NASA/TP-2010-216129 

Michigan Orbit

Observations of

Debris Environ

Observing Years: 2

K. J. Abercromby1

, P. Seitzer2, E

1

ESC Group/Jacobs 

Houston 77058 

2

University of Michigan 

Department of Astronomy 

Ann Arbor, Mich. 48109-1042 

3

NASA Johnson Space Center 

Houston 77058 

August 2010

National Aeronautics and 

Space Administration 

Johnson Space Center 

Houston, TX 77058 

tal DEbris Survey Tele

f the Geosynchronous O

nment 

2004–2006

E. S. Barker3, H. M. Cowardin1, and M. J. Matne

escope 

Orbital 

ey

3 
THE NASA STI PROGRAM OFFICE . . . IN PROFILE 

Since its founding, NASA has been dedicated 

to the advancement of aeronautics and space 

science. The NASA Scientific and Technical 

Information (STI) Program Office plays a key 

part in helping NASA maintain this important 

role. 

The NASA STI Program Office is operated by 

Langley Research Center, the lead center for 

NASA’s scientific and technical information. 

The NASA STI Program Office provides access 

to the NASA STI Database, the largest 

collection of aeronautical and space science 

STI in the world. The Program Office is also 

NASA’s institutional mechanism for 

disseminating the results of its research and 

development activities. These results are 

published by NASA in the NASA STI Report 

Series, which includes the following report 

types: 

• TECHNICAL PUBLICATION. Reports of 

completed research or a major significant 

phase of research that present the results 

of NASA programs and include extensive 

data or theoretical analysis. Includes 

compilations of significant scientific and 

technical data and information deemed to 

be of continuing reference value. NASA’s 

counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and 

extent of graphic presentations. 

• TECHNICAL MEMORANDUM. Scientific 

and technical findings that are 

preliminary or of specialized interest, eg, 

quick release reports, working papers, 

and bibliographies that contain minimal 

annotation. Does not contain extensive 

analysis. 

• CONTRACTOR REPORT. Scientific and 

technical findings by NASA-sponsored 

contractors and grantees. 

• CONFERENCE PUBLICATION. Collected 

papers from scientific and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by 

NASA. 

• SPECIAL PUBLICATION. Scientific, 

technical, or historical information from 

NASA programs, projects, and mission, 

often concerned with subjects having 

substantial public interest. 

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific 

and technical material pertinent to 

NASA’s mission. 

Specialized services that complement the STI 

Program Office’s diverse offerings include 

creating custom thesauri, building 

customized databases, organizing and 

publishing research results . . . even providing 

videos. 

For more information about the NASA STI 

Program Office, see the following: 

• Access the NASA STI Program Home Page 

at http://www.sti.nasa.gov 

• E-mail your question via the Internet to 

help@sti.nasa.gov 

• Fax your question to the NASA Access 

Help Desk at (301) 621-0134 

• Telephone the NASA Access Help Desk at 

(301) 621-0390 

• Write to: 

 NASA Access Help Desk 

 NASA Center for AeroSpace Information 

 7115 Standard 

 Hanover, MD 21076-1320 
NASA/TP-2010-216129 

Michigan Orbit

Observations of

Debris Environ

Observing Years: 2

K. J. Abercromby1

, P. Seitzer2, E

1

ESC Group/Jacobs 

Houston 77058 

2

University of Michigan 

Department of Astronomy 

Ann Arbor, Mich. 48109-1042 

3

NASA Johnson Space Center 

Houston 77058 

August 2010

National Aeronautics and 

Space Administration 

Johnson Space Center 

Houston, TX 77058 

tal DEbris Survey Tele

f the Geosynchronous O

nment 

2004–2006

E. S. Barker

3

, H. M. Cowardin1, and M. J. Matne

escope 

Orbital 

ey

3 
Available from: 

NASA Center for AeroSpace Information National Technical Information Service 

7115 Standard Drive 5285 Port Royal Road 

Hanover, MD 21076-1320 Springfield, VA 22161 

301-621-0390 703-605-6000 

This report is also available in electronic form at http://ston.jsc.nasa.gov/collections/TRS/ 
i 

Contents

Executive Summary ............................................................................................................................. 1 

1.0 Introduction ................................................................................................................ 3 

2.0 Background ................................................................................................................ 3 

3.0 Observation Overview ............................................................................................... 3 

3.1 The MODEST System ............................................................................................... 3 

3.2 Search Strategy ..........................................................................................................4 

3.3 Data Collection ..........................................................................................................7 

3.4 Data Processing ..........................................................................................................8 

3.5 Data Analysis ............................................................................................................. 8 

3.5.1 Correlation of detections ............................................................................................ 9

3.5.2 Orbital elements calculation ...................................................................................... 9 

3.5.3 Comparison of derived orbital quantities with orbital parameters of 

known objects ............................................................................................................ 10 

3.5.3.1 Inclination .................................................................................................................. 11 

3.5.3.2 Mean Motion Determination...................................................................................... 15 

3.5.3.3 RAAN Determination ................................................................................................ 17

3.6 Summary of Data Processing ..................................................................................... 19 

4.0 Results ........................................................................................................................ 19 

4.1 Detection Rates ..........................................................................................................19 

4.2 Location of Field Centers and Detections .................................................................. 19 

4.3 Angular Momentum Vector ....................................................................................... 22 

4.4 No-sees....................................................................................................................... 25 

4.5 Mean Motion Distribution ......................................................................................... 25 

4.6 Inclination Distribution .............................................................................................. 26

4.7 RAAN Distribution .................................................................................................... 26 

4.8 Absolute Magnitude Distribution and Derived Diameters ........................................ 27 

4.9 RAAN vs. INC Distribution ...................................................................................... 28 

5.0 Conclusions ................................................................................................................ 29 

6.0 References .................................................................................................................. 30 

Appendix A: Fields File Example ................................................................................................... 32 

Appendix B: Output File Example .................................................................................................. 33 

Appendix C: Correlation Output ..................................................................................................... 34
ii

Figures

1 Absolute magnitude and derived size distribution, assuming an albedo of 0.175 

and a diffuse Lambertian phase function ................................................................................ 2 

2 The MODEST telescope ......................................................................................................... 4 

3 Inclination vs. launch date ...................................................................................................... 5 

4 A catalog object showing the date of observation vs. inclination. These data show 

the progression of INC over time, with the noise being bad data points ................................ 5 

5 RAAN vs. INC for near-GEO objects .................................................................................... 6 

6 Daily motion for GEO objects (RA vs. DEC) as viewed from CTIO, Chile .......................... 7 

7 Sample mosaic of nine frames of MODEST data. The object (seen as a point) appears 

in the middle of the left-hand side of the figure and traverses to the upper right corner. 

