡  < i`]b!Vg_  i`]b!V	 ̈*! <  ̈* (2) 

here: 

*!  /CCC©a:+u



w

«¬­

+> *  /!®¡©a:ju

m211

We now have an expression for apparent magnitude in terms of object diam D) in metres, albedo 

A), velocity (v) expressed consistently in units such that vt is in AU, phase angle () and time (t), as 

eter (

(

well as solar distance (r) and slope parameter (G). Assuming r ~ 1 AU in the proximity of Earth, and G

= .15 typical for low albedo asteroids, we are able to plot m against a sampling of reasonable D, A, v at 

values, for various time periods. 


Observing 

Object Contact State: 

 Position (Lon, Lat, Alt) 

System  Radiant (RA, Dec) 

 Velocity 

 Error Bars

 

Figure 1. The process flow for PFM image searching, showing tion or importing

of event contact state information and error bars, (2) the selection of a PFM probability clou

: (1) the transcrip

d

members, and the gravitational back integration of each member, resulting in ephemerides for each

member, and a determination of orbit-at-infinity orbital elements, (3) the preprocessing of sky

survey image descriptions into a generic image catalogue, (4) the searching for images based on

PFM ephemerides, and (5) the manual inspection of candidate images for the PFM. 

For 1000 random members 

Generate 

Random 

Alt 

 v 

Lon, Lat, 

RA, Dec,

Integrate 

back in time

Calculate orbital 

elements 

Statistical 

Analysis 

Orbital elements: 

 a, e, i 

 Asc Node 

 Perihelion 

 Anomaly 

 Error Bars 

(1) 

Digital 

Surveys 

Sky Survey 

Pre-processor 

Image 

Catalogue

Manual 

Inspection

Simulated 

Image

Catalogue 

Search 

DISCOVERY!

(3) (4) 

(5) 

Ephemerides for 

Probability Cloud 

Members 

(2) 


In Figure 2 visual magnitudes are plotted for objects with A = 0.05 and 0.25, D = .25 and 1.0 

met s, v = 20, 30, 50 and 70 kms-1, and § = 0o, 30o, 60o, 90o and 120o at 3 hour intervals from 3 hours to 

48 h u

Figure 2. Plot of apparent magnitude over time of a variety of objects having albedo of 0.05 and 0.25, di eter of 

5 and 1.0 metres, approach velocity of 20, 30, 50 and 70 kms-1, and phase angle 0o, 30o, 60o, 90o and 120o, 

suming linear approach. The gray shaded area represents visibility within the CFHTLS images. Lines join points 

2.2 Bottke/Bro elling 

 reassuring that object prediction images could exist, does not 

s permitting successful predetections. For 

re

o rs prior to contact. Symbols in the plot represent each time interval, with lines connecting points 

of like interval. The CFHTLS visibility limit of 24th magnitude is shown for comparison. One observes 

in the plot that there are indeed combinations of PFM physical and dynamical attributes which support 

predetections. In addition to the expected favouring of higher albedo, larger diameter, slower speed, and 

lower phase angle objects, this plot demonstrates that very few objects remain visible for time periods in 

the range of the original project target of 48 hours, and that visibility ranges of 6-12 hours are more 

representative. 

am

.2

as

of equal visibility duration. 

wn/Morbidelli Mod

The simplistic modelling above, although

provide insight into the frequencies of objects with attribute

this we turn Near Earth Asteroid (NEA) dynamical models of Bottke et al. (2002a), fireball size 

frequency distribution and flux model of Brown et al. (2002), and the albedo model of Morbidelli et al. 

(2002a). 


The Bottke 2002a NEA distribution is a 5-intermediate source model of NEA distribution binned 

over orbit semi-major axis (a), eccentricity (e), and inclination (i). In addition to a, e, and i, values for 

longitu

!4 
56  ̄

de of the ascending node (
), the argument of perihelion () and true anomaly (f) are required. 

In the case of the general NEA population, the three angles 
, , and f may be uniformly selected from 

the full 0-360o range, as there is no natural anti-symmetric bias to these elements. However, PFMs are 

characterized within the NEA population as objects which have the immediate potential to collide with 

the Earth. A standard equation for Keplerian motion is: 

  "!/41 (3) 

where r is the object-Sun distance. Re-arranging, we have: 

Y  ,=]d/! "@!/41A/

4 (4)

electing a uniformly random time in the time range of interest, we are able to determine r by 

ing r very closely approximates the Earth-Sun distance. The Earth-Sun distance is readily 

vailable from published theories such as DE405 (NASA JPL planetary position ephemerides available 

mong f, , and 
 characterized by the object 

B<°

, B<°

handled, we must 

t al. 

with ¿ es

(5) 

ear. This is not a large sample 

size at all when we consider that the samples are distributed over more than 15,000 a, e, i bins in the 

ottke distribution, and we still requi

rger sample is used, and resulting frequencies must be scaled back accordingly. 

For albedo modelling we turn to Morbidelli et

 Low, and

olide size and albedo 

models. This sample size is a compromise of reasonable required computation time against granularity 

S t

assum

a

as tables of Chebyshev coefficients and supporting code). 

 Since the argument of perihelion  is defined as an angle from the ecliptic, the circumstance of 

Earth-object collision occurs on the ecliptic, and f is defined as an angle from , we are able to 

determine  from f. There are four possible relationships a

being at the ascending node or descending node, and whether the object is inbound or outbound in its 

orbit in relation to the Sun. These four cases are selected uniformly: 

1) Ascending node, outbound: Y  #$%/! ±, Z  Y, 2°

2) Ascending node, inbound: Y  #$%/! ±, Z  Y, 2°

3) Descending node, outbound: Y  #$%/! ±, ZBY,+2

4) Descending node, inbound: Y  #$%/! ±, Z  B  Y +2 

With approach characteristics now model the size and albedo distributions

which will impact visibility. Brown e (2002) describe a power law for the cumulative number of 

objects (N) colliding with Earth per year diameter D in metr as: 

`]b 3  =  e `]b F V V

where =V  	i , 

 and eV  
 , 

. Assuming a diameter of at least .2 m is required for 

visibility in telescopic images, equation (5) yields a flux of 2800 objects/y

B re a distribution over an albedo range. Therefore, the significantly 

la

 al. (2002a) who define 5 NEO albedo classes: 

Hig(h), Mod(erate), Int(ermediate), Com(etary) with a mean albedo for each, and albedo 

ranges for all but the Com class (for which we will assume the mean value for all samples). They then 

assign differing slope parameter values for each class to simulate a phase angle affect. Finally, they 

model a frequency distribution by class for the NEO population. 

A sample of 10,000,000 objects was generated using the above NEA, b


of result binning. For the strict needs of visual magnitude analysis, a smaller sample size could be used. 

However, other analyses (below) were performed on the model which benefited from the increased 

sample size. Figure 3 shows the visual magnitude distribution of the sample objects plotted over various 

times from 5 minutes to 24 hours prior to Earth contact. As in the simple model of above, a significant 

portion of objects are potentially visible (magnitude <24) in sky surveys in the minutes prior to contact. 

Howev

Figure 3. A visual magnitude plot of 10,000,000 simulated objects generated from the Bottke et al. (2002a) NEA 

distribution, the Brown et al. (2002) bolide size-frequency distribution, and the Morbidelli et al. (2002a) albedo 

distribution. Only objects above .2m in diameter are considered. Objects are selected by adjusting the argument of 

perihelion such that objects collide with Earth. The plot shows the number of objects falling into 1-magnitude wide 

bins over a series of time intervals prior to contact. Top: From foreground to background are the time intervals of 5 

minutes, 15 minutes, 1 hour, and 2 hours to 24 hours in 2-hour increments. Bottom: The same plot with earlier times 

in the foreground. 

er, this visible proportion trails off very quickly in the hours prior to contact, to the extent that 

almost none of the model population have visual magnitude less than 6 hours prior. 

0

500000

1000000

1500000

2000000

1 5 9 131721252933374145 49

Time to

Contact

Frequency

Apparent Magnitude

Bottke/Brown/Morbidelli Distribution

10,000,000 Samples.2m Cut-off 

at05m

at15m

at01h

at02h

at04h

at06h

at08h

at10h

at12h

at14h

at16h

at18h

0

500000

1000000

1500000

2000000

5 1 13 9 2117 2925 3733 4541 49 Time to

Contact

Frequency

Apparent Magnitude

at05m

at15m

at01h

at02h

at04h

at06h

at08h

at10h

at12h

at14h

at16h

at18h

at20h

at22h


3 Determination of PFM Trajectory 

The search for a nearby object in sky surveys requires an accurate ephemeris for the object, with a good 

understanding of the errors in position over time. It is insufficient to use the published orbital elements 

of a PFM, elements that are typically derived using analytical means. The elements are expressed in 

far too little accuracy to be useful; for example a semi-major axis expressed to the precision of .001 AU 

yields errors rivalling the radius of the orbit of the Moon. As well, published orbits are orbits at infinity, 

not reflecting the impact of the Earth’s gravity on the approach trajectory. Instead, an accurate 

translation of the PFM’s contact state into heliocentric coordinates and a full gravitational integration are 

required. 

3.1 Calculating the PFM Heliocentric Contact State 

The heliocentric contact state of an object is represented as a cloud of probability members, each 

member having longitude B, latitude B, height hB, radiant right ascension and declination R and R, 

and velocity v
, all at an epoch t, where each of these values, including the epoch, are generated from a 

Gaussian distribution defined by the reported mean and standard deviations. Each member’s contact 

state is converted to heliocentric coordinates, in preparation for the integration of each member, as 

follows: 

1) The geocentric coordinates centred on Greenwich (xG, yG, zG) are calculated using the WGS84 

theory. 

2) The mean rotation of the Earth  is calculated using the methods of Meeus (1991) Chapter 11. 

3) The apparent sidereal rotation of the Earth ' is calculated from  as described in Chapters 11 and 

21 of Meeus (1991). This involves the calculation of the mean obliquity of the ecliptic !0, the 

nutation in longitude Y, and the nutation in obliquity !. The calculations of nutation and 

obliquity require that the time of the event be expressed in Dynamical Time (TD), not universal 

time (UT). This difference in these timeframes is taken from a table of adjustments available on 

the US Naval Observatory web site (USNO, 2010). 

4) We are then able to rotate (xG, yG, zG) by ' giving the Earth-centred equatorial coordinates with 

respect to the equinox of the date (xE, yE, zE). 

ng 

tly 

xRot yRot zRot

uatorial coordinates for the epoch of the date. The magnitude 

vROT of the velocity is taken from a complete rotation of the earth at the object’s distance and 

5) ([?, \?, ]?) are converted to the equinox J2000 (xEJ, yEJ, zEJ) by converting to spheri!
"

coordinates, precessed to J2000 by the methods of Meeus (1991) Chapter 20, and converti

back to rectangular coordinates. We retain the right J2000 right ascension E for later use. 

6) The apparent contact velocity of the PFM equinox J2000 (vxoJ, vyoJ, vzoJ) is calculated direc

from R, R, and -v
. 

7) The velocity due to the rotation of the Earth (v , v , v ) is the tangent vector at the Earthcentred position expressed in eq

declination. Care must be taken when velocities are tracked in software with respect to solar 

time scales; we must make a sidereal adjustment. (vxRot, vyRot, vzRot) is then calculated from vROT

and E, vzRot being 0. 

8) (vxRot, vyRot, vzRot) are converted to equinox J2000 (vxRotJ, vyRotJ, vzRotJ) as in 5) above. 

9) We arrive at an Earth-centred equatorial J2000 velocity (vxEJ, vyEJ, vzEJ) by summing (vxoJ, vyoJ, 

vzoJ) and (vxRotJ, vyRotJ, vzRotJ). 


10) The Earth-centred equatorial J2000 position (xEJ, yEJ, zEJ) and velocity (vxEJ, vyEJ, vzEJ) are 

converted to heliocentric coordinates (xEH, yEH, zEH) and (vxEH, vyEH, vzEH) by adding the Earth’s 

position at the epoch using the JPL Horizons DE405 ephemeris. The epoch must be expressed in 

ulated in 3). 

11) These equatorial coordinates are converted to heliocentric ecliptical coordinates (xH, yH, zH) and 

ot wanting to re-invent the wheel in the field of numerical integrators, and understanding that this 

plementation of RADAU-15, a 15th-order differential 

equ ed 

by 

publica

the pro

into C+

implem

over 10 5/DE406 ephemerides. A full integrator-toDE

for Mars, with an oscillating .000003 AU error in solar distance after 100 years). This test required the 

imp

meteor

state w

state value and error bars yields a slowly expanding probability cloud representing the possible 

met

initial 

converg

3.3 Co

The to verify the 

resu

Ceplec perform this comparison: the ten largest mass European Network

eve

Networ

orbit-at

Figure thods for the Spurný (1997) events. 

Res

Terrestrial Time (TT), equivalent to TD as calc

(vxH, vyH, vzH) by converting to spherical coordinates, converting to ecliptical coordinates as in 

Meeus (1991) Chapter 12, and converting back to rectangular coordinates. These calculations 

again require !0 and ! as calculated in 3). 

3.2 Integrating the PFM Trajectory 

N

application did not require sophisticated optimizations or approaches in performance, we decided on a 

quick rework of an existing C-language im

ation integrator documented in Everhart (1985). The RADAU family of integrators is characteriz

the use of Gauss-Radau spacings for sequence sub-steps. The work of porting and integrating the 

lly available C-code involved converting C code to C++, the language used in the remainder of 

ject coding, and abstracting the concepts of an integrator, force calculations, and physical objects 

+ interfaces and implementations to facilitate substitution of trial implementations. The initial 

entation of the RADAU integrator was tested by integrating the major objects of the solar system 

0 years, and comparing the results to the JPL DE40

405/406 comparison was performed, with acceptable results (for example: .6” error in solar longitude 

lementation of post-Newtonian adjustments, a refinement not required for the integration of 

oid objects on Earth-approach. These post-Newtonian adjustments require knowledge of velocity 

ithin the inter-object force calculations that is not required by PFM integrations. 

