SMITHSONIAN

CONTRIBUTIONS

to

ASTROPHYSICS

VOLUME 3

SMITHSONIAN

INSTITUTION

WASHINGTON

D.C.

Contents of Volume 3

No. 1. The Regression of the Node of the Quadrantids,hj Gerald

S. Hawkins and Richard B. Southworth. Pages 1-5.

Published October 1, 1958.

No. 2. Catalogs of Meteor Radiants, by Gerald S. Hawkins.

Pages 7-8. Published September 26, 1958.

No. 3. Papers on the Solar Constant. Pages 9-24. Published

December 24, 1958. The Constancy of the Solar

Constant, by Theodore E. Sterne and Nannielou

Dieter (pages 9-12); On Sterne and Dieter's Paper,

"The Constancy of the Solar Constant," by C. G.

Abbot (pages 13-21); The Solar Constant, by L. B.

Aldrich and W. H. Hoover (pages 23-24).

No. 4. Some Stmspot and Flare Statistics, by Barbara Bell and

Harold Glazer. Pages 25-38. Published May 18,

1959.

No. 5. The Doppler Widths of Solar Absorption Lines, by

Barbara Bell and Alan Meltzer. Pages 39-46. Published May 13, 1959.

No. 6. A Fluid-Dynamic Mechanism of Meteorite Pitting, by

David T. Williams. Pages 47-67. Published August

12, 1959.

No. 7. Periodic Orbits of a Planetoid Passing Close to Two

Gravitating Masses, by Robert R. Newton. Pages

69-78. Published August 4, 1959.

No. 8. Meteor Trains, by Robert F. Hughes. Pages 79-94. Published September 21, 1959.

No. 9. Geodetic Uses of Artificial Satellites, by George Veis.

Pages 95-161. Published June 24, I960.

Smithsonian

Contributions to Astrophysics

VOLUME 3, NUMBER 1

THE REGRESSION OF THE NODE

OF THE QUADRANTIDS

by GERALD S. HAWKINS AND RICHARD B. SOUTHWORTH

SMITHSONIAN INSTITUTION

Washington, D. C.

1958
Publications of the Astrophysical Observatory

This series, Smithsonian Contributions to Astrophysics, was inaugurated

in 1956 to provide a proper communication for the results of research conducted at the Astrophysical Observatory of the Smithsonian Institution.

Its purpose is the "increase and diffusion of knowledge" in the field of

astrophysics, with particular emphasis on problems of the sun, the earth,

and the solar system. Its pages are open to a limited number of papers by

other investigators with whom we have common interests.

Another series is Annals of the Astrophysical Observatory. It was started

in 1900 by the Observatory's first director, Samuel P. Langley, and has been

published about every 10 years since that date. These quarto volumes, some

of which are still available, record the history of the Observatory's researches

and activities.

Many technical papers and volumes emanating from the Astrophysical

Observatory have appeared in the Smithsonian Miscellaneous Collections.

Among these are Smithsonian Physical Tables, Smithsonian Meteorological

Tables, and World Weather Records.

Additional information concerning these publications may be secured

from the Editorial and Publications Division, Smithsonian Institution,

Washington, D. C.

FEED L. "WHIPPLE, Director,

Astrophysical Observatory,

Smithsonian Institution.

Cambridge, Mass.

For sale by the Superintendent of Documents, U. S. Government Printing Office

Washington 25, D. O. - Price 15 cents
THE REGRESSION OF THE NODE

OF THE QUADRANTIDS1

By GERALD S. HAWKINS

 2 AND RICHARD B. SOUTHWORTH

Between January 2 and 4 each year the earth

passes through the Quadrantid meteor stream,

a shower comparable in intensity to the

Perseids of August and the Geminids of

December. The radiant is located in the

obsolete constellation of Quadrans Muralis,

from which the stream takes its name, which is

a position close to the junction of the modern

constellations Draco, Hercules, and Bootes.

Unlike the Perseids and Geminids, the Quadrantid stream is of short duration and most of

the activity is confined to a period of 24 hours.

The exact time of maximum of the shower

defines the point at which the orbit of the

stream intersects the orbit of the earth, or, in

the case of the Quadrantids, the descending

node of the stream.