This image is the width (RA) of the FOV but only one-fourth of the height (DEC). 

Streaks in this image are stars ................................................................................................. 8 

8 Geometry for computing orbital parameters ........................................................................... 11 

9 INC comparison for correlated targets separated into functional (F) and 

nonfunctional (NF) categories. CY 2004 is on the left, CY 2005 is in the center, 

and CY 2006 is on the right .................................................................................................... 12 

10 INC comparison for correlated targets separated into functional (F) and 

nonfunctional (NF) categories, concise range ......................................................................... 13 

11 INC error as a function of INC, entire range .......................................................................... 14 

12 INC error as a function of INC, concise range ....................................................................... 14 

13 Comparison of inferred and known mean motion .................................................................. 15 

14 Comparison of inferred and known mean motion, concise range ........................................... 16 

15 Mean motion error vs. ACO mean motion. Solid lines are the slopes associated 

with the data ............................................................................................................................ 16 

16 Comparison of inferred and known RAAN ............................................................................ 17 

17 RAAN error as a function of INC (focus on larger errors) ..................................................... 18 

18 RAAN error as a function of INC (focus on smaller errors)................................................... 18 

19 Location of field centers ......................................................................................................... 20 

20 Probability of finding specific orbits based on field center locations during 2004–2006....... 21 

21 Possible population of UCTs and CTs based on statistical sampling ..................................... 21 

22 Angular momentum vector of an orbit .................................................................................... 22

23 Polar coordinates for objects, CY 2004 .................................................................................. 23 

24 Polar coordinates for objects, CY 2005 .................................................................................. 24 

25 Polar coordinates for objects, CY 2006 .................................................................................. 24 

26 Polar coordinates with probability and detections overlaid for all 2004–2006 data. 

The CTs are solid diamonds and the UCTs are open diamonds ............................................. 25 

27 Mean motion distribution for CT and UCT objects ................................................................ 26 

28 Distribution of INC for CTs and UCTs .................................................................................. 27 

29 Distribution of RAAN for CT and UCT. The location of the data found is 

biased by the field center selection and the DOY ................................................................... 27 

30 Absolute magnitude and derived size distribution, assuming an albedo of 0.175 and 

a diffuse Lambertian phase function ....................................................................................... 28

31 RAAN vs. INC for CT and UCT objects ................................................................................ 29 

32 RAAN vs. INC for CT and UCT data for all 3 years .............................................................. 29 
iii

Tables

1 Inclination Errors for CY 2004, CY 2005, and CY 2006 ....................................................... 12 

2 Mean Motion Errors ................................................................................................................ 15 

3 RAAN Errors .......................................................................................................................... 17 

4 Statistics Data Collection ........................................................................................................ 19 

 
iv

Acronyms

ACO assumed circular orbit 

CCD Charge-Coupled Device 

CDT CCD Debris Telescope 

CIS Commonwealth of Independent States 

CT correlated target 

CTIO Cerro Tololo Inter-American Observatory 

CY calendar year 

DEC declination 

DOY day of year 

F functional [used only in figure callouts] 

FOV field of view 

FWHM full width at half maximum 

GEO geosynchronous orbit 

GEODSS Ground-based Electro-Optical Deep Space Surveillance 

HA hour angle 

INC inclination 

JSC Johnson Space Center 

LST local sidereal time 

MODEST Michigan Orbital DEbris Survey Telescope 

NF nonfunctional [used only in figure callouts] 

OH oxygen-hydrogen-bond emission 

RA right ascension 

RAAN right ascension of ascending node 

RMS root mean square 

S/N signal to noise 

SATRAK satellite missile tracking program 

SGP Simplified General Perturbation code 

SSN Space Surveillance Network 

TDI time delay integration 

TLE two-line element 

UCT uncorrelated target 

UT universal time 
1

Executive Summary 

NASA uses the Michigan Orbital DEbris Survey Telescope (MODEST), the University of Michigan’s 

0.61-m aperture Curtis-Schmidt telescope at the Cerro Tololo Inter-American Observatory in Chile, to 

help characterize the debris environment in geosynchronous orbit; this usage began in February 2001 and 

continues to the present day. Detected objects that are found to be on the U.S. Space Surveillance Network 

cataloged objects list are termed correlated targets (CTs), while those not found on the list are called 

uncorrelated targets (UCTs). 

This Johnson Space Center report provides details of observational and data-reduction processes for the 

entire MODEST dataset acquired in calendar years (CYs) 2004, 2005, and 2006. Specifically, this report 

describes the collection and analysis of 42 nights of data collected in CY 2004, 23 nights of data collected 

in CY 2005, and 35 nights of data collected in CY 2006. 

MODEST is equipped with a 20482048-pixel charged coupled device camera with a 1.3 by 1.3 deg field 

of view. This system is capable of detecting 19th-magnitude objects using a 5-s integration that 

corresponds to a 10-cm diameter, 0.175-albedo object at 36,000 km altitude assuming a diffuse 

Lambertian phase function. The average number of detections each night over all 3 years was 18. On 

average in CY 2004, 72% of the detections were CTs and 27% were UCTs; in CY 2005, 74% of the 

detections were CTs and 26% were UCTs; and in 2006, 76% of the detections were CTs and 24% were 

UCTs. 