The resulting integration back in time of a collection of probability points generated from contact 

eoroid paths. Figure 4 is a sample illustration of the Bunburra Rockhole event, generated from an 

contact sate provided by Pavel Spurný in a private correspondence (Spurný, 2009). The 

ence of the probability cloud towards the eventual error bars in the original state is evident. 

mparison to Ceplecha Analytical Orbits 

 analytical orbit-at-infinity calculation methods of Ceplecha (1987) provide the means

lting orbits from the back-integration technique. Two sets of fireball orbits derived using 

ha’s calculations were used to

nts from 1993-1996 documented in Spurný (1997), and 10 more recent unpublished European 

k events provided by Spurný in a private correspondence (Spurný, 2010). For the purposes of 

-infinity calculations, the back-integrations are stopped at 2-months prior to Earth contact. 

5 demonstrates the good correspondence between the me

ults on the later events await Spurný’s publication of his results. 


Figure 4. The RADAU-15 generated probability cloud for the Bunburra Rockhole effect. Meteoroid contact position, 

velocity and error bars were provide by Pavel Spurný in private correspondence (Spurný, 2009). The illustrations show 

the probability at the time of contact, and 1, 2 and 3 hours prior to contact. The viewer is a consistent 9100 km distance 

from the cloud’s mean point. 

Figure 5. A list of the 10 highest mass events from Spurný (1997) showing the published orbital elements calculated using 

Ceplecha (1987) calculations compared to the orbit at infinity elements calculated using the project’s software ClearSky’s 

integration technique. Semimajor axis, eccentricity, inclination, longitude of the ascending node a d argument of perihelion 

are listed. Standard deviations are listed beside each element. ClearSky elements are displa d in blue if outside the 

published error bars. Published elements are displayed in red if outside the ClearSky calculated error bars. Note that the 

ascending nodes are numerically close, but are consistently flagged as being out of the corresponding error bars. 

n

ye


The close correspondence of orbit elements from the Ceplecha and integration techniques serves 

as both a validation for the time-honoured analytical method, and as a confirmation the integration 

technique does accurately reproduce object approach trajectories. However, the small but systematic 

variance in longitude of ascending node garnered further attention. Section 11 of Ceplecha (1987) 

describes in detail the impact of Earth’s gravity on calculating velocity and radiant direction of a meteor, 

this impact being removed prior to the calculation of orbital elements. However, in formula (48) of 

Section 11, Ceplecha makes the assumption that the longitude of the ascending node (
) of the orbit can 

rds 

ds 

ristics and the length of time the meteoroid is influenced by Earth’s gravity. 

he largest calculated variance in 
 is .15° for Spurný (2010) event EN231006. Figure 6 demonstrates 

e shift in ascending node of approximately .1° of the Bunburra Rockhole event. A consequence of this 

variance in 
 that has not been quantified is the dependency in the Ceplecha calculations of all other 

orbit elements except semimajor axis on 
 and LSUN. Further quantification of the impact is noted as 

possible future work. 

Figure 6. The shift 
 of the ascending node 
 of the instantaneous orbit of the Bunburra Rockhole meteoroid. From left to 

right, top to bottom, the progress of the shift is shown, 4, 3, 2, and 1 hours prior to contact, at contact, and at contact with the 

shift highlighted. The rightmost diagonal lines represent the instantaneous orbits at the ascending node on the near side of 

the Sun. The leftmost lines represent the orbits at the descending node on the far side of the Sun. 

4 Searching Sky Surveys 

4.1 Image Frustums 

’s position 

into ob

be directly derived from the solar longitude of the Earth (LSUN) at the time of impact. This is true of the

instantaneous orbit of the meteoroid, but not its orbit at infinity. The instantaneous 
 is drawn towa

the limiting value LSUN as the meteoroid approaches the Earth. The magnitude of this shift in 
 depen

on the approach characte

T

th

Astronomical images are typically thought of as two-dimensional rectangular projections onto the 

celestial sphere. Such images may be defined by the right ascension () and declination () of the four 

corners of the image, or by the  and  of the image centre, width and height of the image, and the 

rotation around the image centre. The computations involved in determining the location of a fast 

moving object in relation to a long image exposure involves several conversions of the object

server centred  and  as both the object and observer move over time. These conversions, 

although not complex, are computationally expensive as they involve trigonometric transformations. 

Since the position of an object is relative to the observer, there is little opportunity to optimize this 

heavy computation against multiple images, or against multiple image surveys. I therefore developed an 

image representation scheme which supports a front-end loaded one-time optimization of individual 

image representations, while reducing the object-image computation complexity. 


A single survey image in reality is a projection of a three-dimensional volume of space. 

Assuming a rectangular image, this volume is a frustum as shown in Figure 7. A frustum is defined as 

the portion of a solid lying between two planes. An image frustum is the portion of a square pyramid 

lying between a front viewing plane and an arbitrary depth of field plane. This real-world frustum space 

can be transformed into a three dimensional rectangular 2x2x1 frustum space to which object position 

intersections are easily calculated. The determination of the image frustum and the calculation of the 

transformation into a rectangular frustum space are costly, but may be performed once per image 

description with the resulting transformation being stored and associated with the image description. 

Viewing frustums and the related transformations have been used for decades in rendering three 

imensional world scenes onto a two-dimensional view port (screen). In particular, I have leveraged the 

unpublished lecture notes and course exercises by Beatty (1980). 

frustum in heliocentric space, and the rectangular frustum space. Any astronomical image is a 

 transformation matrix 

Tf to th

d

Figure 7. An image 

representation of the three dimensional frustum volume defined by the observer location, the field and depth of view 

of the image, the line of sight, and the rotation of the image. Points in heliocentric space may be easily transformed 

into points in the frustum space, facilitating image-object intersection and object motion characterization. 

An image frustum is defined by a set of parameters: observer position (dx, dy, dz), a line of sight 

(sx, sy, sz), horizontal and vertical fields of view (h, v), a near view distance (d, taken as a distance 

closer to the observer than the typical in-atmosphere meteor distance), and a depth of field (f, taken as 

infinity). It can be shown that the real-world frustum space may be transformed into a rectangular 

frustum space based on a number of constituent transformations using the above frustum parameters. A 

PFM position (or the position of any solar system object) in heliocentric coordinates (x, y, z) may be 

translated to the image frustum space (xf, yf, zf) by the simple application of a 4x4

e homogenous coordinates (x, y, z, 1), where Tf is the matrix product of a series of constituent 

transformations: 

Hx> c>  ́> 	IHμI  ¶x ̄> c ̄>  ́ ̄> · ̄ ̧ (6) 

An object’s position with respect to the 2x2 image frustum front face is: 


x1  'o

»o

+> c1  -o

»o

 (7) 

where 	+ W x W 	 1 1 and 	+ W c W 	 correspond to the object being on the image. Additional outputs 

of the above transformation are four values called edge coordinates, which allow for quick object-image 

checking, prior to performing the above divisions in calculating x1 and c1: 

! 1⁄4 · ̄ < x ̄ : left edge 

 1⁄4 · ̄  x ̄ : right edge 

C 1⁄4 · ̄ < c ̄ : bottom edge 

+1⁄2+· ̄  c ̄ : top edge 

In all cases, the edge coordinate 7 exhibits the properties: 

7  
 the position is inside the edge 

7 3⁄4 
 the position is outside the edge 

 As long as the 4x4 T transformation matrix is calculated before search time, the computation 

req nd 

9 ad ed 

to p the 

har

oordinates to end-of-exposure coordinates. 

ownloaded image databases. Indexes are maintained on the image catalogue to 

cilitate searching by survey name, time fram , or both. The image catalogue is recreated from scratch 

to avoid the concerns of needing a sophisticated 

nderlying database technology that could handle both efficient insertion and querying. The download 

odic replacement of the survey 

ata, or as a net-change update. If the downloaded survey catalogue is represented in an easily parsed 

xed form, then the survey imp

meta-data. If the survey data is difficult to parse, a survey plug-in may be developed to implement the 

port. Figure 8 describes the contents of the generic image catalogue records. 

lt a h based on ephemerides is a 

eneric method which is independent of the source of the image and the target being searched. The 

f

uired to determine an object-image intersection at a single point in time is the 12 multiplications a

ditions required to calculate the xf,, yf, and wf values, and the 4 additions and 4 comparisons requir

erform the edge coordinate checks. The edge coordinates provide a means to quickly determine 

c acteristics of an object’s motion on, off, or through the image by comparing beginning-of-exposure 

c

4.2 Automated Downloads and Pre-processing 

The object-image intersection process described above assumes the opportunity to possess precalculated image frustum descriptions and transformations prior to executing object searches. I have 

developed a generic image catalogue data base which serves to: 1) maintain local copies of available 

image databases, 2) provide a generic representation of the images databases, 3) support the storage of 

the above pre-calculated data, and 4) provide indexing to support various object search use cases. The 

image catalogue developed for this project is implemented as a flat file of generic image data referring 

back to local copies of d

fa e

on every download cycle. This approach was taken 

u

of updates from each image survey can be implemented as either a peri

d

fi ort may be implemented by simply defining the survey catalogue in 

im

4.3 General Use of the Image Search Algorithm 

The image representation described above and the resu ing se rc

g


Image Collect of the image survey, database, or collection. E.g. “CFHT Catalogue”, “Catalina 

”. 

ion The name

Catalogue

Image File py of each image survey is described by one or more file names, and a description of 

of these files. The image catalogue points to the file number and file offset 

n image in this set of files. 

The local co

the format 

corresponding to a

Image Offset the image file where the source description of the image may be found (see Image The position in 

File). 

Right Ascensio ascension of the centre of the image. n The right 

Declination nation of the centre of the image. The decli

Width The width of the image in radians. 

Height The height of the image in radians. 

Start Time The start ate and time of the image exposure. d

Exposure The length of the exposure in seconds. 

Starting Frustum The parameters used to describe the image frustum at the beginning of the exposure, and the 

trix used to convert object positions to the frustum space. 

ch axis 

ont face 

 Observer distances to the front and back faces 

contents of the 4x4 transformation ma

The frustum description includes: 

 Frustum rotations around ea

 Dimensions of the frustum fr

 16 numbers corresponding to the Tf image frustum transformation. 

Ending Frustum The parameters used to describe the image frustum at the end of the exposure (See Starting 

Exposure) 

Figure 8. Image catalogue record description. 

technique is therefore easily adapted to any use where the image source and target object are in motion. 

Whereas the original need of this project was to provide a flexible system that would support a variety of 

asily extended to cover other image sources, such as 

hoto collections. In addition, support sky surveys may 

FHTL

Coulee (Hildebrand, et al., o images have yet been found. The implementation of Spacewatch 

telescopic sky surveys, the approach can be e

spacecraft image databases, and amateur astrop

be searched for any solar system object. For example, in support of the article Gilbert and Wiegert 

(2009), ClearSky was used to search the CFHTLS for images of three main-belt comets: 133P/ElstPizzaro, P/2005 U1 (Read), and 176P/LINEAR. Images of 176P/LINEAR were located, including a set 

of three images dated 2007 January 15. Figure 9 shows the image search result file for that period. 

Figure 10 shows the three image simulations, and the corresponding close inspection images created by 

Wiegert from CFHTLS image downloads. 

5 Results to Date and Future Work 

At the time of writing, this project has not yielded a discovery of a PFM image, however searching will 

continue. The results of the project have been of a more indirect nature, with our gaining understanding 

of PFM visibility and the nature of PFM orbits. The project has also contributed to the science with a 

confirmation of the heavily relied-upon analytical methods of the past 30 years, and by providing a 

useful general image catalogue search technique. 

5.1 Image Searches 

C S image searches have been performed on two collections of European Network events as 

documented in Spurný (1997) and Spurný (2010), as well as three individual events: Grimsby 

(McCaus 010 d Buzzard land, et al., 2 ), Bunburra Rockhole (Bland, et al., 2009) and (Spurný, 2009), an

 2009). N


 represented in an Microsoft Excel spreadsheet tab. The result 

e URL for downloading the CFHTLS image), object visibility, 

bject in the image. The X,Y coordinates of the object in the image (ranging from -1 to 1) are 

ation of the image. The green arrow has been added to show the position of the object. 

Figure 9. One image result from the CFHTLS catalogue search result file for 176P/LINEAR for the period of January 2007. 

Three images were located, the details of each circumstance

file text contains image description information (including th

and the position of the o

reversed due to the orient


Image 889493 

2007/01/15 09:33:29 UT 

Image 889504 

2007/01/15 10:15:40 UT 

Image 889515 

2007/01/15 10:56:21 UT 

Figure 10. Top row: Detail from the three simulated CFHTLS images from 2007 January 15 showing object 

176P/LINEAR. The green arrow has been added to highlight the object position. Note the slight movement in the 

object. Bottom row: Extractions from the actual CFHTLS images created by Dr. Paul Wiegert. The red arrow 

indicates the actual object; the blue arrow indicated the expected position based on the MPC orbit published at the 

time. Orientations between the simulations and the extractions are opposite. 

.2 Modelling Results 

s the project progressed, the realization developed that the chance of linking a fireball observation to a 

rendipitous PFM image is low. The modelling performed shows that a sufficiently large event in any 

ne given meteor detection network is, at the optimistic end, a yearly event. Conservatively, in the case 

f ASGARD, it is a decadal event. Survey effectiveness analyses show that the chances for telescope 

etection can be severely reduced by object or solar geometry, as well as the quickly reducing apparent 

agnitude of the PFM. Finally, the chance of success is further reduced by the unmodelled but 

vidently small probability of a survey telescope being pointed at the correct field in relation to its 

overall sky coverage capability or preference possibility of s enticing. Of 

particula ine i ject whom I 

have disc volv ager ble, and 

 

 

(McMillan, 2010) and Catalina (Beshore, 2010) sky survey downloads are complete, and discussions are 

ongoing regarding access to the PanSTARRs (Jedicke, 2010) survey data. Contact state information on 

any additional significant fireball events is most welcome. As described above, the search techniques 

ave shown useful in discovering serendipitous images of other solar system objects. 