The Quadrantids move in a direct orbit of

high inclination so that we would expect

perturbations by the planets to cause a slow

regression of the node. Thus the regression of

the node is also of interest from the point of

view of celestial mechanics. Visual observations have been made on the shower over the

past 100 years, but these are necessarily sparse

because of its short duration and because of the

winter weather conditions at the time of maximum. In 1953 the Super-Schmidt cameras of

the Harvard Meteor Project made photographic

observations on this stream. Kadar observations, which of course are independent of cloud,

daylight, and other adverse seeing conditions,

are also available on a continuous basis since

1950. In this paper we present the best

material available for determining the time of

maximum of the Quadrantid shower and its

changes through the years 1835 to 1954.

Table 1 contains recent determinations of

the time of maximum activity and of the

duration of the Quadrantid shower. The

position of the earth in its orbit is used to

measure the times of maximum in order to have

a fixed scale. This position is designated by

the angle, measured at the sun, between the

earth and the vernal equinox of 1950, i. e., the

heliocentric longitude of the earth referred to

the equinox of 1950. At this season the

earth moves l?02 in longitude per day.

Only since 1921 have the visual Quadrantid

observations been sufficiently homogeneous to

permit grouping data from different sources to

construct a curve of shower activity. Prentice

(1940) has published the results of the principal

meteor watches carried out by the British

Astronomical Association in the first week of

January each year from 1921 to 1940. He has

graphed the hourly rate, that is, the number of

Quadrantids visible in one hour to a single

visual observer in clear weather, as a function

of the orbital position of the earth, and has

obtained a well defined point of maximum.

In this paper, we have corrected Prentice's

data according to the following precept. Other

things being equal, the number of meteors of

one stream that strike the atmosphere above a

given area on the earth will be very nearly

proportional to the sine of the angular elevation

of the radiant point above the horizon. The

position of the Quadrantid radiant is known

within at most five degrees, and its angular

elevation is readily computed for any time and

place of observation. Observed rates have

thus been corrected to the rate which would

have been observed had the radiant been in the

1

 Research supported jointly by the Army, Nary, and Air Force, under contract with the Massachusetts Institute of Technology.

•Harvard College Observatory andjBoston University.

• Harvard College Observatory.

487416—68
SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 3

TABLE 1.—Maximum and duration of Quadrantid shower

Year

1921-40

1951

1950-52

1953

1954

Method of observation

Visual

Radar

Radar

Radar

Photographic

Source

Prentice (1940)

Millman and McKinley (1953)

Hawkins and Almond (1952)

Bullough (1954)

This paper

Earth 8 longitude

at maximum

(Equinox 1950)

1O2?92

102. 74

102. 60

102. 66

102. 52

Duration*

0?56

0. 14

1.3

1.0

<1.0

•Length of time (measured by sun's longitude) that hourly rate of shower was more than half the maximum hourly rate.

zenith, but all other circumstances unchanged.

This corrected rate is a more reliable measure

of the activity of the shower, while the uncertainties of the correction itself, though not

trivial, can hardly affect this investigation.

Prentice's results, corrected as described, are

shown in figure 1.

The second author has determined the time

of photographic maximum of the 1954 shower

from records obtained with the Baker SuperSchmidt cameras in New Mexico. A maximum

hourly rate of 13 meteors, photographed by at

least one of the cameras, occurred between 0330

and 0530 Mountain Standard Time on Jan. 3,

1954. The hourly rate was less than one on

the preceding and following nights. The variation in rate during the early morning of

January 3 does not differ significantly from the

variation that would be predicted by the

change in elevation of the radiant alone. A

photographic rate of 13 with these cameras

corresponds to a visual rate of approximately

26. The photographic data appear in table 1

with an assumed duration of one day at onehalf or more of maximum hourly rate. Fisher

(1930) has published a complete summary of

the published Quadrantid observations prior to

1927. Table 2 contains all observations in

his list (except those also included in Prentice's

analysis) which yield a corrected rate of at

least 20 Quadrantids per hour for a time

recorded with an uncertainty of two hours or

less. These observations are not direct measures of the time of maximum activity of the

Quadrantid shower. The rates are very high

compared with those in figure 1, however, and

TABLE 2.—Hourly rates of Quadrantids*

Earth's longiYear

1859

1863

1864

1864

1872

1873

1878

1879

1880

1880

1894

1897

1903

1903

1904

1908

1908

1909

1922

Date

January 2

2

2

3

2

2

2

2

2

3

2

2

3

4

4

3

4

3

3

GCT

22*5

23.6

23.