Estimates can be made from the correlated objects as to the errors associated with the derived quantities 

of range, inclination (INC), and right ascension of ascending node (RAAN) compared to the quantities 

determined using an assumed circular orbit. The average INC root mean square (RMS) error is 0.06 for 

functional CTs and 0.13 for nonfunctional CTs. Since RAAN is ill-defined at small values of INC, the 

RMS error for RAAN is calculated only for objects with an INC greater than 1. The average RAAN RMS 

error is 10 for functional objects and 6 for nonfunctional objects in CY 2004, 29 for functional objects 

and 8 for nonfunctional objects in CY 2005, and 14 for functional objects and 12 for nonfunctional 

objects in CY 2006. The mean motion error is 0.0014 for functional objects and 0.010 for nonfunctional 

objects in CY 2004, 0.0008 for functional objects and 0.0068 for nonfunctional objects in CY 2005, and 

0.0015 for functional CTs and 0.0096 for nonfunctional CTs in CY 2006. This error analysis of CT values 

for INC, RAAN, and mean motion lends credibility to the determination of the UCT orbital distributions. 

Figure 1 shows the size distribution of 2,589 objects detected in the data processed for CYs 2004, 2005, 

and 2006. The actual peak of the absolute magnitude distribution for the functional correlated targets is 

10th magnitude, whereas the peak was 11th magnitude in 2002–2003. An absolute magnitude of 11.5 corresponds to objects with average diameters of 4 m, assuming an albedo of 0.175 and a diffuse Lambertian 

phase function. This result generally agrees with the known sizes of intact satellites. The absolute magnitude 

distribution for the UCTs is broad but starts to roll off near 25 cm diameter or 17.5 magnitude. This roll 

off in the distribution reflects the detection capability of MODEST, not the true nature of the population. 

The true population is believed to continue at the same slope through fainter magnitudes. 
2

Figure 1. Absolute magnitude and derived size distribution, assuming an albedo of 0.175 and a 

diffuse Lambertian phase function. 

 
3

1.0 Introduction 

Orbital debris is a concern to all nations that use satellites or launch space vehicles. The debris field 

scattered near Earth’s geosynchronous orbit (GEO) poses a threat to anything residing in or passing 

through it. To mitigate risk and minimize this environment’s expansion, the debris environment must be 

understood. NASA uses the Michigan Orbital Debris Survey Telescope (MODEST), a University of 

Michigan-owned 0.61-m aperture Schmidt telescope at the Cerro Tololo Inter-American Observatory 

(CTIO) in Chile, to help characterize this environment in GEO. The objectives for this survey are to 

determine the extent and character of debris in GEO, specifically by obtaining distributions for the 

brightness, inclination (INC), right ascension of ascending node (RAAN), and mean motion for the 

debris. 

2.0 Background 

The GEO environment’s debris population has a high potential for collision with operational satellites due 

to the extremely long lifetimes of debris and satellites. Space-faring nations have been placing satellites 

into GEO since the mid- to late-1960s. Along with operational satellites, debris has been placed into 

GEO. This debris consists of dead satellites, rocket body upper stages, deployment hardware, small debris, 

etc. To date, two breakups have been reported in GEO. The first of these, the 1978 breakup of an EKRAN 

2 satellite, Space Surveillance Network (SSN) 10365, went unreported prior to its identification in 1992 

by the Commonwealth of Independent States (CIS).1

 In 1992, a Titan 3C Transtage breakup, SSN 3432,1,2

produced at least 20 pieces of debris. Ground-based Electro-Optical Deep Space Surveillance (GEODSS) 

telescopes tracked these objects for a few days after the event; all but eight pieces have been lost. 

NASA used the Charged-Coupled Device (CCD) Debris Telescope (CDT), a transportable 32-cm 

Schmidt telescope, to conduct initial GEO surveys. The CDT was shipped to the Hawaiian island of Maui 

for a survey of the GEO environment conducted by NASA from 1992 through 1994.3

 Results from the 

survey indicated that, to a limiting apparent magnitude of 17 (~60 cm in diameter), about 27% of all objects 

in GEO are debris. The actual debris population will be much larger due to the presence of objects smaller 

than 60 cm in diameter. NASA moved the CDT to Cloudcroft, NM, for further GEO studies, where data 

were collected from November 1997 to December 2001. Due to funding issues, the CDT was shut down 

in December 2001. 

The MODEST program benefited from the data collected by the CDT. The CDT determined the rate at 

which most GEO objects are traveling. 

3.0 Observation Overview 

3.1 The MODEST System 

The MODEST system uses the University of Michigan’s Curtis-Schmidt telescope located at the CTIO in 

Chile. Since February 2001, the telescope has been dedicated to optical studies of orbital debris for 

NASA’s Orbital Debris Program Office at the Johnson Space Center (JSC). 

The telescope is a 0.61-m aperture f/3.5 Schmidt of classical design, with a CCD mounted at a Newtonian 

focus. The CCD is a thinned, backside-illuminated device manufactured by SITe. The format is 2048

2048 pixels, each of which is 24 microns square. This provides a 2.318-arc-seconds/pixel sampling and a 

1.31.3-deg field of view (FOV). 
4

A 5-s exposure through a broad R filter centered at 630 nm and 200 nm wide (full width at half maximum 

[FWHM]) produces a signal-to-noise (S/N) = 10 on a point source detection of 18th R magnitude under 

typical dark sky conditions at Tololo. 

A picture of the MODEST telescope is shown in Figure 2. 

Figure 2. The MODEST telescope. 