. However the uccess remains

r note is the level of genu

ussed the work. Those in

nterest shown for this pro

ed in sky surveys seem e

by the many people with 

 to make their data availa

h

5

A

se

o

o

d

m

e


those analysing various fireball events are eager to provide and transform their data for use in this 

project. 

5.3 Orbit Determination Results 

A major accomplishment of this project was the confirmation of the Ceplecha (1987) orbit determination 

methods, and the offering of an adjustment of that work to account for a shift in the PFM’s longitude of 

the ascending node. In verbal conversations with Dr. Pavel Spurný and others, it has been stated that 

this validation of Ceplecha’s methods has not been done before, even though they are widely used. 

There can now be an increased level of confidence in the orbits derived from those methods. 

Acknowledgements 

I thank Dr. Paul Wiegert (UWO) for his support and technical assistance in this project, Dr. Peter Brown 

(UWO) and Dr. Pauline Barmy (UWO) for their support and advice, Rob Weryk (UWO) and Zbyszek

Krzeminski (UWO) for their infinite patience in explaining the ASGARD system and for preparing data 

for my analysis, Dr. Pavel Spurný (Astronomical Institute, Academy of Sciences of the Czech Republic) 

for his explanations and data allowing me to compare methods to the Ceplecha work, and my wife 

Angela for her proof-reading. 

t 

of C the 

Nat he 

Cen

ork is based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre 

s part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and 

cience 688. University of Waterloo, Ontario: Unpublished. 

Access to the CatalinaSky Survey Catalogue (Personal email). 

M., & Wiegert, P. A. (2009, June). Searching for main-belt comets using the Canada-France-Hawaii Telescope 

Legacy Survey. Icarus , 201 (2), pp. 714-718. 

This work is based in part on observations obtained with MegaPrime / MegaCam, a joint projec

FHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by 

ional Research Council (NRC) of Canada, the Institut National des Science de l'Univers of t

tre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This 

w

a

CNRS 

References 

Beatty, J. (1980). Computer S

Beshore, E. (2010, June 02). 

Bland, P. A., Spurný, P., Towner, M. C., Bevan, A. W., Singleton, A. T., Chesley, S. R., et al. (2009). A Eucrite Delivered 

from an Aten-type Orbit: The Last Link in the Chain from 4 Vesta to Earth. 40th Lunar and Planetary Science 

Conference, (Lunar and Planetary Science XL), held March 23-27, 2009 in The Woodlands, Texas, id.1664 . 

Bottke, W. F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H. F., Michel, P., et al. (2002a). Debiased Orbital and 

Absolute Magnitude Distribution of the Near-Earth Objects. Icarus , 156 (2), 399-433. 

Bowell, E., Hapke, B., Domingue, D., Lumme, K., Peltoniemi, J., & Harris, A. W. (1989). Application of photometric 

models to asteroids. Asteroids II; Proceedings of the Conference, Tucson, AZ, Mar. 8-11, 1988 (A90-27001 10-91) , 524-

556. 

Brown, P., Spalding, R. E., ReVelle, D. O., Tagliaferri, E., & Worden, S. P. (2002). The flux of small near-Earth objects 

colliding with the Earth. Nature , 420, 294-296. 

Ceplecha, Z. (1987). Geometric, dynamic, orbital and photometric data on meteoroids from photographic fireball networks. 

Astronomical Institutes of Czechoslovakia, Bulletin , 38 (July 1987), 222-234. 

CFHT. (2009, 11 12). Canada-France-Hawaii Telescope Legacy Survey. Retrieved 11 14, 2009, from Canada-France-Hawaii 

Telescope: http://www.cfht.hawaii.edu/Science/CFHTLS/ 

Gilbert, A. 


Hildebrand, A. R., Milley, E. P., Brown, P. G., McCausland, P. J., Edwards, W., Beech, M., et al. (2009). Characteristics of a 

at Buzzard Coulee, Saskatchewan, Canada, November 20, 2008. 40th Lunar and 

ar and Planetary Science XL), held March 23-27, 2009 in The Woodlands, Texas, 

cMillan, R. (2010, June 01). The Spacewatch image catalogue textual log (Personal email). 

eeus, J. (1991). Astronomical Algorithms. Richmond, Virginia: Willman-Bell, Inc. 

., Bottke, W. F., Michel, P., & Tedesco, E. F. (2002a). From Magnitudes to Diameters: The Albedo 

arth Objects and the Earth Collision Hazard. Icarus , 158 (2), 329-342. 

Bright Fireball and Meteorite Fall 

Planetary Science Conference, (Lun

id.2505 . 

Jedicke, R. (2010, May 27). Access to the PanSTARRS Image Catalogue (Private conversation). Breckenridge, Colorado. 

Jenniskens, P., Shaddad, M. H., Numan, D., Elsir, S., Kudoda, A. M., Zolensky, M. E., et al. (2009). The impact and recovery 

of asteroid 2008 TC3. Nature , 458 (7237), 485-488. 

McCausland, P. J., Brown, P. G., Hildebrand, A. R., Flemming, R. L., Barker, I., Moser, D. E., et al. (2010). Fall of the 

Grimsby H5 Chondrite. 41st Lunar and Planetary Science Conference, held March 1-5, 2010 in The Woodlands, Texas. , 

p. 2716. 

M

M

Morbidelli, A., Jedicke, R

Distribution of Near E

Spurný, P. (2009, February 27). State vector for the Bunburra Rockhole meteor (Personal email) . 

Spurný, P. (1997). Exceptional fireballs photographed in central Europe during the period 1993-1996. Planetary and Space 

Science , 45, 541-555. 

Spurný, P. (2010, May 13). Recent European Network event tables (Personal email). 

Wiegert, P., Balam, D., Moss, A., Veillet, C., Connors, M., & Shelton, I. (2007). Evidence for a Color Dependence in the 

Size Distribution of Main-Belt Asteroids. The Astronomical Journal , 133 (4), 1609-1614. 


Data Reduction and Control Software for Meteor Observing Stations Based on 

CCD Video Systems 

J. M. Madiedo1• J. M. Trigo-Rodríguez2• E. Lyytinen3

Abstract The SPanish Meteor Network (SPMN) is performing a continuous monitoring of meteor 

activity over Spain and neighbouring countries. The huge amount of data obtained by the 25 video 

observing stations that this network is currently operating made it necessary to develop new software 

packages to accomplish some tasks, such as data reduction and remote operation of autonomous systems 

based on high-sensitivity CCD video devices. The main characteristics of this software are described 

here. 

Keywords meteor · meteoroid · fireball · software · meteor showers 

1 Introduction 

Since 2006 the SPanish Meteor Network (SPMN) has performed continuous monitoring of meteor and 

fireball activity over Spain and neighbouring countries. For this purpose, we mainly employ all-sky 

CCD cameras and high-sensitivity CCD video devices to monitor the night sky (Trigo-Rodríguez et al., 

2006a, 2007a, 2007b; Madiedo, 2007). In addition, we have employed daytime CCD video cameras 

since 2007 in order to monitor fireball activity over 24 hours and increase the opportunities for meteorite 

recovery in Spain. As a result of this effort, a total of 25 observing stations are currently in operation. 

Several of them have been configured to work in a fully autonomous way. The two main cores of the 

Network are located in the regions of Catalonia and Andalusia. As these are separated by about 1000 

km, there is a higher probability of clear skies and of meteor activity being recorded every night. The 

establishment of 25 meteor observing stations implies that a large amount of data needs to be reduced. 

This made it necessary to develop new software tools in order to perform a fast analysis of our data. The 

main features of these new packages are presented here. 

2 Description of the Observing Stations and Procedures 

Trigo-Rodríguez et al. (2004) previously reported the first steps in the development of the SPMN that 

employed low-scan-rate all-sky CCD cameras with +2/+3 meteor limiting magnitude. Since 2006 the 

 

J. M. Madiedo ( ) 

Facultad de Ciencias Experimentales, Universidad de Huelva. 21071 Huelva (Spain). E-mail: madiedo@uhu.es

J. M. Trigo-Rodríguez 

Institut de Ciències de l’Espai–CSIC, Campus UAB, Facultat de Ciències, Torre C5-parell-2a, 08193 Bellaterra, Barcelona, Spain; Institu 

d’Estudis Espacials de Catalunya (IEEC), Edif. Nexus, c/Gran Capità, 2-4, 08034 Barcelona, Spain 

E. Lyytinen 

Kehäkukantie 3B, 00720 Helsinki, Finland.


SPMN started to establish observing stations based on video systems to analyze meteor activity 

(Madiedo and Trigo-Rodríguez, 2007; Trigo-Rodríguez, 2007a, 2007b). These employ several highsensitivity Watec CCD video cameras (models 902H and 902H Ultimate from Watec Corporation, 

Japan) to monitor the night sky. The cameras generate video imagery at 25 fps with a resolution of 

720x576 pixels. These cameras are connected to PC computers via a video acquisition card. The 

computers use the UFOCapture software (Sonotaco, Japan) to automatically detect meteor trails and 

store the corresponding video sequences on hard disk. The cameras are arranged in such a way that the 

whole sky is monitored from every station and, so, this maximizes the common atmospheric volume 

recorded by the different systems. These devices are equipped with a 1/2" Sony interline transfer CCD 

image sensor with their minimum lux rating ranging from 0.01 to 0.0001 lux at f1.4. Aspherical fast 

lenses with focal length ranging from 3.8 to 6 mm and focal ratio between 1.2 and 0.8 are used for the 

imaging objective lens. In this way, different areas of the sky can be covered by every camera and pointlike star images are obtained across the entire field of view. 

Since 2007 we also started to employ CCD video systems to monitor the sky during the day 

(Madiedo and Trigo-Rodríguez, 2008). Daytime CCD video cameras work in the same way as nocturnal 

cameras do, but in this case lower-sensitivity devices are employed in order to avoid image saturation 

due to sunlight. These are endowed with slower optics (f1.4) and are arranged so that a part of the 

landscape falls within their field of view. In this way, identifiable structures or buildings appearing in 

the images can be used for image calibration to obtain the equatorial coordinates of fireballs. 

3 Data Reduction Software 

For data reduction we have developed a new software called Amalthea. This is a MS-Windows 

compatible package that has been programmed in C and C++ programming languages. The main 

characteristics of this software are described below. 

3.1 Image and Video Processing 

Amalthea was designed to analyze CCD images containing meteor trails and also video files recorded by 

our high-sensitivity CCD video devices. In many cases these images contain artefacts that may 

negatively interfere with data analysis. For this purpose, a wide number of image transformation filters 

have been implemented in the software. These include, for instance, light-pollution removal, brightness 

and contrast enhancement and video deinterlace filters. Some of these image transformation procedures 

allow enhancement of the video images before they are used for the astrometric analysis. For instance, 

our software automatically stacks the frames contained in video files in order to increase the number of 

stars available for the astrometric analysis described below. 

3.2 Astrometry 

Meteor and stars positions are obtained from static CCD images or from video sequences recorded by 

devices that monitor the night sky. The procedure we follow to obtain the equatorial coordinates of the 

meteor along its path have been described by Trigo-Rodriguez et. al (2007a). In a first stage, reference 

stars must be specified in order to apply a fitting method that allows conversion between plaque 

coordinates and equatorial coordinates. Then, by measuring the plaque coordinates of the meteor, these 

positions are automatically transformed by Amalthea into their corresponding equatorial counterparts. 


It must be taken into account that in most cases we employ video devices that provide interlaced 

video sequences. These sequences must be deinterlaced by our software in order to remove some 

artefacts that could interfere in the astrometric reduction. Besides, depending on observing conditions in 

the area where the video stations are located, the number of reference stars in the corresponding video 

files can be very low, which is not enough to perform a good astrometric analysis. To solve this problem 

the software follows two different strategies. On one side, it stacks the frames contained in the video 

files in order to increase the signal to noise ratio of the resulting image. The number of reference stars in 

the resulting image is significantly higher. On the other side, as the cameras are pointed towards fixed 

altitude and azimuth coordinates, reference stars obtained at different times can be taken into account for 

a given measurement. 

To perform the astrometric reduction the user manually clicks on the reference stars that must be 

taken into consideration for the corresponding calculations. Then, the user selects which fitting method 

must be used to convert from plaque coordinates to equatorial coordinates. Several options are available 

for this. Then the calculation is performed and the position of the reference stars is back-calculated by 

Amalthea in order to establish the error (standard deviation) of this calculation. In this way, the user, if 

necessary, can repeat the calculations by removing those stars which give rise to higher errors or include 

new ones. 

Once we can convert between plaque and equatorial coordinates, plaque coordinates of meteors 

are specified by the user by clicking on the corresponding positions along the meteor trail. Their 

equatorial counterparts are then automatically provided by Amalthea. This can be done on static CCD 

images or on animated video sequences. In the latter case, time information necessary to calculate 

meteor velocities and decelerations is automatically obtained from the video file. In the former case, 

time information can be specified by the user if, for instance, a rotary shutter has been used. 

3.3 Meteor Atmospheric Trajectory 

Amalthea keeps a database with the geographic position of all the observing stations established by the 

SPMN. For meteors recorded simultaneously from at least two different observing stations the software 

can calculate its atmospheric trajectory and radiant once the above-described astrometric procedure has 

been performed. In order to do this the software uses the well-known planes intersection method 

(Ceplecha, 1987). If time information is available, velocities and decelerations are also calculated along 

the meteor trail. This allows us also to obtain the pre-atmospheric value of the meteor velocity, Vinf. 

3.4 Orbital Parameters 

The orbital and radiant parameters of the meteor are calculated according to the procedure described by 

Ceplecha et al. (1987). For this purpose, the values of the pre-atmospheric velocity, Vinf, radiant position 

and meteor apparition time are used, together with the average velocity corresponding to an averaged 

meteor position (latitude, longitude and altitude) along the meteor trail. 