0.7

23.6

6.

4.2

6.4

20.

0.5

19.2

5.2

20.2

2.8

5.2

17.2

16.7

5.4

6.7

Observed

rate

~ 6 0

48

50-60

60?

21

37

34

> 4 2

11

6

40

64

8.5

60?

> 2 0

6.8

12.6

180

40-50

Corrected

rate

~260

48

192-231

130?

70

41

44

> 4 4

61

~ 6 0

160

85

42

98?

> 2 4

28

52

210

57V71

tude (Equi

1950)

103?35

102. 86

103. 09

103. 16

103. 05

103. 07

102. 57

102. 54

102. 85

103. 04

103. 26

102. 66

102. 96

103. 24

103. 09

102. 55

103. 54

102.80

103. 03

•When the hourly rate WBS less than 20, the observations are not included.
NO. 1 QUADRANTID NODAL REGRESSION

120

• 1921,1923-40

61922

>.4O

I

3Q -

20 -

10 -

^

-

—V ""*

1

• *

i \

*+ Duratio yn

1 1 1

}

\

1

1

1

" -

O

\

I

t

\

\

^ -

-

-

ior.5

102°.0 102°.5 103°.0

Earth's Longitude (Equinox 1950)

103°.5

FIGURE 1.—Corrected visual hourly rate of the Quadrantid meteor stream, plotted against the longitude

of the earth at time of observation.

in view of the measures of duration in table 1,

it is clear that these rates were observed at

times not more than a few hours distant from

the time of maximum.

The earliest observations that can be identified with some confidence as referring to the

Quadrantid shower appear in table 3. Most

of them report only that an uncommon number

of meteors was seen at a particular place on a

particular night. In order to analyze these

observations, it has been necessary to assume

a specific time of night. South of 55° north

latitude, the Quadrantid radiant rises very

little above the horizon until after midnight

and does not reach maximum elevation until

after dawn; consequently most Quadrantids

are seen after midnight. For this reason,

3 a. m. local time has been assumed, except

for Bossekop at 70° north latitude where the

radiant elevation varies relatively little, and

except where the time is more specifically

reported. Some of these observations are

published in several places; the authority cited

is the one on whom most reliance is placed.

The double entry for the year 1835 represents

divergent reports of the same observation.

Figure 2 plots the measures of the epoch of

maximum Quadrantid activity in tables 1 to 3

against the year of observation. Data from

table 1 appear as crosses, from table 2 as solid

circles, and from table 3 as open circles. The

graph clearly shows a downward trend: the

straight line drawn through the points corresponds to a mean regression of the node of
SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 3

104'

103*

1

O

-

_

1

1

o

1

1

* •

\

1

1 1

O WtfiO •> Umwal Utter Fnqmriej

CtmcM How* RttN!

0 151-260 Ptr H«r

4) 101-150 fw Hev

• 81-100 Ptf How

• ZtMOPtrmw

X 0«*mln«Bont tfTTm. ot Htfmtm

*

1 I

) 1

-

i i

1820 1860 1880 1900

Year of Observation

1920 1940 1980

FIGURE 2.—The earth's longitude corresponding to the maximum of the Quadrantid meteor stream,

as observed in various years.

0?006 per year. Recent observations of the

Quadrantids in 1956 (Hines and Vogan, 1957)

are consistent with this conclusion.

Certain observations of the Quadrantid

shower show that in particular years, and

perhaps in particular places, the maximum

hourly rate is much greater than the normal

maximum rate. In figure 1, Prentice's data for

1922 clearly exhibit this phenomenon. In

some cases these unusually high rates occur

for only a few hours; at Jodrell Bank the

maximum rate in 1953 was approximately

three times the maxima seen in 1950 to 1952,

and apparently, as also in figure 1, only the

peak of the frequency curve was much higher

than normal. In such an event the duration,

when measured between the times at which

the rate was one-half of the maximum rate, is

TABLE 3.—Nights of unusually high meteor frequency

Year

1835*

1838

1839

1840

1841*

Date

Jan. 2-3 after midnight

[Jan. 1-2 4 a. m. to dawn

Jan. 2-3 after midnight

Jan. 2-3

Jan. 2-3 towards morn.