3.2 Search Strategy

Numerous studies4,5 provide compelling arguments that most uncontrolled debris objects in GEO should 

be at INCs less than or equal to 15. Orbits of uncontrolled GEO objects oscillate around the stable 

Laplacian plane, which has an INC of 7.5 with respect to the equatorial plane. This oscillation is 

dominated by the combined effects of the Earth’s oblateness (J2 term) and solar and lunar perturbations. 

The INC oscillation period is about 50 years. During the first 25 years, an uncontrolled object with an 

initial INC of 0 will gradually increase in INC until its INC has peaked at 15. During the next 25 years, 

this same object’s INC will gradually decrease until it has returned to its original INC, in this case, 0, 

and it will begin its oscillation cycle again. Most uncontrolled objects with a different initial INC will 

follow the same 50-year pattern of increasing their INC to 15, decreasing to 0, and then returning to 

their original INC. (There are some cases in which the INC will first decrease to 0.) Depending on the 

insertion RAAN, an uncontrolled object’s oscillation can be out of phase with other objects, although 

these examples are few. 

Figure 3 shows the INC of objects in GEO plotted against their launch date. These data were taken from 

the element set file as of day 365, year 2003, and plots 2,884 objects. All objects plotted have mean motions of less than 1.1 revs/day. The oldest have already peaked in INC and are now approaching 0 INC 

again. Figure 4 shows one catalog object’s progression in INC over time. This object’s INC increased to 

15 and is on its way toward decreasing back to 0. There is also a strong correlation between an object’s 

INC and its RAAN, as illustrated in Figure 5. 
5

Figure 3. Inclination vs. launch date. 

Figure 4. A catalog object showing the date of observation vs. inclination. 

These data show the progression of INC over time, with the noise being bad data points. 
6

Figure 5. RAAN vs. INC for near-GEO objects. 

Figure 6 illustrates the daily motion for a set of objects having mean motions less than 1.1 revs/day and 

INCs less than 17. These data are for a given date and time in 2003. Since most orbital debris will be 

associated with operational satellites, searches need to be made above or below the equator at the appropriate times to maximize the detection rate of the debris. While there may be a few very interesting 

objects outside of this envelope, most debris will be found near or inside it. As a result of the systematic 

orientation of the orbital planes, objects with a given INC will be above (or below) the Earth’s equator at 

the same time. 

To date, the best way found to represent orbital debris magnitude variations as a function of phase angle 

is a Lambertian phase function, in which the maximum brightness is observed at the 0 phase angle.6

 To 

detect the smallest debris possible, it is best to observe them under nearly face-on (small phase angle) 

solar illumination. This condition is most closely reached for objects near the anti-solar point. Since 

Earth's shadow projected into space has a finite angular diameter, on the order of 17 at geosynchronous 

distances, it is impossible to meet the condition of exact face-on illumination (phase angle = 0). 

From MODEST’s location, orbital longitudes from 25°W to 135°W can be seen. Each night, MODEST 

observers determine a specific right ascension (RA) and declination (DEC) that is the closest to the antisolar point as possible without being in the Earth’s shadow. The telescope then stares at that location for 

the night. However, on nights near the equinoxes when the shadow overlaps the region of interest, two 

fields are observed by switching locations halfway through the night, with the first half of the night 

leading the shadow of the Earth and the second half of the night trailing the shadow. All telescope-pointing locations are determined prior to the start of the run. The location of the moon also plays a role as to 

when observations can occur. As a general rule, observations take place ±1 week around the new moon. 
7

Figure 6. Daily motion for GEO objects (RA vs. DEC) as viewed from CTIO, Chile. 

3.3 Data Collection 

The telescope tracks the RA and DEC at the sidereal rate. During the 5-s exposure, the charge on the 

CCD is shifted in reverse so that the objects are seen as a point source and the stars are seen as streaks. 

This mode is known as time delay integration (TDI). Thus, the system has peak sensitivity to objects with 

the expected motion of GEO objects. Objects orbiting the Earth can appear as streaks depending on their 

altitude and INC. 

The standard exposure time is 5 s with a total time between exposures of 37.9 s. An S/N of 10 corresponds 

to about an 18th-magnitude limit for one detection. The frame number, RA, DEC, instrumental magnitude, 

epoch, observation date, and universal time (UT) are calculated for each detection of each object. The instrumental magnitude is transformed to an R magnitude by observing standard Landolt stars. A broad R 

filter centered at 630 nm and with FWHM = 200 nm is used for observing. This passband maximizes the 

final S/N of faint objects by minimizing the signal from the night sky. It also minimizes the scattering of 

moonlight below 400 nm and OH emissions above 800 nm. Four independent detections are required to 

consider a source a real object. At the first detection, a computer program (debris finder) determines 

where the next detection should be for the object given a rate box movement of ±2 arc-second/second in 

hour angle (HA) and ±5 arc-second/second in DEC. For GEO objects, the total time spent in the FOV is 

generally 5 min. Figure 7 shows a mosaic of nine frames in a MODEST data set. The object can be seen 

traveling from the middle left to the upper right as time increases. 
8

Figure 7. Sample mosaic of nine frames of MODEST data. The object (seen as a point) 

appears in the middle of the left-hand side of the figure and traverses to the 

upper right corner. This image is the width (RA) of the FOV but only 

one-fourth of the height (DEC). The streaks in this image are stars. 

In addition to computer detection of objects, a manual review of one night is conducted every 4 months. 

The manual review consists of two people observing the frames collected in a given night and recording 

the frames in which objects are seen. These manual observations are then compared to the computer 

detections to make sure the computer code is catching all the objects it should. In all manual reviews to 

date, the computer has found 100% of the objects it should, so extreme confidence is established in the 

ability to find objects that fall within the rate box. 

3.4 Data Processing 

A real-time data reduction pipeline has been implemented at MODEST that performs the following steps: 

 Removes the instrumental signature on each image. This involves subtracting the bias over-scan 

from each amplifier section, subtracting a master bias to remove low-level bias structure, and 

dividing by a normalized flat field to remove pixel-to-pixel sensitivity variations. 