The procedure implemented in the Amalthea software has been tested with the Dutch Meteor 

Society (DMS) orbit calculation software (Langbroek, 2004) and the MORB software developed by the 

Ondrejov Observatory (Ceplecha et al., 2000). Although the DMS software does not provide any error 

parameters, we always found that the results provided by this package and Amalthea are very similar, 

with differences that are very small and within the error bars provided by Amalthea (Tables 1 and 2). 

However, significant discrepancies were found for the case of the MORB software. When this situation 


was analyzed in detail, we found that the origin of these is related to a bug in the calculation of the 

geocentric radiant in the MORB software. 

Table 1. Comparison between orbital parameters calculated by Amalthea and the DMS software for different 

meteors recorded by the SPMN. Equinox (2000.00).

SPMN Code Software q(AU) a(AU) e i(°)  (°)  (°) 

080806 

Amalthea 0.9482D0.0003 9.65D1.5 0.902D0.016 113.58D0.15 149.82D0.32 139.1491D0.00003 

DMS 0.948 9.63 0.902 113.60 149.80 139.15 

MORB 9.558D0.001 21.36D7.76 0.955D0.016 111.79D0.15 152.87D0.35 139.1481D0.0003 

210110 

Amalthea 0.9543D0.0002 2.85D0.02 0.665D0.003 48.80D0.06 202.46D0.08 301.615D0.00002 

DMS 0.954 2.83 0.663 48.81 202.47 301.612 

MORB 0.9667D0.0006 15.47D5.11 0.937D0.020 44.92D0.28 195.55D0.38 301.6113D0.00003 

071106 

Amalthea 0.9774D0.0003 17.31D5.6 0.943D0.018 161.35D0.09 167.74D0.22 236.5034D0.00003 

DMS 0.977 16.96 0.942 161.36 167.68 236.505 

MORB 0.9864D0.0017 63.44D88.29 0.984D0.021 156.93D0.80 185.0D2.3 236.50565D0.00007 

Table 2. Comparison between geocentric radiant position and pre-atmospheric velocities (geocentric, Vg and 

heliocentric, Vh) calculated by Amalthea and the DMS software for different meteors recorded by the SPMN. 

Equinox (2000.00). 

SPMN 

Code Software R.A.(o) DEC.(o) Vg(km/s) Vh(km/s) 

080806 

Amalthea 46.85D0.051 57.29D0.05 58.79D0.20 40.73D0.20 

DMS 46.85 57.29 58.79 40.73 

MORB 46.47D0.13 57.070D0.05 58.78D0.20 41.34D0.18 

210110 

Amalthea 230.03D0.1 66.57D0.03 29.80D0.20 38.61D0.21 

DMS 230.10 66.54 29.79 38.59 

MORB 227.23D0.10 67.41D0.03 29.79D0.05 41.77D0.22 

071106 

Amalthea 156.51D0.1 21.41D0.05 70.90D0.20 41.76D0.20 

DMS 156.52 21.40 70.80 41.65 

MORB 156.20D0.30 21.53D0.30 70.90D0.20 42.20D0.22 


3.5 Meteorite Fall Analysis 

Very bright fireballs can be the source of potential meteorite producing events. So, the analysis of these 

events is fundamental in order to locate, recover and study the corresponding fragments. For this 

purpose it is necessary to calculate the atmospheric trajectory of the fireball and also to model the socalled dark flight, which is the portion of the trajectory followed once the particle has been decelerated 

in such a way that no light is emitted. The atmospheric trajectory is determined by following the 

procedures described above. Then, our Amalthea software solves the aerodynamic equations that 

describe the dark flight of the meteoroid. To do this, information about the particle and its terminal point 

must be entered. A standard Runge-Kutta procedure is followed in order to integrate the position of the 

particle from the terminal height to the ground. Wind data are also taken into account by entering, as a 

function of height, latitude and longitude, the values of atmospheric pressure, temperature and wind 

velocity and direction. The resulting meteorite impact position is shown both numerically and drawn on 

a map. 

In order to test the calculation procedure implemented in Amalthea, we have compared the 

results provided by our software to those provided by the software developed by Z. Ceplecha, P. Spurny 

and J. Borovicka for the case of the Villalbeto de La Peña meteorite fall (Trigo-Rodríguez et al., 2006b). 

The fall of this L6 chondrite occurred on January 4, 2004 in north-west Spain (Trigo-Rodríguez et al., 

2006b; Llorca et al., 2005). Both software packages provide the same result. 

3.6 Meteor Spectra Analysis 

Some of the all-sky CCD cameras and high-sensitivity video devices employed by the SPMN are 

endowed with holographic diffraction gratings (600 to 1200 lines/mm) in order to obtain meteor spectra. 

Typically we can obtain these spectra for meteors as bright as mag. -4 or lower without using any image 

intensifier device. These spectra are very useful in obtaining chemical information about meteoroids 

(Trigo-Rodríguez et al., 2009). 

The Amalthea software is able to analyze these spectra when they are recorded on AVI video 

files or on static all-sky CCD images. These raw spectra must be calibrated in order to take into account 

the response of the camera to different wavelengths. This information can be taken from the 

documentation provided by the manufacturer of the camera or can be experimentally obtained by 

comparing a known spectrum of an astronomical object with the spectrum obtained by the camera for 

the same source. Once this calibration is performed, the software identifies the main meteor emission 

lines. Figure 1 shows an example of the emission spectrum of a sporadic fireball recorded by the SPMN 

from Sevilla on May 27, 2010, at 3h19m40.1 D 1s UTC. The two most prominent lines correspond to 

NaI -1 (589.5 nm) and CaI-1 (422.7 nm). 

4 Description of the SPMN Video Station Control Software 

The number of SPMN video meteor stations has increased from 2 in 2006 to 25 in 2010. This has 

resulted in the necessity to address two main issues that have arisen from this situation: the 

establishment of a system to check the large volume of data provided by these observing stations in 

order to identify multiple-station events and potential meteorite dropping events, and the necessity to 

locate several autonomous meteor observing stations in remote locations or in places where no direct 

human intervention is always possible. Thus, during 2009 new software packages have been developed 


in order to achieve a fully robotic operation of several video meteor observing stations. These new 

packages also allow the systems to be remotely controlled though an Internet connection. A prototype 

robotic video station was setup by the University of Huelva in the environment of the Doñana Natural 

Park (south-west of Spain) in April 2009 (Madiedo et al, 2010). This station was fully operative till 

the robotic system was completely developed in August 2009. Nowadays, three robotic video meteor 

stations are operative in the south of Spain. Two of them are located in the western area of Andalusia, in 

the provinces of Huelva and Sevilla. The latest one has been setup in Sierra Nevada (Granada), in the 

eastern part of this region. 

0

10

20

30

40

50

60

70

380 430 480 530 580 630

Wavelength (nm)

Intensity (arbitrary units)

Figure 1. Sporadic fireball recorded from Sevilla on May 27, 2010, at 3h19m40.1 D 1s UTC with a high-sensitivity 

CCD video camera endowed with a diffraction grating and its emission spectrum analyzed by the software 

Amalthea. 

 

The PC computers that control the new robotic stations have been configured so that they are 

automatically switched on and off when data acquisition must start and finish, respectively. When the 

PCs are started, one of our recently developed software packages starts the data acquisition software 

(UFOCapture) and monitors that this application is properly working during the whole observing 

session. We have also developed another software package that automatically checks the meteor trails 

recorded by the system. Then, if a very bright fireball is detected (typically mag. -12 or brighter) which 


could give rise to a potential meteorite fall, an email is automatically sent to the operator together with 

the corresponding images. 

These robotic stations provide a huge volume of data, as they are currently an average of over 

1000 meteors per month. In order to handle this information, we have also developed a software package 

that is automatically started when the observing session is over. Then, this application checks every 

meteor trail recorded on hard disk. These data are compressed and sent to a FTP server for further 

processing. The application also checks other data stored by this FTP server, as data from different 

robotic stations are also placed there, and identifies which meteor trails have been simultaneously 

recorded from at least two different locations. The operator receives an automatic email with these data, 

which can be reduced to obtain the atmospheric trajectory of the corresponding meteoroid and also 

radiant and orbital information. 

5 Conclusions 

A continuous effort is being made by the Spanish Meteor Network in order to improve and expand our 

meteor observing stations based on high-sensitivity CCD video devices. Software engineering has been 

one of our priorities in the latest years and, as a result, a new software package for data reduction has 

been developed and successfully tested with other existing applications. However, significant 

discrepancies have been detected with the results provided by Ondrejov's orbits calculation software 

(MORB). This is due to the fact that MORB software does not calculate as a result of an incorrect 

calculation of the geocentric radiant. Besides, the possibility of installing high-sensitivity video systems 

in remote locations made necessary the development of robotic systems that are able to operate in a fully 

autonomous way and also to automatically notify the occurrence of remarkable events. Several software 

packages have been also developed in order to accomplish these tasks. 

 

References 

Ceplecha, Z. (1987) "Geometric, dynamic, orbital and photometric data on meteoroids from photographic meteor networks", 

Bull. Astron. Inst. Czechols. 38, 222-234. 

Ceplecha Z., P. Spurný, J. Borovika (2000) Meteor Orbit (MORB) software. Ondrejov Observatory. Czech Republic. 

Langbroek, M. (2004) Meteor Orbit Calculation software. Dutch Meteor Society. 

Llorca, J., Trigo-Rodríguez, J. M., Ortiz, J. L., Docobo, J. A., García-Guinea, J., Castro-Tirado, A. J., Rubin, A. E., 

Eugster, O., Edwards, W., Laubenstein, M., Casanova, I. (2005) " The Villalbeto de la Peña meteorite fall: I. Fireball 

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Planets, 102, 133-139. 

Madiedo, J.M., Trigo-Rodríguez, J. M., Ortiz, J. L., Morales, N. (2010) "Robotic Systems for Meteor Observing and Moon 

Impact Flashes Detection in Spain", Advances in Astronomy, doi:10.1155/2010/167494. 

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fireball monitoring", European Planetary Science Congress, Abstract EPSC2008-A-00319. 

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Network”, Astron. & Geoph. 47:6, 26. 

Trigo-Rodríguez, J.M., Borovika, J., Spurný, P., Ortiz, J.L., Docobo, J.A.., Castro-Tirado, A..J., Llorca, J. (2006b) " The 

Villalbeto de la Peña meteorite fall: II. Determination of atmospheric trajectory and orbit", Meteoritics and Planetary 

Science 41:4, 505-517. 

Trigo-Rodríguez J.M., Madiedo J.M., Castro-Tirado A.J., Ortiz J.L., Llorca J., Fabregat J., Vítek S., Gural P.S., Troughton 

B., Pujols P., and Gálvez F. (2007a) “Spanish Meteor Network: 2006 continuous monitoring results”, WGN J. of IMO 

35, 13-22. 


Trigo-Rodríguez, J.M., Madiedo, J.M., Llorca, J., Gural, P.S., Pujols, P., Tezel, T. (2007b) “The 2006 Orionid outburst 

imaged by all-sky CCD cameras from Spain: meteoroid spatial fluxes and orbital elements”, Mon. Not. R. Astron. Soc. 

380, 126-132. 

Trigo-Rodriguez, J.M., Madiedo, J.M. Williams, I. P. (2009) "The outburst of the a Cygnids in 2007: clues about the 

catastrophic break up of a comet to produce an Earth-crossing meteoroid stream". Mon. Not. R. Astron. Soc. 392, 367–

375. 


The Updated IAU MDC Catalogue of Photographic Meteor Orbits 

V. Porubcan1• J. Svoren2• L. Neslusan2• E. Schunova3

Abstract The database of photographic meteor orbits of the IAU Meteor Data Center at the Astronomical Institute SAS has gradually been updated. To the 2003 version of 4581 photographic orbits compiled 

from 17 different stations and obtained in the period 1936-1996, additional new 211 orbits compiled 

from 7 sources have been added. Thus, the updated version of the catalogue contains 4792 photographic 

orbits (equinox J2000.0) available either in two separate orbital and geophysical data files or a file with 

the merged data. All the updated files with relevant documentation are available at the web of the IAU 

Meteor Data Center. 

Keywords astronomical databases · photographic meteor orbits 

1 Introduction 

Meteoroid orbits are a basic tool for investigation of distribution and spatial structure of the meteoroid 

population in the close surroundings of the Earth’s orbit. However, information about them is usually 

widely scattered in literature and often in publications with limited circulation. Therefore, the IAU 

Comm. 22 during the 1976 IAU General Assembly proposed to establish a meteor data center for collection of meteor orbits recorded by photographic and radio techniques. The decision was confirmed by the 

next IAU GA in 1982 and the data center was established (Lindblad, 1987). 

 The purpose of the data center was to acquire, format, check and disseminate information on 

precise meteoroid orbits obtained by multi-station techniques and the database gradually extended as 

documented in previous reports on the activity of the Meteor Data Center by Lindblad (1987, 1995, 

1999 and 2001) or Lindblad and Steel (1993). 

 Up to present, the database consists of 4581 photographic meteor orbits (Lindblad et al., 2005), 

63.330 radar determined orbit: Harvard Meteor Project (1961-1965, 1968-1969), Adelaide (1960-1961, 

1968-1969), Kharkov (1975), Obninsk (1967-1968), Mogadish (1969-1970) and 1425 video-recordings 

(Lindblad, 1999) to which additional 817 video meteors orbits published by Koten el al. (2003) were 

added. 

 

V. Porubcan ( ) 

Astronomical Institute of the Slovak Academy of Sciences, 059 60 Tatranská Lomnica, Slovakia; Faculty of Mathematics, Physics and Informatics, Comenius University, 84248 Bratislava, Slovakia. E-mail: porubcan@fmpb.uniba.sk 

J. Svoren • L. Neslusan 

Astronomical Institute of the Slovak Academy of Sciences, 059 60 Tatranská Lomnica, Slovakia 

E. Schunova 

Faculty of Mathematics, Physics and Informatics, Comenius University, 84248 Bratislava, Slovakia 


2 Photographic Orbits 

In 2001 the MDC was moved from the Lund Observatory to the Astronomical Institute of the Slovak 

Academy of Sciences in Bratislava. As it is operating for about twenty years and collecting data acquired already since 1936, it accumulated a large number of meteoroid orbits obtained from different 

sources providing them to researchers for various studies. 