Jan. 2-3 or 3-4

1848 Jan. 2-3

1848 Jan. 2-3

1857 Jan. 2-3

•Entry omitted In figure 2.

Place observed

Mornez, Switzerland

Mornez, Switzerland

Near Geneva, Switzerland

Bossekop, Norway

Ghent, Belgium

Switzerland?

Parma, ItalyAachen, Germany

England?

Assumed

local

time

5*4

3

h

24*

Earth's

longitude

{equinox

1950)

103?68

102. 76

103. 92

103. 48

103. 41

104. 15

or 105.17

103. 33

103. 34

104.06

Authority

Wartmann (1841)

Fisher (1930)

Wartmann (1841)

Fisher (1930)

Quetelet (1861)

Fisher (1930)

Fisher (1930)

Fisher (1930)

Fisher (1930)
NO. 1 QUADRANTID NODAL REGRESSION

shorter. Millman and McKinley (1953) have

suggested that the short duration observed

in 1951 was probably due to a similar abnormal

concentration. Their actual maximum hourly

rate cannot be compared with visual rates,

however, without a detailed determination of

the sensitivity of their equipment.

Almost all of the visual hourly rates in table 2

exceed the maximum, 38 Quadrantids per hour,

of the curve of activity drawn in figure 1.

Since low hourly rates do not indicate the time

ot maximum of the shower, they have been

omitted from table 2 and figure 2; nonetheless

the average of all Quadrantid corrected rates

reported before 1921 (Fisher, 1930) is 52 meteors

per hour. No significant correlation with

year of observation is to be found in these reported rates; they do not tend to decrease from

1859 to 1920. In the absence of any regular

program of observation, the appearance of few

or no Quadrantids is unlikely to have been

reported. The evidence, therefore, does not

support an hypothesis of decreased average

Quadrantid activity, and the visual rates before

1921 probably refer principally to years of uncommon activity. Also most of the observations in table 3 probably represent uncommon

years, since a normal maximum rate of approximately 40 per hour would not have appeared

remarkable in an era when the Leonids had

displayed 500 per hour, and the Perseids were

showing 150 per hour.

Years of unusual Quadrantid activity represent, on the simplest hypothesis, condensations

or regions of unusually high density in the

otherwise nearly uniform distribution of meteors

along the orbit of the Quadrantid stream. The

observations do not determine how exactly

these condensations follow the same orbit as

the continuous stream, but no significant deviation has been seen. In particular, the 1922

measures in figure 1 do not indicate such a

deviation, since the difference in longitude between the highest 1922 measure and the peak

of the curve is almost exactly the regression of

the node in the nine years between 1922 and

the mean date, 1931, of the other measures in

the figure. It is concluded that the node of

the observed portion of the Quadrantid meteor

stream has regressed steadily since its discovery, at the rate of 0?6 per century, and that

there are isolated streams of meteors embedded

in the continuous stream.

References

BULLOUGH, K.

1954. Jodrell Bank Annals, vol. 1, p. 68.

FISHER, W. J.

1930. Harvard Coll. Obs. Circ, No. 346.

HAWKINS, G. S., and ALMOND, M.

1952. Monthly Notices Roy. Astron. Soc. London,

vol. 112, p. 219.

HlNES, C. O. AND VOGAN, E. L.

1957. Can. Journ. Phys., vol. 35, p. 703.

MILLMAN, P. M., AND MCKINLET, D. W. R.

1953. Journ. Roy. Astron. Soc. Canada, vol. 47,

p. 237.

PBENTICB, J. P. M.

1940. Journ. Brit. Astron. Assoc, vol. 51, p. 19.

QtTETELET, A.

1861. Physique du Globe, Brussels, pp. 290-312.

WABTMANN, L. F.

1841. Bull. Acad. Roy. Bruxelles, vol. 8, p. 226.

Abstract

Observations of the longitude of the descending node of the Quadrantid meteor stream from 1838 to 1954 are

assembled and discussed. It is concluded that the majority of the older observations were made in years of unusually

high activity. The descending node of the observed stream has regressed 0!6 per century.