 Finds potential debris candidates, which are either point sources or short streaks (<10 pixels 

long). This debris finder is insensitive to the 32-pixel-long star streaks. 

At the end of the night, a frame-to-frame correlator is run on the candidate lists from all survey images. 

The output of this correlator is a list of all potential debris candidates that appear in four or more frames, 

along with their positions and magnitudes. It is assumed that real objects move linearly through subsequent 

frames. 

A nightly manual review is performed at the telescope of all candidates that have five or less detections. 

False positives (largely due to cosmic rays and the end of star streaks) are rejected by the operator. Experience has shown there are no false positives with six or more detections. 

3.5 Data Analysis 

This section describes the process of converting the lists of observations (date, UT, RA, DEC, and magnitude) from the position files into lists of cataloged objects, both correlated targets (CTs) and uncorrelated 

targets (UCTs), as well as their derivable orbital parameters. 
9

3.5.1 Correlation of detections 

Once the data are received by JSC, the correlation of detections is conducted. For each exposure, the day, 

year, UT, and the field center of the FOV are determined. Then, using an augmented version of the 

Simplified General Perturbation code (SGP), the satellite catalog is compared to the RA, DEC, and time 

of each exposure to determine whether an object might be in the FOV. An attempt to correlate all 

satellites within a 1 radius of the center of the FOV with any detected object is carried out. The results are 

then output to a file containing all information for all exposures within a given night. Appendix C lists a 

subset of the file. The program is written with a larger FOV than the true one so that, if any pointing 

errors arise, a possible correlation still can be obtained. 

To correlate an object that was predicted to be in the FOV with an object found in a specific frame, a missed 

distance is calculated. Missed distance is defined as the absolute value of the squared difference between 

the observed and the predicted RA and DEC positions. A nightly offset, calculated by taking the average 

value of the missed distance, is subtracted from the missed distance . Epoch dates (age of an element set) are 

known to impact the accuracy of where an object is predicted vs. where it is actually located on a given 

night. This missed distance is not expected to change dramatically as the accuracy of the catalog from yearto-year stays consistent. 

If the missed distance is within 0.025°, the software counts the object as a CT. If an object in the FOV 

cannot be correlated to an object in the catalog, that object is labeled as a UCT. If an object is predicted to 

be in the FOV but is not seen, it is termed a “no-see.” Each correlation is inspected by hand and an 

override of a computer correlation or non-correlation is possible. On average, 10% of the correlations are 

done by hand while the computer correlates the remaining 90% of the objects. Most of the hand correlations are done when there are multiple objects, both observed and predicted, in the FOV at the same 

time. 

3.5.2 Orbital elements calculation 

The orbit fit program uses a multidimensional simplex optimization routine to fit an orbit to the observations.7

 The observations consist of a series of time-tagged RA and DEC points. The optimization routine 

finds an orbit that, when propagated to a state vector at the times of individual observations, would appear 

in the correct positions as viewed from the telescope (with Earth rotation and telescope location included). 

The parameter to be optimized is the angular distance (averaged over the number of unique observations) 

between the predicted positions and the computed positions. 

Standard Kepler orbital elements tend to be very poor-fitting parameters, especially for orbits with nearzero inclinations and low eccentricities (eg, GEO orbits) in which elements such as ascending node and 

argument of perigee become ill-defined. However, an ideal one-to-one conversion exists between any 

ideal Kepler orbit and a state vector (both referenced to the same epoch). State vectors are attractive 

candidates for fitting an orbit because they can be varied smoothly without any ill-defined points, at least 

over a wide range of possible values. 

However, using an ideal Kepler orbit may be inadequate for actual orbit fitting. It would also be useful to 

include at least the most basic of perturbing terms for realistic orbit predictions. This is accomplished by 

using the SGP propagator,8

 which includes estimates of the effects of the J2 term in the Earth’s 

geopotential. The input for SGP is a two-line element (TLE) set that has the same form as classical Kepler 

orbital elements. 

The fitting procedure varies the pseudo-state-vector parameters (defined at a reference epoch for that 

observation), which are converted directly to Keplerian orbital elements. This Kepler orbit is then treated 

as the elements of a TLE appropriate for the SGP subroutine. SGP then delivers position predictions at 
10

each of the observation times for that orbit, and these positions are compared to those actually measured 

until a best-fit solution is achieved. Only the TLE orbit is then recorded that produced the optimized fit.

In general, short-arc data are of insufficient quality to compute an accurate orbit eccentricity. However, 

by penalizing any eccentricity above zero in the optimization portion of the code, a circular-orbit solution 

can be found. 

3.5.3 Comparison of derived orbital quantities with orbital parameters of known objects 

The accuracy of the orbital parameters, mean motion, INC, and RAAN for debris can be inferred from the 

observations of CTs. The error seen in the orbital parameter is due largely to departures from the circular 

orbit approximation used to calculate the orbital element. In this report, assumed circular orbit (ACO) is 

the term that describes the orbital element derived from the assumption of a circular orbit. In a similar 

fashion, the terms “known elements” or “SATRAK [Satellite Tracking (Government owned propagator)]

elements” are used interchangeably for elements obtained from cataloged TLE sets. In this report, the terms 

“inferred” and “known” are used most of the time when discussing data stemming from SATRAK or 

TLEs. 

The viewing geometry for computing the orbit of an object that passes through the FOV is illustrated in 

Figure 8. The rectangular geocentric equatorial coordinate system is used. The X-axis points in the direction of the vernal equinox, the Y-axis lies in the plane of the equator and points towards longitude 90, and 

the Z-axis points towards the celestial north pole. Both the orbital INC, i, and the RAAN can be 

calculated using the spherical triangles in Figure 8. From the spherical triangle defined by points A – the 

RAAN; B – the sub-Earth satellite position; and P – the Earth’s pole, 

i = cos-1sin(CBA)cos(BC)

 = sin-1tan(BC)/tan()

RAAN = LST + 

where CBA is the angle at which the object crosses the FOV, BC is the sub-satellite latitude,  (angle 

CA) is the longitude difference between the sub-satellite longitude and the orbit’s ascending node, and 

LST is the local sidereal time. The proper quadrant for the longitude difference can be determined by 

inspection. A reasonable estimate of an observed debris object’s altitude can be obtained from the 

distance the object moves along the arc AB during the exposure sequence and by assuming that the object 

is in a circular orbit. By knowing the altitude, the mean motion can be determined. 
11

Figure 8. Geometry for computing orbital parameters. 