 The last but one version of photographic data, the 1990 version, contained data on 3518 meteors 

with precisely reduced orbits, but only of about 90% of them had also at disposal also complete geophysical data (Lindblad, 2001). In many cases the orbital and geophysical data were not published at the 

same time and in some cases one set was not published and the data had to be obtained by correspondence with the investigator or are remain missing. This was also the case with the last 2003 version of 

the catalogue containing 4581 precisely reduced meteor orbits (Lindblad et al., 2005), where originally 

not all orbits were published with all the catalogued parameters. 

 The data for the 2003 version were compiled from 17 different stations or investigators listed in 

Table 1, where Code in the first column is the letter code assigned to the investigator and the catalogue 

comprises the orbits obtained over the period of sixty years (1936-1996). 

 Traditionally, the previous versions consisted of two independent files separately with the orbital 

file (orb.dat) and geophysical file (geo.dat). In the new version and for convenience of further treatment 

with the data both files were also merged, introduced in a new format and writing the data in a single file 

designated all2003.dat and sorted by the date of meteor detection. 

 The database can be downloaded from the IAU MDC site from the address: 

http:/www.astro.sk/~ne/IAUMDC/Ph2003/database.html together with relevant documentation. 

Table 1. IAU MDC catalogue of photographic orbits. Code – investigator or station code letter, N – the total number of reduced orbits per station / investigator. 

 Code N Investigator/Station 

W 166 Whipple (small camera) 

 J 413 Jacchia (Super-Schmidt) 

H 313 Hawkins and Southworth (Super-Schmidt) 

P 353 Posen and McCrosky (Super-Schmidt) 

S 314 McCrosky and Shao (Super-Schmidt) 

G 25 Gale Harvey, New Mexico State University 

D 636 Babadzhanov et al., Dushanbe (small camera) 

O 459 Shestaka et al., Odessa (small camera) 

K 206 Kiev (small camera) 

C 103 Ceplecha (small camera) 

E 335 Ceplecha and Spurný, European Network 

F 334 McCrosky, Prairie Network 

I 259 Halliday et al., MORP Network 

N 259 Koseki, Nippon Meteor Society 

T 85 Ohtsuka, Tokyo Meteor Network 

U 66 Ochai et al., Nippon Meteor Society 

B 435 Betlem et al., Dutch Meteor Society 

R 22 Trigo-Rodriguez et al., Spanish Meteor Network 

 Sum 4792 


3 New Version of the Catalogue 

Since 1996 additional new photographic meteor orbits are acquired and can be catalogued. Some of 

them are older and were not yet included in the catalogue and the rest are new orbits recorded in the last 

few years. Though the present catalogue of 4581 orbits is covering the whole year observations rather 

uniformly, dominant in the number of orbits are the Perseids and Geminids. The recent exceptional returns of the Leonids greatly improved their orbital statistics, but more of them were not yet published 

and cannot be included in the catalogue. 

At the present, there are 211 new meteoroid orbits which can be included in the new version of 

the catalogue and thus the number of the orbits of the MDC catalogue increased to 4792. The new orbits 

are compiled from seven sources and consists of 27 Perseids recorded during the exceptional shower return in 1993 (Spurny, 1995), 75 Leonids observed during the 1998 shower outburst (Betlem et al., 

1999), 10 Leonids from the 2002 storm (Trigo-Rodriguez et al., 2004), 19 bright fireballs recorded within the European Fireball Network between 1990-2004, 22 fireballs recorded within the Spanish Meteor 

Network in 1991-2004, 52 exceptional bolides from the EN observed in 2006-2007 (Spurny, 2010) and 

6 fireballs recorded in Japan in the beginning of nineties. 

 In order to resolve any potential inconsistencies in the published orbital and geophysical parameters, these have been checked by a standard checking procedure as applied to the sets of orbits in the 

previous version of the catalogue. 

 The check of consistency of the orbital and geophysical data is made in two steps: (a) Assuming 

that the published radiant and velocity at the time of detection were correct, the orbital elements are recalculated; (b) As sometimes errors appear also in the published geophysical (encounter) data, the radiant coordinates and the geocentric velocity are recalculated from the published orbital elements utilizing the optimal method of theoretical radiant prediction for a given orbital geometry (Neslušan et al., 

1998). 

 In the new version of the catalogue also the error bars of the orbital and geophysical parameters 

derived by individual investigators, if available will be added and included to the both data files. 

 At the next step we plan to innovate the catalogue more regularly that is after any new set of 

meteoroid orbits is published or submitted for inclusion in the catalogue and information about any updating of the database will be announced on web page of the IAU MDC. 

Acknowledgements 

The authors acknowledge support from VEGA - the Slovak Grant Agency for Science (grants Nos. 

1/0636, 2/0022 and 2/0011). 

References 

H. Betlem, P. Jenniskens, J. van't Leven, R. Ter Kuile, C. Johannink, H. Zhao, C. Lei, G. Li, J. Zhu, S. Evans, P. Spurny, 

Very precise of 1998 Leonid meteors. Meteoritics and Planet. Sci. 34, 979 (1999) 

P. Koten, P. Spurny, J. Borovicka, R. Stork, Catalogue of video meteor orbits 1. Publ. Astron. Inst. Sci. Czech Rep. 91, 1–32 

(2003) 

B.A. Lindblad, The IAU Meteor Data Center in Lund. In: Z. Ceplecha, P. Pecina (eds.) Interplanetary Matter, Proc. 10th 

ERAM. Astron. Inst. Czechosl. Acad. Sci., Prague, 201–204 (1987) 

B.A. Lindblad, D.I. Steel, In: Asteroids, Comets, Meteors, Milani et al. (eds.), 497 (1993) 

B.A. Lindblad, The IAU Meteor Data Center in Lund. Earth, Moon and Planets, 68, 405 (1995) 


B.A. Lindblad, A survey of meteoroid orbits obtained by two station video observations. In: Meteoroids 1998, W.J. Baggaley 

and V. Porubcan (eds.), Bratislava, 274 (1999) 

B.A. Linbdlad, IAU Meteor Data Center. In: Meteoroids 2001, B. Warmbein (ed.), ESA SP-495, 71 (2001) 

B.A. Lindblad, L. Neslusan, V. Porubcan, J. Svoren, IAU Meteor Database of photographic orbits-version 2003. Earth Moon 

Planets, 93, 249–260 (2005) 

L. Neslusan, J. Svoren J, V. Porubcan, A computer program for calculation of a theoretical meteor-stream radiant. Astron. 

Astrophys., 331, 411 (1998) 

P. Spurny, EN Photographic Perseids. Earth, Moon and Planets, 68, 529 (1995) 

P. Spurny (2010) Private comm. 

J.M. Trigo-Rodriguez, J. Llorca, E. Lyytinen, J.L. Ortiz, A.S. Caso, C. Pineda, S. Torrell, 2002 Leonid storm fluxes and 

related orbital elements. Icarus 171, 219 (2004) 



CHAPTER 10: 

THE FUTURE OF OBSERVATIONAL TECHNIQUES AND 

METEOR DETECTION PROGRAMS 


French Meteor Network for High Precision Orbits of Meteoroids 

P. Atreya1• J. Vaubaillon • F. Colas2• S. Bouley2• B. Gaillard2• I. Sauli2• M.-K. Kwon2

Abstract There is a lack of precise meteoroids orbit from video observations as most of the meteor 

stations use off-the-shelf CCD cameras. Few meteoroids orbit with precise semi-major axis are available 

using film photographic method. Precise orbits are necessary to compute the dust flux in the Earth’s 

vicinity, and to estimate the ejection time of the meteoroids accurately by comparing them with the 

theoretical evolution model. We investigate the use of large CCD sensors to observe multi-station 

meteors and to compute precise orbit of these meteoroids. An ideal spatial and temporal resolution to get 

an accuracy to those similar of photographic plates are discussed. Various problems faced due to the use 

of large CCD, such as increasing the spatial and the temporal resolution at the same time and 

computational problems in finding the meteor position are illustrated. 

Keywords meteor · CCD · observation 

1 Introduction 

Meteor astronomy has implemented video techniques for all-night observations in addition to visual and 

photographic during the past decade. The IMO Video Meteor Network [1], Polish Fireball Network [2], 

Spanish Meteor Network [3], Dutch Meteor Society [4] and Czech Meteor Network [5] are few of the 

meteor networks actively operating in Europe. Detection and analysis software such as Metrec, 

Meteorscan and UFOcapture eases the tedious setup and encourages professional and amateur 

astronomers alike to set up meteor stations. 

 These networks have thrived from off-the-shelf video cameras and lenses. One of the major 

drawbacks from these configurations is the astrometric quality of data acquired. The typical cameras 

used (Watec, Mintron etc.) with 640 × 480 pixels, along with medium angled lens (~50°), have spatial 

resolution of 0.08°/pixel. This corresponds to a resolution of 140 m if the meteor is at 100 km distance 

from the camera. This causes a large uncertainty in velocity, and thereafter, in the semi-major axis of the 

meteoroids. For example, a typical meteor with velocity of 39.9 km/s corresponds to semi major axis of 

5 AU, whereas, velocity of 40.0 km/s corresponds to 10 AU, a change of 0.1km/s in velocity 

corresponding to 5 AU in this particular case [6]. Semi-major axis is very sensitive to velocity 

component of the meteoroids, and thus we need 10 order of magnitude better spatial resolution than 

most of these off-the-shelf cameras for precise meteor velocity and semi-major axis. 

The need for more precise orbital elements of meteoroids is imminent for modeler’s. Figure 1 

shows the node of different trails (1817-1913 AD) of Draconid stream for the year 2011. Only with high 

resolution observation and precise semi major axis, it is possible to identify the exact trail that will cause 

the outburst on 8th October, 2011. Similarly, the 2009 Leonids outbursts were predicted to occur due to 



P. Atreya ( ) • J. Vaubaillon • F. Colas • S. Bouley • I. Sauli • M.-K. Kwon 

IMCCE, 77 Avenue Denfert Rochereau, 75014, Paris, France. E-mail: atreya@imcce.fr 

B. Gaillard 

Lheritier, 10 avenue de l’Entreprise, 95862 Cergy, France


trails from 1533 AD and 1536 AD [7], whose radiants differ by 0.9°. But the observations made from 

current instruments were not able to identify the exact trail from which the outburst occurred. So there is 

need for better accuracy, which can be obtained by higher temporal and spatial resolutions. 

Figure 1. The node of Draconids meteoroid stream with trails from 1817 – 1913 AD for the 2011 outburst. 

 There are generally two ways to increase the spatial resolution of the camera system, i.e. to use a 

large CCD and to use a narrow lens. However, only increasing the spatial resolution is not sufficient for 

obtaining precise velocity. A simple simulation was performed to identify the spread of meteor in a 

single image for a fixed high resolution of 0.01°/pixel for various frame rates. Figure 2 shows the length 

of a meteor (in pixels) for different temporal resolution for slow (angular speed of 10°/s) and fast 

meteors (angular speed of 30°/s). 

For the typical video frame rate of 25Â30 fps the slow meteor will be spread out across 40 pixels, 

whereas the fast meteor will be spread more than 100 pixels. Thus it will be difficult to compute the 

position of meteor within 1 pixel accuracy as its spread across too many pixels. When the frame rate is 

increased to 100 fps, the meteor is spread across only 10Â30 pixels. Thus increasing frame rate is 

essential if spatial resolution is increased to estimate the meteor position accurately in the images. Due 

to this reason, even if narrow lens are used with small CCDs with video frame rate, it will have 

computational disadvantages. 

There are also several disadvantages of using large CCDs. The time to read a single frame in a 

CCD is inversely proportional to the size of the CCD. Table 1 shows the frame rate of different size of 

CCDs from JAI camera company. Only the smallest CCD have temporal resolution of 100 or better, 

which is preferred for good spatial resolution. An external rotating shutter can be used to provide good 

temporal resolution.


Figure 2. The length of a meteor for different temporal resolution for two typical meteor speed. 

 The spatial resolution of set to 0.01 deg/pixel 

 

Table 1. The frame rate of different sizes of CCDs. 

Camera ID Size of CCD [Pixels] Max Frame Rate 

RM-6740CL 648 × 484 200 

CM-140GE 1392 × 1040 31 

CM-200GE 1628 × 1236 25 

BM-500GE 2456 × 2048 15 

AM-1600GE-F 4872 × 3248 3 


2 Lheritier Camera 

Lheritier, a French camera and system vision company, has developed an interline progressive scan 

camera LH11000. It uses Kodak Kai 11002 sensor with 4032 × 2688 effective pixels of 9 μm size. The 

readout noise is ~30 e-, with gain of 0Â30 DB. The images are saved in 16 bit format. It takes 149 ms to 

read a single image, and the frame rate is 6.7 fps. The minimum and maximum shutter speeds are 0.8 ms 

and 52428 ms respectively. This camera was tested for military and aviation environment and can 

withstand Â10°C to 50°C and humidity of 100% non condensing. 

 Figure 3 shows the modification of CCD readout method to mimic electronic shutter system. The 

top part of the figure shows the basic procedure of CCD system. The signal denotes the exposure 

duration (10 ms), and all the images are stored separately. This is not ideal because of the “dead time” of 

149 ms after every image. A modification to a CCD system was made by introducing a ”break” period 

(10 ms) which means that during this period the CCD is closed as shown in the bottom section of the 

figure. The images are stacked onto the CCD (N = 50 times), and read out only once. This method not 

only decreases the dead time of the camera, but due to stacking of the images, causes an effect very 

similar to the external rotating mechanical shutter. The “signal”, “break” and the total exposure duration 

can be modified to suit fast and slow meteors. This method was possible as Lheritier company 

developed a way to “close” the CCD completely, which is used as “break” duration. This also implies 

that there is no upper limit to the size of CCD that can be used for the detection of meteors due to low 

temporal resolution. The dead time of reading a single image can be reduced by making longer 

exposures. 