Errors associated with determining the orbital parameters are dependent on the time span over which the 

observations were obtained, the INC of the orbit, the eccentricity of the orbit, and the actual pixel size of 

the CCD. 

The root mean square (RMS) of the error is calculated for most of the elements using the calculated 

element and the TLE element for the CT objects. In addition, for some elements, the category of CT is 

further broken into functional and nonfunctional objects. The distinction is whether or not the object is 

believed to be station-kept. Station-kept is defined as those objects that are allowed to drift in the northsouth direction but not in the east-west direction. If an object is station-kept, it is called a functional CT; if 

not, that object is termed a nonfunctional object. There are two reasons for this distinction. First, it is 

believed that nonfunctional objects should show similar characteristics to orbital debris, thus giving a 

better estimate of the imposed error on the determination of the orbit. Second, it is possible that a 

maneuver occurred with a functional object after the TLE was published and before the object was 

observed. If this is the case, the TLE and the calculated element would show differences that are not 

errors in the process of calculating the orbit but rather, show that the object is no longer in the same orbit. 

However rare as this case may be, it should be considered. 

3.5.3.1 Inclination 

The inclination of the orbit is the least error-prone of the elements calculated for most objects. The RMS 

error for INC is shown in Table 1. The errors are similar for all years, meaning that regardless of the 

locations observed the errors are consistent. The data in the table also break down the errors for functional 

and nonfunctional objects. Functional objects are those that are believed to be actively station-keeping, 

whereas nonfunctional objects appear not to be station-kept. Although small, the RMS error does improve 

in calendar year (CY) 2005 and CY 2006 for the nonfunctional objects. 
12

Table 1. Inclination Errors for CY 2004, CY 2005, and CY 2006 

Types of Error 

(reported in degrees) Functional Objects Nonfunctional 

Objects 

RMS 2004 0.06 0.23 

RMS 2005 0.07 0.08 

RMS 2006 0.06 0.08 

This difference may reflect a significant change made to the telescope in March 2005. Prior to that time, 

the telescope was moved by hand with pointing determined by mechanical setting circles. In March 2005, 

NASA funded a major upgrade to this telescope with all new drives, computer control, and encoders on 

both axes. This significantly improved the pointing and tracking of the telescope. 

Figure 9 shows the ACO INC vs. predicted INC for both functional and nonfunctional targets. The solid 

line indicates where the quantities are equal. All 3 years show good agreement, and this was an expected 

result. Few objects are seen as outliers, but those that were seen off the line were investigated. These 

objects were found to have eccentricities larger than 0.4. With the circular orbit assumption, it is 

understandable that the INC would be off, even slightly, for these objects. 

Figure 9. INC comparison for correlated targets separated into functional (F) and nonfunctional (NF) categories. 

CY 2004 is on the left, CY 2005 is in the center, and CY 2006 is on the right. 
13

In Figure 10, the same data are used; however, the scale is much smaller so that the region less than 1° 

can be investigated. This change in region is defined as a concise range and will be used throughout the 

rest of this report. The 2002–2003 MODEST data showed the INC was being underestimated. However, 

this is not seen as clearly in these later data sets. Data collected in 2005 show more bias towards 

underestimation; however, 2004 and 2006 show data on both sides of the line. The authors now feel it is 

the lack of data that is causing the appearance of the underestimation of INC. This is supported further by 

the fact that, in 2005, fewer nights were observed and fewer objects were detected. 

Figure 10. INC comparison for correlated targets separated into functional (F) 

and nonfunctional (NF) categories, concise range. 

An examination of the error in INC vs. the ACO INC was investigated, the results of which are shown in 

Figure 11 and Figure 12 for both the entire range and a more concise range of inclinations, respectively. 

This examination was conducted to determine whether large errors were seen at any specific INC or 

within functional or nonfunctional objects. For all years, functional objects gather near 0°, with only 2005 

data showing the underestimation of the INC. Nonfunctional objects have an equal spread between overand underestimation of INC throughout all INC ranges. 
14

Figure 11. INC error as a function of INC, entire range. 

Figure 12. INC error as a function of INC, concise range. 
15

3.5.3.2 Mean Motion Determination 

The usual mean motion for geostationary objects is near 1.0027 revs/day. The RMS error for mean motion 

is shown in Table 2. The errors are very small for all years, meaning that regardless of the locations 

observed, the errors are consistent. The errors for nonfunctional objects are slightly larger than those for 

functional objects, but again, the errors for all cases are very small. 

Table 2. Mean Motion Errors 

Types of Error Functional Objects Nonfunctional Objects 

RMS 2004 0.0014 0.0102 

RMS 2005 0.0008 0.0068 

RMS 2006 0.0015 0.0096 

The data for mean motion are plotted in a similar fashion to that seen in the section for inclination. First, a 

comparison of ACO mean motion vs. predicted (TLE) mean motion is shown in Figure 13, and a more 

concise range of mean motions using the same data is shown in Figure 14. The data shown in Figure 13 

center around the mean motion of 1, which is to be expected. Some of the data fall above and below these 

data, meaning the data were collected on both sub-synchronous and super-synchronous GEO objects. Figure 

14, in which the data are shown in a more concise range of values, shows a straight line through a 

predicted value of 1.0027 revs/day, but that value has a range of possible values for the ACO mean 

motion. No reason can be found to explain the results. Although this looks like a large error, by 

examining the range in values it is seen that this error is very small. 

The data in Figure 15 shows the error in mean motion vs. the ACO mean motion. The spread in the error 

is spaced equally between negative and positive values in error. However, there is a slight slope from the 

upper left to the lower right seen, specifically, in both sets of data. This was also seen in the 2002–2003 

data, and no reason for this slope could be obtained. 

Figure 13. Comparison of inferred and known mean motion. 
16

Figure 14. Comparison of inferred and known mean motion, concise range. 

Figure 15. Mean motion error vs. ACO mean motion. Solid lines are 

the slopes associated with the data. 
17

3.5.3.3 RAAN Determination 

The calculation of RAAN is very difficult to determine accurately when the INC of the orbit is near 0. 

Therefore, a breakdown of the data is shown for all objects and then for objects with calculated INCs 

greater than 1. The latter case is one thought to be more like debris. RMS error data for RAAN are shown 

in Table 3. As shown, the largest error occurs when objects with less than 1 INC are included. Once 

those are removed, the error is much smaller and is similar in order to the error seen with nonfunctional 

objects. This makes sense as most nonfunctional objects will have INCs greater than 1. 

Table 3. RAAN Errors 

Type of Error 

(reported in degrees) All objects All objects 

INCs > 1

Non-functional 

objects 

RMS 2004 79 11 1.1 

RMS 2005 77 3 1.2 

RMS 2006 82 5 2.3 

The data shown in Figure 16 are for the calculated RAAN vs. predicted RAAN. Here it is shown clearly 

that the RAAN calculation for functional CTs, which nominally have 0 inclination, are erroneous. 

Nonfunctional CTs have good agreement with the predicted value of RAAN, showing that the calculation 

of RAAN is a valid calculation. 

Figure 16. Comparison of inferred and known RAAN. 

Figure 17 shows the error in the RAAN calculation compared to the ACO INC. Notice that objects with 

large errors are associated with very small INCs and are usually CT objects. Some interesting structure 

arises when the same plot is focused on the smaller errors, as shown in Figure 18. The 2002–2003 data 

showed two sets of arcs seen in the nonfunctional CT data both above and below the zero error line. 

However, the 2004–2006 data show only one of the arcs, the one stemming from below the zero line. 

Objects found along this arc do not have anything in common in regards to date of collection, time of 
18

year, object number, or eccentricity. The only factor they have in common is that the lower the INC, the 

higher the error. It appears, however, that the RAAN results are slightly underdetermined; therefore, 

underdetermining lessens as RAAN increases. 

Figure 17. RAAN error as a function of INC (focus on larger errors). 

Figure 18. RAAN error as a function of INC (focus on smaller errors). 
19

3.6 Summary of Data Processing 

Once the data are collected, the subsequent processing steps performed are as follows: 

1) Objects are identified as either CTs or UCTs. 

2) Orbital elements (INC, range, RAAN, mean motion) for CTs are calculated from circular orbit 

fits, and biases or errors are determined to be applied to the UCT elements 

3) Sizes of detected objects are estimated, assuming an average albedo of 0.175 and Lambertian 

phase function. 

4) Probability of detection, defined as the likelihood of detection in a given orbit, is calculated based 

on the location of the telescope at a given time and date. 

4.0 Results 

4.1 Detection Rates 

Forty-two nights of data were reduced for CY 2004, starting with day of year (DOY) 018 and ending with 

DOY 344. For CY 2005, 23 nights of data were reduced, starting with DOY 017 and ending with DOY 343. 

In CY 2006, 35 nights of data were reduced, starting with DOY 29 and ending with DOY 330. In Table 4, 

the data collected are broken down into the different years. For each year, the percentage of CTs and 

UCTs observed, the average number of CTs and UCTs detected each night for all locations, and the average 

number of CTs and UCTs detected per night, when not on the GEO belt, are shown; ie, for those objects 

with INCs <1°. The GEO belt is the nominal location of spacecraft that are being station-kept. Most of the 

objects in this regime are CTs; this is shown by the larger decrease in average number of objects collected 

for the CTs vs. the UCTs. 

Table 4. Statistics Data Collection 

Year % CTs % UCTS Avg. # of CTs 

each night 

Avg. # of UCTs 

each night 

Avg. # of CTs – 

no belt 

Avg. # of UCTs – 

no belt 

2004 72% 27% 18 7 10 7 

2005 74% 26% 17 6 11 6 

2006 76% 24% 19 6 9 4 

4.2 Location of Field Centers and Detections 

During a normal 2-week telescope run, the strategy was to keep the RA unchanged while offsetting in DEC 

by ±1.2 degrees each night. In addition, the RA was chosen based on the location of the anti-solar point 

and the closest proximity to that point possible without being in the shadow of the Earth. The data in 

Figure 19 shows, using dots, a snapshot view of where objects are expected to be located given an RA 

and a DEC. These data are a snapshot of DOY 365 for 2003. The overall view of the plot will be similar 

regardless of the day used. The near-solid line of dots near 5° DEC is the location of the GEO belt as seen 

from CTIO. The red squares show the observing location of the telescope for each night in 2004, the blue 

squares show the locations for each night in 2005, and the green squares show the locations for each night 

in 2006. Overlapping of field locations, which occurred each year, is visible in the graph, especially near 

12° and 14° RA. Note: The size of the square on the plot does not depict the size of the FOV for the 

telescope. 
20

Figure 19. Location of field centers. 

Once the field centers are determined, the data are run through a code that determines the probability of 

detecting an object in a specific orbit while at that FOV and specific given time. A probability chart is 

shown in Figure 20. The different colors represent the probability of detection. The redder the color or the 

closer the probability is to 1, the greater the likelihood an object in that orbit was detected. Overlaid on 

the probability chart are the actual detections for the 3 years of data; CTs are solid diamonds and UCTs 

are open circles. Notice that most of the objects detected were in the red region of probability, which 

means it is likely that all objects in that region were detected. Once the probability chart was created, it 

was determined that in future telescope runs, FOV locations could be predetermined by filling in areas of 

the probability chart. Through collecting a larger number of nights, it is possible to assess a population 

from these probability data. 