Figure 3. Modification of basic CCD readout method to mimic electronic shutter system.

Figure 4 shows an example of meteor detected (raw image) with LH11000 camera, modified 

shutter system and Nikon 85 mm F1.4 lens (FOV 28° × 18°). The meteor was captured during Lyrid 

observation campaign on 22nd April, 2010 at 00:56:50 UT from Observatory of Haute Provence (OHP), 

France. The spatial resolution is ~0.007° or ~25”. The signal and break duration was set to 10 ms and the 

total exposure of the image was 1 second (N = 50 loops). 

 


Figure 4. Example of a meteor (raw image) with 10 ms signal, 10 ms break and total exposure of 1 seconds. 

 The intensity plot for few breaks is shown in Figure 5. The distance between the peaks are ~40 

pixels. With the spatial and temporal resolution of 0.007°/pixel and 10 ms respectively, the angular 

velocity is ~28°/s, which agrees with those of general meteors. Precise position and velocity can be 

computed by fitting different types of curves in the reduced data. Figure 4 and smoothness of the 

intensity curve of Figure 5 proves that this new method of electronic shutter works. 

3 French Meteor Network 

The first video meteor network will be started in France under PoDeT-MET project. The primary aim of 

this network is to get high precision orbits of meteoroids. The Lh11000 camera is equipped with Cannon 

50mm F1.2 lens (FOV 40° x 27°) and have spatial resolution of 0.01° which is ~8 times higher than the 

numerous off-the-shelf systems. This corresponds to 17.4m resolution if the observed meteor is at a 

distance of 100 km. The first dedicated triple station network will be set up in south of France during 

2010Â2011. The first station will be set up at Pic du midi Observatory, at the height of 3000m. The other 

two stations will be set ~100 km further away. An all sky camera will also be installed to compliment 

the high precision cameras. The network will be expanded to other areas of France in future. 

 


Figure 5. The intensity of meteor breaks along Y axis. 

Starting a remote and automated camera network has many challenges. A single image from the 

LH11000 camera is 20 MB in size. This results in 400+ GB of raw data every night from a single 

camera. One of the big challenge is to develop a very fast and yet efficient and automated method to 

detect meteor. The false detections have to be limited, as the number of images that can be transferred 

are limited by low bandwidth internet. One of the most important factors in computing precise orbits of 

meteoroids is to estimate the meteor position in the image with less than 1 pixel uncertainty. Most of the 

software for processing meteor images were written for off-the-shelf cameras, and many modifications 

would have to be made so that the required accuracy can be achieved. Other challenges include 

developing a cooling system for the camera to reduce CCD noise while heating up the lens area to 

prevent condensation. 

Acknowledgements 

The authors would like to thank Lheritier company for all the support. This project is funded primarily 

by Paris city grants 

References 

1. Molau, S.: 2003, The AKM video meteor network,Proceedings of the Meteoroids 2001 Conference, pp. 315 -318 

2. Olech, A.; Zoladek, P.; Wisniewski, M.; Krasnowski M.; Kwinta, M.; Fajfer, T.; Fietkiewicz, K.; Dorosz, D.; Kowalski, 

L.; Olejnik, J.; Mularczyk, K.; Zloczewski, K.:2006, Polish Fireball Network, Proceedings of the IMC 2005, pp.53-62 

3. Trigo-Rodriguez, J. M.; Madiedo, J. M.; Castro-Tirado, A. J.; Ortiz, J. L.; Llorca, J.; Fabregat, J.; Vitek, S.; Gural, P. S.; 


Troughton, B.; Pujols, P.; Galvez, F.: 2007, Spanish Meteor Network: 2006 continuous monitoring results, WGN, 35, 1, 

pp. 13-22 

4. Miskotte, K.; Johannink, C.: 2006, Taurids 2005: results of the Dutch Meteor Society, WGN, 34, 1, pp. 11-14 

5. Koten, P.; Borovicka.J.; Spurn, P.; Evans,S.; Stork,R.; Elliott, A.: 2006, Double station and spectroscopic observations 

of the Quadrantid meteor shower and the implications for its parent body, MNRAS, 366, 4, pp. 1367-1372. 

6. Barentsen, G., 2009, Meteor Astrometry: What accuracy do we need, Proceedings of the IMC 2009, in press. 

7. Jenniskens, P., 2006, Meteor Showers and their Parent Comets, Cambridge University Press, UK 


BRAMS: the Belgian RAdio Meteor Stations 

H. Lamy1• S. Ranvier • J. De Keyser • S. Calders • E. Gamby • C. Verbeeck2

Abstract In the last months, the Belgian Institute for Space Aeronomy has been developing a Belgian 

network for observing radio meteors using forward scattering technique. This network is called BRAMS 

for Belgian RAdio Meteor Stations. Two beacons emitting a circularly polarized pure sine wave toward 

the zenith act as the transmitters at frequencies of 49.97 and 49.99 MHz. The first one located in 

Dourbes (Southern Belgium) emits a constant power of 150 Watts while the one located in Ieper 

(Western Belgium) emits a constant power of 50 Watts. The receiving network consists of about 20 

stations hosted mainly by radio amateurs. Two stations have crossed-Yagi antennas measuring 

horizontal and vertical polarizations of the waves reflected off meteor trails. This will enable a detailed 

analysis of the meteor power profiles from which physical parameters of the meteoroids can be obtained. 

An interferometer consisting of 5 Yagi-antennas will be installed at the site of Humain in order to 

determine the angular detection of one reflection point, allowing us to determine meteoroid trajectories. 

We describe this new meteor observing facility and present the goals we expect to achieve with the 

network. 

Keywords radio meteors · forward scattering 

1 Introduction 

The Earth’s atmosphere is constantly hit by thousands of meteoroids with sizes ranging from 

submillimeters to several meters. Their estimated cumulative mass is in the range [40-100] tons per day. 

They play a crucial role in a number of astronomical and aeronomical studies and, given their intercept 

velocities in excess of 11 km/s, they pose a significant threat to spacecraft. Traditionally, they have been 

detected by visual means or with radars during their interaction with the atmosphere. Here we propose to 

study the meteoroid population with the BRAMS (Belgian RAdio Meteor Stations) network, a set of 

radio receiving stations using forward scattering techniques and two dedicated beacons as transmitters. 

The BRAMS network will be finished by the end of 2010. Its current state is described in section 2 

while section 3 is devoted to the objectives of the project. In the conclusion, the advantages of a forward 

scattering system over traditional radar systems will be shortly discussed. 

2 The BRAMS Network 

In 2009 the Belgian Institute for Space Aeronomy (BISA) initiated the development of BRAMS, a 

Belgian network of radio receiving stations using forward scattering techniques to detect meteors. This 



H. Lamy ( )$&*
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Belgian Institute for Space Aeronomy, Avenue Circulaire 3, 1180 Brussels, Belgium. E-mail: herve.lamy@aeronomie.be 

C. Verbeeck

Royal Observatory of Belgium, Avenue Circulaire 3, 1180 Brussels, Belgium


project is carried out in collaboration with about 20 Belgian radio amateurs or groups of amateur 

astronomers which will host several stations throughout the country (see black squares on Figure 1). 

Figure 1. Geographical distribution of the stations of the BRAMS network. The black squares represent the 

receiving stations while the two triangles represent the two beacons (Ieper in the West and Dourbes in the SouthEast). The biggest cities of Belgium, represented by rhombs, have been added to facilitate identification of the 

stations. 

 The transmitters are two dedicated beacons located in Ieper and Dourbes (the two triangles on 

Figure 1). They emit a pure sinusoidal wave with a constant power of respectively 50 and 150 watts, at 

frequencies respectively of 49.99 and 49.97 MHz. These frequencies are protected avoiding ambiguity 

about the origin of detected meteor echoes. The beacon in Ieper is a crossed 2-element Yagi antenna 

which has been constructed in 2008 by radio amateurs from the VVS (Vereniging Voor Sterrenkunde -

Flemish association of amateur astronomers). It emits toward the zenith with a HPBW (Half-Power 

Beam Width) of ~100° (see Figure 2) which covers a large surface of the sky at altitudes between 90 and 

120 km. The theoretical total gain of this antenna is 5.9 dBi. The beacon in Dourbes is under 

construction and will be active in September 2010. It will be similar to the one in Ieper but will use a 

8m× 8m grid as the reflector to increase the power emitted upward (HPBW ~64° -see Figure 2). With 

this grid, the total gain is increased by 3.6 dB as compared to the Ieper beacon. The stability of the 

frequency of the Dourbes beacon is secured with a GPS disciplinated OCXO (Oven-Controlled Crystal 

Oscillator) 10 MHz reference. 

 A typical receiving station is made of a 3-element Yagi antenna linked to a ICOM ICR75 

receiver by a coaxial cable. The received signal is sampled and stored on a local PC. With 20 receiving 

stations spread over Belgium, we will increase both the number of meteor detections and the chances of 

having the same meteor detected simultaneously by several stations. This last point is essential for the 

determination of meteoroid trajectories since each detection gives information only about one point of 

the trajectory. This requires a very good synchronization of the stations. The stations will be 

synchronized by using the NTP (Network Time Protocol) application and a local GPS as reference 

clock. Accuracy of 1 ms is expected. Each station will generate approximately 1 GB of data per day. 

First these data will be temporarily stored on local hard disks then later archived with the IT facilities of 


Figure 2. Theoretical radiation pattern (in dB) of the two beacon antennas (circularly polarized). 

Solid line: Dourbes beacon (with a 8m  8m grid). Dashed line: Ieper beacon.

BISA, where all data will be analyzed and become available to the scientific community. In these data 

there will be a large number of meteor echoes but also a large number of “spurious” echoes such as 

reflection of radio waves on planes, sporadic Es, thunderstorms, etc. as well as local broad-band 

interferences. A software is currently developed to automatically select meteor echoes only. 

The station in BISA (located in Uccle in the South of Brussels) is also equipped with an 

additional antenna, a crossed 3-element Yagi, connected to a low noise amplifier (MITEQ AU-1138) 

and a software defined radio receiver (USRP2). With this setup, we will measure both polarizations 

(horizontal and vertical) of the meteor echoes and combine them to obtain the total power reflected by 

the meteor. This will allow us to perform quantitative analyses of the signal in order to retrieve physical 

parameters of the meteoroids. 

An interferometer made of 5 Yagi antennas will be installed in the radio astronomical site of 

Humain in order to determine the angular direction of one reflection point with an accuracy Á 1-2°. 

Humain is located at approximately 60 km north-east of Dourbes. We will use the 5 antenna 

configuration of [8] consisting of two orthogonal linear arrays of 3 antennas with the central one 

common to both arrays. The central antenna will be a crossed 3-element Yagi antenna used in order to 

obtain the total power of the incoming waves like in the BISA station. To get information on the angular 

direction of the reflection point, the phase of the signals from the 5 antennas are compared. For this 

purpose, the analog-to digital converters of the five USRP2 receivers are synchronized. In addition, the 

frequency stability of the receivers is ensured by a 10 MHz reference similar to the one used for the 

beacon in Dourbes. 


3 Objectives of the Project 

By using the BRAMS network, we plan to reach the objectives described below. They are separated 

according to whether they can be achieved with a single station, with several stations or with several 

stations and the interferometer. 

1. By using data from a single receiving station, the activity profiles of meteor showers (number of 

echoes versus time) can be obtained by subtracting sporadic meteor echoes from all echo counts. 

These activity profiles must be corrected for the observability function of the station, which 

describes its sensitivity for detecting meteoroid echoes from a specific direction in the sky ([7], 

[15], [13]). The activity profiles of the main meteor showers will be studied and compared to 

results in the literature. Mass indexes and flux densities will be calculated for meteor showers 

and sporadic background using the method developed by [1] and [11], [12]. 

2. Simultaneous detection of a meteor by several stations allows in principle to retrieve some 

information about the meteoroid trajectory. We will test a method proposed by [9] exploiting the 

fact that a meteor trail is tangential to a family of ellipsoids with the receivers as one focal point 

and the transmitter as the other one (specularity condition). If the meteor is also detected by the 

interferometric station in Humain, the problem is simplified since then we know the angular 

direction of the reflection point for this particular geometry. The height of this reflection point 

can be obtained for shower meteors but is still unknown for sporadic meteors. However, for 

underdense meteors, it can be estimated from the exponential decay of the power profile (with 

the use of a good atmospheric model such as MSISE-00) and for overdense meteors, it can be 

estimated with the method proposed by [5]. With the 3-D position of one specular point and with 

detections of the meteor by other stations, we can retrieve the trajectory of the meteoroid even 

for sporadic meteors ([16]). Eventually the goal is to produce a map in Sun-centered ecliptical 

coordinates of the distribution of meteor radiants and to compare it to similar ones obtained by 

optical or radar means (e.g. [4]). 

3. For a given meteor, when the geometry is fully resolved, the study of the power profiles give 

access to several important physical parameters if the technical characteristics of the receiving 

station (antenna gains, polarization of the reflected wave, calibration of the acquisition card, etc.) 

are perfectly known [16]. These characteristics will only be known for the stations in BISA and 

in Humain. For the others, we will only have reasonable estimates. The electron line density at 

the reflection point can be computed from the maximum of the power profile. If the electron line 

density is obtained in several points of the meteoroid trail (from multi-station observations), the 

initial mass of the meteoroid can be estimated with models of meteoroid ablation in the Earth’s 

atmosphere (e.g. [3]). The ambipolar diffusion coefficient can be obtained from the exponential 

decay of underdense meteors and yields information on the meteor’s height. The speed of the 

meteoroid can be determined by several methods: a) from Fresnel oscillations if these are present 

and if the signal-to-noise ratio of the data is large enough, b) from initial rise times of the power 

profiles if the meteor is observed by several stations (requiring a good synchronization from the 

various stations) and c) from the Doppler effect for head echoes (see below). 

4. Head echoes are associated with the ionized region in front of the meteoroid. Therefore, these 

echoes in spectrograms show a large Doppler effect due to the high velocity component of the 


object along the line-of-sight. If such an echo is detected by at least 3 stations, we can in 

principle retrieve the total velocity of the meteoroid [10], [14]. In combination with an ablation 

model, the meteoroid mass and density can be estimated. Comparison with the results on head 

echoes obtained with High-Power Large-Aperture radars will be considered. 

5. Once we have the radiant of individual meteors and also an estimate of the relative intercept 

velocity of the incoming particle, the next step is to calculate the orbital parameters of the 

detected meteoroids. A correction must be applied for the acceleration produced by the 

gravitational focusing of Earth as well as for the Earth’s heliocentric velocity. Knowing the 

orbital parameters contributes to a better understanding of the distribution and evolution of 

material in the Solar System. 

6. Another advantage of having stations with dual polarized antennas is the ability to investigate the 

polarization of the received waves. Since most of receiving stations can detect only one 

polarization, it is very important to determine the depolarization coefficient of the reflections on 

the meteor trail. The rotation of the polarization plane of the incoming wave can be due to 

ionospheric Faraday rotation or as a result of the scattering from meteor trails. We will 

investigate whether the depolarization depends on the type, the trajectory, or the size of the 

meteor trail. To our knowledge, very few similar measurements have been done with a forwardscatter system (see however [2]). 

4 Conclusion 

The BRAMS network will be a very useful tool to better characterize the distribution of meteoroids in 

the Solar System. Most researchers employ a backscatter set-up rather than a forward-scatter system, as 

the latter has a much more complicated geometry. However, backscatter systems suffer from the echo 

ceiling selection effect, which limits their views on faint and fast meteors. Forward-scatter setups are 

much less vulnerable to this selection effect, hence yielding a less biased meteoroid population. To our 

knowledge, there are only two other forward-scatter systems run by professional astronomers: the 

Bologna-Lecce-Modra system [6] and the HRO system at the Kochi University in Japan [17]. The 

former has only 2 receiving stations and no interferometric capabilities while the latter has only 6 

stations. BRAMS will feature at least 20 stations that will allow improved multi-station analysis and will 

also have the additional advantage of an interferometric system. 

Acknowledgements 

BRAMS is a project of the Belgian Institute for Space Aeronomy which is funded by the Belgian SolarTerrestrial Center of Excellence (STCE -http://www.stce.be). This project is carried out in collaboration 

with many radio amateurs from Belgium, in particular with several members from the VVS (Vereniging 

Voor Sterrenkunde). We would like to thank them for their participation in this project. 


References 

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163, (2008). 

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International Meteor Conference 2006, Eds. F. Bettonvil & J. Kac, 117-125, (2007). 


The New Meteor Radar at Penn State: Design and First Observations 

J. Urbina1• R. Seal2• L. Dyrud3

Abstract In an effort to provide new and improved meteor radar sensing capabilities, Penn State has 

been developing advanced instruments and technologies for future meteor radars, with primary 

objectives of making such instruments more capable and more cost effective in order to study the basic 

properties of the global meteor flux, such as average mass, velocity, and chemical composition. Using 

low-cost field programmable gate arrays (FPGAs), combined with open source software tools, we 

describe a design methodology enabling one to develop state-of-the art radar instrumentation, by developing a generalized instrumentation core that can be customized using specialized output stage 

hardware. Furthermore, using object-oriented programming (OOP) techniques and open-source tools, 

we illustrate a technique to provide a cost-effective, generalized software framework to uniquely define 

an instrument’s functionality through a customizable interface, implemented by the designer. The new 

instrument is intended to provide instantaneous profiles of atmospheric parameters and climatology on a 

daily basis throughout the year. An overview of the instrument design concepts and some of the 

emerging technologies developed for this meteor radar are presented. 

Keywords meteor radar · FPGAs · software radar · open source 

1 Introduction 

Meteoroids impact and disintegrate in the Earth’s atmosphere daily. Current estimates for this global 

meteor flux vary from 2,000-200,000 tons per year, and estimates for the average velocity range 

between 10 km/s and 70 km/s [Taylor, 1995; Ceplecha et al al., 1998; Janches et al., 2000b; Cziczo et 

al., 2001; Mathews et al., 2001]. The understanding of the properties of the meteor flux is important for 

several fields of study which range from solar system evolution to imaging of gravity waves in the 

mesosphere. For example, meteoric metals are one of the sources of metal and ion layers in the 

mesosphere/lower thermosphere (MLT) region. They are also the source of condensation nuclei which is 

needed for the formation of noctilucent clouds (NLC) [Kelly and Gelinas, 2000; Smith et al., 2000; Liu 

et al., 2002; Rapp et al., 2003]. Yet, the basic properties of this global meteor flux, such as average 

mass, velocity, and chemical composition remain poorly understood [Mathews et al., 2001]. 

It is still unknown how the changes in the meteor flux will influence these phenomena, because 

current modeling efforts of the physics and chemistry of meteor atmospheric entry and ablation require 

better observational constraints [McNeil et al., 2002; Pellinen-Wannberg et al., 2004; Plane, 2004]. We 



J. Urbina ( ) 

315 EE East, University Park, PA 16802. Phone: 814-863-5326; Fax: 814-863-8457; E-mail: jvu1@psu.edu 

R. Seal 

University Park, PA 16802 

L. Dyrud 

Applied Physics Laboratory, John Hopkins University, Columbia, MD, 20723 


believe much of the mystery surrounding the basic parameters of the meteor input exists for two reasons: 

1) The unknown sampling biases of different meteor observation techniques, and 2) The lack of 

continuous and routine measurements of radar meteors using advanced techniques. In an effort to 

provide new and improved meteor radar sensing capabilities, Penn State has been developing advanced 

instruments and technologies for future meteor radars, with primary objectives of making such 

instruments more capable and more cost effective in order to study the basic properties of the global 

meteor flux. With the rapid emergence of new standards and protocols in wireless communication, many 

functions of traditional radio receivers are being implemented in software [Mitola, 2000; Reed, 2002]. 

These new radio receivers are called software radios since their implementation relies heavily on digital 

signal processing techniques and require fewer radio frequency components than classic analog radios. 

 We describe in the this paper the current implementation of an open source VHF software radar 

system as a first step towards developing a new generation of radar systems for meteor and aeronomical 

science. In section 2, we describe the analysis and design of the system. Section 3 is devoted to a 

discussion of the software architecture and system configuration. We present first meteor observations in 

section 4. Finally, in section 5, a summary of the paper is presented. 

2 System Analysis and Design 

Precise definition of the problem domain is the first stage of design known as requirements analysis 

[Fowler, 2004]. This section discusses the techniques used to analyze, model, and implement the design 

of the data acquisition presented in this paper. Detailed discussion of both hardware and software are 

combined to better communicate their interdependence. 

2.1 Requirements Analysis 

Definition of the system’s capabilities and features are best defined by users (domain experts) of the 

system. A preliminary list of requirements were created as a first step in the design process: 

1. System users are primarily scientists. 

2. Users need the ability to configure the system to meet their own specifications. 

3. System configuration should be stored for later re-use. 

4. Multiple configurations, cycled at predetermined intervals, are sometimes necessary for a single 

experiment. 

5. The system will use the Linux Operating System. 

6. Some experiments require large bandwidths and high storage rates. 

7. Minimal real-time processing and plotting tools are necessary to ensure proper setup and 

equipment function. 

8. Data headers are needed for data storage and retrieval. A standard format will be required. 

9. Analysis software will be required for post processing. 

10. Software should be able to accommodate newer hardware revisions with minimal effort. 

11. Documentation is a critical component. 

This list served as the framework for the design and each item was categorized according to a function. 

Primary tasks were identified and further refinement produced smaller, well-defined subtasks. 


 From this requirement analysis, 5 primary functions and 4 supporting subfunctions were defined. 

These tasks, having well-defined boundaries, partitioned the system into 5 primary programs of 

operation: 1) System Configuration Program, 2) Data Collection Program, 3) Real-Time plotting 

Program, 4) Post Processing Software, and 5) Data Formatting Routines. Next, the process of hardware 

selection followed. Hardware was categorized as follows: 1) Wide-Band digital receiver, 2) High speed 

general purpose computer, 3) High speed, large capacity data storage, 4) Radar pulse controller, and 5) 

Antenna Configuration and Control System. Due to space limitation and relevance of the acquisition 

system, only the wide-band receiver implementation is described below. For a complete discussion of 

the integration of these four components, please see [Seal, 2010]. 

2.2 Software Radar System 

The software-defined radio for radar systems takes advantage of existing open source radio software 

created by the GNU Software Radio for AM, FM, and HDTV signal detection [http://www.gnu.org/ 

software/gnuradio/]. The system is built around a PC with a 2.6 GHz AMD Phenom X4 Quad-core 

processor, 4 GB DDR2 RAM, with 16 1 TB SATA hard drives, and Gentoo Linux operating system. 

Commercially available PC boards will be used for radar controller and digitization/processing 

purposes. The functional diagram of the transmitting and receiving modules of the VHF radar system is 

shown in Figure 1. 

Figure 1. Functional diagram of the transmitting and receiving module 

of the 50 MHz Defined Radar for Meteor and Aeronomical Science. 

The received signal from the antenna is passed through an analog band-pass filter tuned to the 

desired operating frequency. The next stage is a low-noise amplifier with programmable gain that boosts 

the signal level further. The output of this amplifier is passed through a protection circuit before it is sent 

to the digital receiver units where the carrier signal is sampled at 64 MHz (50 MHz carrier signal is 

translated to 14 MHz into the first Nyquist zone of 32 MHz) and then is digitally down converted and 

decimated in software to produce quadrature and in-phase baseband signals. The dynamic range of the 

system is about 90 dB. To ensure coherence of the transmitter/receiver, a 10 MHz oven controlled local 

oscillator is used to produce the clocks required by different parts of the system including the radio 

frequency gated signal for the transmitter. The desired frequency of operation is selected by software 

and set to 50 MHz (the system can be tuned to any value between 1 and 100 MHz with adequate RF 

front-end circuitry). Each A/D inside the digital receiver card can operate at a maximum speed of 80 

Msamp/s per unit channel. With one digital receiver board the system will support a total of 4-complex 


channels to serve a 4-receiver interferometric radar. If more channels are needed, the system can easily 

be extended to 8, 16, 32, 64, or 128 complex channels with additional receiver boards. 

 The system operates as follows: data acquisition software is used to load and initiate the 

frequency synthesizer board (that provides all the required clock for the system), load the radar 

controller card, configure the digital receiver boards, initiate data collection, and route the digital 

samples to a disk file as they become available. The radar controller will provide four control signals: a 

sample start trigger to the receiver board, blanking, T/R switching, and RF pulse. Additional control 

pulses, e.g., coding, etc., can also be provided by the counter/timer card if needed. The frequency 

synthesizer card will have three (more can be provided if needed) additional frequency outputs, which 

may be useful in frequency domain interferometry measurements. Four 5kW (20kW total peak power) 

transmitters with two pairs of T/R switches are used to excite the interferometric antenna. The 

transmitter has about 1 MHz bandwidth and a duty cycle of 10%. 

 Radar data collection begins when a trigger signal is applied to the external gate of the universal 

software radio peripheral (USRP). Next, the user application requests data from the USRP, via the 

driver’s interface. When data is available, the user application selects a segment of data and copies it 

into a secondary, user allocated buffer system. This secondary system allows data sharing among 

multiple processes by utilizing the POSIX shared memory library and the tmpfs [Robbins, Online] file 

system. Tmpfs transparently allows large regions of PC RAM to be used as a standard storage device. 

This filesystem is, by default, dynamically resizable through the use of swap space. For high speed 

operation, a fixed size tmpfs is required; preventing interaction with swap space which drastically 

degrades performance. The POSIX shared memory library uses the tmpfs filesystem to allocate regions 

of memory included in the requesting process’s own address space; providing data sharing among 

processes. E¿cient buffer operation in a read/write system is accomplished using the 

producer/consumer (P/C) threading model [Binstock, Online]. The P/C model requires two threads: the 

producer thread handles data writes to the buffers, and the consumer thread manages data reads. 

Synchronization is controlled through a shared variable that tracks dirty buffers (buffers containing 

pending data). In this model, the consumer thread starts the sequence, requesting data from the first 

buffer. If data is not available, the consumer thread is put to sleep. Then, the producer begins filling 

buffers at a continuous rate; waking the consumer thread upon completion of a buffer. This operation 

continues indefinitely using a predetermined number of buffers. Non-real-time operating systems can 

impose unpredictable latencies [Seelam, Online]; violating real-time operation. Applying the P/C model, 

latencies can be masked through buffering; bypassing the need for a real-time operating system. 

Additionally, use of this model, combined with shared memory regions, allow for multiple levels of realtime processing to occur simultaneously. This approach preserves storage device bandwidth which is 

critical for high speed, real-time data writing. This provides a major advantage over older systems in 

which the storage device spent a large amount time seeking to satisfy system reads and writes; further 

limiting bandwidth. 

3 First Radar Observations 

We have conducted first radar observations with the software radar system in conjunction with four 5-

element Yagi antennas for transmission and a 50-MHz transmitter with peak power of 20 kW. On 

reception, we used five 5-element Yagi antennas in a cross configuration. The experiment was carried 

out with an inter-pulse period (IPP) of 1 ms and pulse width of 1 km range resolution. After a quick

analysis of the meteor trails of the received data, the first results of the new system look promising. 


Figure 2 shows In-Phase and Quadrature raw voltages of an underdense meteor trail. Clearly present in 

the signal is the attenuation or classical exponential decay of these type of reflections. 

Figure 2. In-Phase and Quadrature raw voltages an underdense meteor trail detected on May 5, 2010.

4 Summary 

We have presented an overview of the implementation of a new meteor system based on open source 

hardware and software tools. This system will be used by Communication and Space Sciences 

Laboratory at Penn State University to conduct meteor research. The acquisition system enables the 

operation of the radar with bandwidths approaching 10 MHz and data throughput greater than 30 MB/s. 

The system is flexible and is easily reconfigurable, allowing the user to implement newer ionospheric 

experiments. We will make our software radar control programs available freely through the Open 

Source software development web site of SourceForge at: [http://sourceforge.net]. 

Acknowledgements 

This work is supported by the National Science Foundation under grants: ATM-0638624 and ATM0457156 to Penn State University. 

References 

Binstock, A.,The producer/consumer threading model. 

[http://www.intel.com/cd/ids/ developer/asmo-na/eng/columns/performance/52523.htm]. 

Ceplecha, Z., J. Borovicka,W. G. Elford, D. O. Revelle, R. L. Hawkes, V. Porubcan, and M. Simek, Meteor phenomena and 

bodies, Space Science Reviews, 84, 327471, 1998. 

Cziczo, D. J., D. S. Thomson, and D. M. Murphy, Ablation, flux, and atmospheric implications of meteors inferred from 

stratospheric aerosol, Science, 291, 17721775, 2001. 

Fowler, M. UML Distilled Third Edition. Pearson Education, Inc., 2004. 

Janches, D., J. D. Mathews, D. D. Meisel, and Q. H. Zhou, Micrometeor Observa¬tions Using the Arecibo 430 MHz Radar, 

Icarus, 145, 5363, 2000b. 


Kelly, M. C., and L. J. Gelinas, Gradient drift instabililty in midlatitude sporadic E layers: localization of physical and 

wavenumber space, Geophysical Research Letters, 27, 457, 2000. 

Liu, A. Z., W. K. Hocking, S. J. Franke, and T. Thayaparan, Comparison of Na lidar and meteor radar wind measurements at 

Starfire Optical Range, NM, USA, Journal of Atmospheric and Terrestrial Physics, 64, 3140, 2002. 

Mathews, J. D., D. Janches, D. D. Meisel, and Q.-H. Zhou, The micrometeoroid mass flux into the upper atmosphere: 

Arecibo results and a comparison with prior estimates, Geophys. Res. Lett., 28, 1929, 2001. 

Mitola, J. III Software Radio Architecture: Object Oriented Approaches to Wireless Systems Engineering, John Wiley and 

Sons Inc., 2000. 

McNeil,W. J., E. Murad, and A. J. M. C. Plane, Models of Meteoric Metals in the Atmosphere, pp.265, Meteors in the Earths 

atmosphere. Edited by Edmond Murad and Iwan P. Williams. Publisher: Cambridge, UK: Cambridge University Press, 

2002., p.265, 2002. 

Pellinen-Wannberg, A., E.Murad, B. Gustavsson, U. Brandstrom, C. Enell, C. Roth, 

I. P. Williams, and A. Steen, Optical observations of water in Leonid meteor trails, Geophys. Res. Lett., 31, 3812, 2004. 

Plane, J. M. C., A time-resolved model of the mesospheric Na layer: constraints on the meteor input function, Atmospheric 

Chemistry and Physics, 4, 627638, 2004. 

Rapp, M., F. Lubken, P. Hoffmann, R. Latteck, G. Baumgarten, and T. A. Blix, PMSE dependence on aerosol charge number 

density and aerosol size, Journal of Geophysical Research (Atmospheres), 108,81, 2003. 

Reed, J. H., Software Radio A Modern Approach to Radio Engineering, Prentice Hall Communications Engineering and 

Emerging Technologies Series, 2002. 

Robbins, D., Common threads: Advanced filesystem implementors guide, part 3. 

[http:// www-128.ibm.com/developerworks/library/l-fs3.html]. 

Seal, R., J. Urbina, M. Sulzer, S. Gonzalez, N. Aponte, Design of an FPGA-based radar controller, National Radio Science 

Meeting, Boulder, CO, January 3-6, 2008. 

Seal, R., A new generation of meteor radar systems, MS thesis, Penn State University, University Park, PA, 16802, 2010. 

Se	lam, S., J. S.^
], and P._	""	<, Automatic i/o scheduler selection for latency and bandwidth optimization, 4th Inter

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Taylor, A.D., The Harvard Radio Meteor Project meteor velocity distribution reap-praised, Icarus, 116, 205-209,1995. 


Maximizing the Performance of Automated Low Cost All-sky Cameras 

F. Bettonvil1

Abstract Thanks to the wide spread of digital camera technology in the consumer market, a steady increase in the number of active All-sky camera has be noticed European wide. In this paper I look into 

the details of such All-sky systems and try to optimize the performance in terms of accuracy of the astrometry, the velocity determination and photometry. Having autonomous operation in mind, suggestions are done for the optimal low cost All-sky camera. 

Keywords all-sky · meteor camera · performance 

1 Introduction 

Since the 1960s and 1970s automated networks of meteor cameras have been in use to collect data on 

fireballs and recover meteorites. Well known are the Prairie Network (United States), the Meteorite Observation and Recovery Program MORP (Canada) and the European Network (former Eastern Europe), 

being examples of professional projects from that time. The European Network is still in operation nowadays [Spurný 2010, Flohrer 2006] and also other networks arose both on professional level (e.g. 

ASGARD in Canada [Brown 2010]; DFN in Australia [Bland 2008]) as well as amateur networks like 

the Polish Fireball Network [Olech 2006], and many others. Building and operating fireball patrol stations have always been well in reach for amateurs. Nowadays, with digital recording methods being 

used everywhere, this is true even more. Much digital imaging is done with sensitive (intensified) video 

cameras; in this paper on the contrary I will look into DSLR cameras with fisheye lens, because of their 

much higher resolution (10 Mpixel and more, compared to ~600x800 for standard video techniques) and 

which could be purchased for just under 1000EUR. I aim in this paper at an autonomously working station, which is easy to built and easy in use. Details of the setup are given in Table 1. 

With the above as baseline, the goal we try to achieve is: (1) Accurate astrometry (error in semi 

major axis 9a < 0.01AU) [Vaubaillon 2007], (2) Accurate velocity determination (idem), (3) Proper 

photometry (for mass estimates and trail density distributions, but no requirement defined). 

Table 1. Evaluated hardware setup

Camera Canon EOS 350D (6 Mpxl) 

Lens Full frame Sigma 4.5mm F/2.8 fisheye 

Exposure control Canon TC80N3 timer controller; twilight switch. No PC 

Timing GPS/DCF clock for time reference marks in star trails 

Chopper LC-TEC optical shutter (modulation freq. 10-100 Hz) 

 

F. Bettonvil ( ) 

Astronomical Institute, Utrecht University, Princetonplein 5, NL-3584 CC Utrecht, The Netherlands. E-mail: F.C.M.Bettonvil@astro.uu.nl 


2 Astrometry 

One camera pixel equals on average ~5’ and the plate reduction error of the combination camera-lens 

turns out to be of the same order [Bettonvil 2006]. When assuming that the error in radiant position 

caused by astrometry is of the same amount, we can calculate the effect on the orbital elements, which is 

illustrated in Table 2 for an asteroidal fireball (being an example of the type of fireballs that is of most 

interest for meteorite recovery). It shows that the error in the semi major axis is just within our goal2. 

Table 2. Effect of errors (respectively in radiant position (error A) and velocity (error B)) on the orbital elements for 

an I-Aquarid [Bettonvil 2006].

Radiant 

Radiant Observed Geocentr. Heliocentric Error A Error B 

R.A. [] 342,959 343,201 D0,100 - 

Decl [] -05,281 -07,367 D0,100 - 

Heliocn. Longitude [] 288,647 - - 

Heliocent. Latitude [] -0,179 - - 

Velocity [km/s] 32,292 30,183 34,967 - D0,096 

Orbital elements 

Longitude of ascending node [] () 322,528 D0,339 D0,024 

Inclination [] (i) 0,322 D0,161 D0.019 

Argument of perihelion [] () 131,029 D0,432 D0,057 

Semi major axis [AU] (a) 1,6758 D0,0095 D0,0135 

Perihelion distance [AU] (q) 0,2415 D0,0012 D0,0011 

Aphelion distance [AU] (Q) 3,1102 D0,0178 D0,0282 

Eccentricity [AU] (e) 0,8559 D0.0001 D0,0018 

For automated operation a window cover is required however, which either could be a hemispherical acrylic dome or watchmaker’s glass (Figure 1 left). Although the first seems preferred due to 

the (insensitive) perpendicular penetration of the light beam, performance was measured too be bad due 

to local irregularities (Figure 1 right). A watchmaker’s glass appears to be fine. 

Figure 1. (left) Watchmaker’s glass; (right) measured difference in star position between an acrylic dome and 

watchmaker’s glass for several stars in azimuthal direction. The measurement resolution was 1 camera pixel. The 

single high outlier for the acrylic dome is real. 

 

2Also the other orbital elements are affected by a change in radiant position, and even , which is due to the ecliptical origin 

of the investigated meteor. 


3 Velocity Determination 

For measurement of the velocity, I chose not to use a conventional rotating chopper in front of the lens, 

but instead a liquid crystal shutter (LC-TEC 2010), mounted between lens and camera [Bettonvil 2007b, 

2010]. Advantage is that the chopper frequency can be more accurate (crystal operation, no rotating 

parts, no wind influence). Optical ray tracing and measurements showed that no significant aberrations 

occur [Bettonvil 2010]. 

Instead of direct measurement of the chopper breaks, frequency analysis with FFT is used, 

which, after doing simulations and tests, gave velocity errors of 0.2-0.5%, 3-5 times better than conventional choppers [Bettonvil 2008]. A 0.3% velocity error (Table 2, error B) is required to stay within our 

requirements for the error in semi major axis (9a < 0.01AU). 

4 Photometry 

DSLR camera’s, when read out in RAW mode, allow up to 10-15 bit dynamical range, much more than 

video camera’s (7-8 bit). Nevertheless, because in photography exposures are being integrated over a 

(much) longer time, the noise and dark level easily go up to unacceptable levels, reducing the effective 

dynamical range. Dark level and noise is mitigated by: (a) subtraction of 2 successive images; (b) the 

use of low camera sensitivity (i.e. ISO setting); (c) short exposure times. Sensor cooling with Peltier 

elements is a very effective method [Bettonvil 2007a], but disregarded here, due to its complexity. 

 Saturation of fireballs is also to be avoided, which is the second reason for choosing low sensitivity. Figure 2 (left) shows the relation between ISO setting and brightness for fireballs and stars. It 

confirms that ISO 100 (is lowest value, resulting in noise counts of ~100) is preferred for allocating sufficient dynamical range for bright fireballs (~mv = -12). The sensitivity for stars is of course low then 

(+2), which affects the number of reference stars for astrometry. It is solved by combining multiple exposures. Figure 2 (right) shows the measured linearity of the camera as derived from stars. It shows nonlinearity in the order of 0.1mag. 

Figure 2. (left) Faintest detectable stars and meteors, as derived from the noise level, and brightest detectable stars 

and meteors before saturation occurs, as function of ISO speed; (right) linearity of the camera response for stars.


For cometary fireballs [Jenniskens 2006], with v = 25 km/s and at 100 km distance, we can write 

for the relation between mass M and brightness mv: 

 (1) dM

dmv

abs 
 0.92@100.9330.4mv

A photometry error of 0.1 mag results then in a ~10% error in the estimate of the mass of the meteoroid, 

which seems acceptable. 

5 Conclusions 

It seems that useful astrometry, velocity determination and photometry, of bright fireballs can be done 

with a DSLR camera with full frame fisheye lens. Part of the camera is an optical Liquid Crystal shutter. 

Operation with very low sensitivity (ISO100) as well as short exposure times is recommended to maximize dynamic range and avoid saturation. 

366

References 

Bettonvil F (2010) Digital All-sky cameras V: Liquid Crystal Optical Shutters. In: Proceedings of the International Meteor 

Conference 2009. International Meteor Organization, Hove. in print 

Bettonvil F (2008) Determination of the velocity of meteors based on sinodial modulation and frequency analysis. Earth, 

Moon and Planets 102, pp 205-208. 

Bettonvil F (2007b) Digital All-sky cameras III: A new method for velocity determination. In: Bettonvil F, Kac J (eds) Proceedings of the International Meteor Conference 2006. International Meteor Organization, Hove, pp 138-141 

Bettonvil F (2007a) Digital All-sky cameras II: Effect of Peltier cooling on fixed pattern noise. In: Bettonvil F, Kac J (eds) 

Proceedings of the International Meteor Conference 2006. International Meteor Organization, Hove, pp 134-137 

Bettonvil F (2006) Orbit Calculation of the August 15, 2002 Fireball over the Netherlands. In: Bastiaens L, Verbert J, Wislez 

J, Verbeeck C (eds) Proceedings of the International Meteor Conference 2005. International Meteor Organization, Hove, 

pp 171-178 

Brown P, Weryk R, Kohut S, Edwards W, Krzeminski Z (2010). WGN. pp. 25-30. 

Bland P, Spurný P, Shrbený L, Borovika J, Bevan A, Towner M, McClafferty T, Vaughan D, Deacon G (2008). Asteroids, 

Comets, Meteors 2008. LPI Contribution No. 1405 paper id. 8246 

Flohrer J, Oberst J, Heinlein D, Grau T, Spurný P (2006) European Planetary Science Congress 2006. Berlin. pp 518 

LC-TEC (2010) http://www.lctecdisplays.com, LC-TEC Displays AB, Tunvgen 281, 781 73 Borlänge, Sweden 

Olech A, Zoladek P, Wisniewski M, Krasnowski M, Kwinta M, Fajfer T, Fietkiewicz K, Dorosz D, Kowalski L, Olejnik J, 

Mularczyk K, Zloczewski K. (2006) In: Bastiaens L, Verbert J, Wislez J, Verbeeck C (eds) Proceedings of the International Meteor Conference 2005. International Meteor Organization, Hove, pp 53-62 

Jenniskens P (2006) Meteor Showers and Their Parent Comets. Cambridge University Press, Cambridge. pp 802 

Spurný P, Borovika J, Shrbený L (2007) Near Earth Objects, our Celestial Neighbors: Opportunity and Risk. In: Valsecchi 

G, Vokrouhlický D, Milani A (eds) Proceedings of IAU Symposium 236. Cambridge University Press, pp 121-130 

Vaubaillon J (2007) priv. comm. 

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