Figure 21 shows the population prediction based on where and when the telescope looked for objects and 

where the objects were found. Each object is given a weight that depicts how many times that object 

should be counted for a statistical sampling of the data. This weight is the inverse of the number of times 

a random object in that orbit would be expected to have been observed. For instance, an object in the 

GEO belt could be expected (on average) to be observed multiple times over a set of observation runs. Its 

weighting would therefore be less than one. This procedure statistically removes multiple observations of 

the same object. At the other extreme, there are orbits that have a probability of less than one of detecting 

an object in them due to the observation times and pointing directions. The weighting of an object in such 

an orbit would be greater than one, indicating that each object seen is a sample from a larger, undetected 

population. This method can be statistically extrapolated to estimate the unseen population. 
21

Figure 20. Probability of finding specific orbits based on field center locations 

during 2004–2006. 

Figure 21. Possible population of UCTs and CTs based on statistical sampling. 

Note that Figure 21 also shows the UCTs and CTs combined in one line as well as the UCTs alone for all 

2004-2006 data. The objects are binned by absolute magnitude. The error bars are a statistical estimation. 

The power law distribution for breakups is plotted with these data.9

 Aligning this power law distribution 

line with the UCT data demonstrates that, if it were not for the fall off in detections due to the telescope 
22

size, UCT objects would continue to be found at the rate the black line suggests. This analysis is purely 

statistical, but shows a valuable result of the continuing increase of the number of UCTs as absolute 

magnitude increases and size decreases. 

4.3 Angular Momentum Vector 

As previously discussed in Section 3.2, the orbits of GEO and near-GEO objects undergo precession under 

the influence of Earth’s oblateness and the gravity of the sun and the moon. As this precession occurs, the 

ascending node also precesses such that, to the first order for “perfect” GEO objects, there is a one-to-one 

correspondence of INC to ascending node. A simple formula to show this relationship between INC i and 

RAAN is given by 

2

2

1 [ ( )]

1 [ ( )] ( )

x Cos RAAN

x Cos RAAN Cos i



 

where 

(7.5 )

(7.5 )





Cos

Sin

x  . 

This behavior can best be seen by the path of the angular momentum vector of the orbit, which traces an 

arc during this precession cycle centered about a line tilted 7.5 with respect to north pole, as shown in 

Figure 22. An easy way to show the angular momentum vector for measured objects is to plot the orbital 

data in a polar graph with the ascending node as the polar angle and the INC as the radius. 

Figure 22. Angular momentum vector of an orbit. 

In Cartesian terms, 

( ).

( )

y i Sin RAAN

x i Cos RAAN





In these coordinates, the path traced out during the precession cycle is a loop. Objects found to reside on 

or near this idealized loop represent GEO or near-GEO objects at various stages in their orbital evolution 
23

or are objects perturbed by solar radiation pressure. Debris from energetic breakups may stray further 

from this idealized path, depending on how strong the delta-velocity was they received at breakup. 

Data collected in CY 2004, CY 2005, and CY 2006 are shown in Figure 23, Figure 24, and Figure 25, 

respectively. The plot has four subplots, which are termed polar plots due to the coordinate system shown. 

The upper left image shows only the functional CTs as red solid circles. One can see the data clustering 

around X = 0 and Y = 0. This was an expected result. The next two subplots show the nonfunctional CTs 

and the UCTs as blue open circles and green open circles, respectively. The data in these subplots show 

similar trends of the progression in orbital evolution or perturbations. The UCT data are more scattered; 

one theory being explored is that the solar radiation pressure is affecting these objects more than the 

nonfunctional CTs due to size and mass. Once all the data are plotted together, there appears to be an inner 

circle of data in all three data types. The data shown for all 3 years have similar trends. 

Figure 23. Polar coordinates for objects, CY 2004. 
24

Figure 24. Polar coordinates for objects, CY 2005. 

Figure 25. Polar coordinates for objects, CY 2006. 
25

Figure 26 shows the probability of detection data converted into polar data and overlaid with detections. 

This type of data is helpful to show where the next observing run should focus and to determine whether 

initial observations are in the right place. 

Figure 26. Polar coordinates with probability and detections overlaid for all 2004–2006 data. 

The CTs are solid diamonds and the UCTs are open diamonds. 

4.4 No-sees 

Data reduction includes predicting which known satellites from the U.S. SSN catalog will be seen in 

which observational frame. If a satellite is predicted to be present but evidence for its presence is not 

found, it is listed as a “no-see.” There are multiple potential reasons for an object’s non-detection, such as 

having too faint a visual magnitude or being outside of the rate box. It is important to understand why an 

object is not seen as this aids in our understanding of the debris environment and determining the limits of 

this method of analysis. Lack of detection of an object does not necessarily mean the object is not present; 

it can as easily indicate changes in the orbital elements, a breakup, or even changes in orientation. A detailed no-see analysis was completed for the 2002–2003 data, and it is not believed that the results differ 

for this set of data. Refer to the 2002–2003 report for more details. 

4.5 Mean Motion Distribution 

The mean motion of most GEO objects is very close to 1 rev/day. The actual value usually seen for functional CTs in the TLEs shows a value closer to 1.0027 revs/day. Figure 27 compares mean motions for 

functional and nonfunctional CTs and UCTs. As expected, the large percentage of functional CTs is seen 

near a mean motion of 1 (98 % of the objects). In addition, a large percentage of the nonfunctional CTs is 

also seen near 1 (45% of the objects collected). However, there are more nonfunctional CTs spread 

throughout the various mean motions, similar to that of the UCTs. The UCTs have the highest percentage 

of objects near 1 rev/day at 22 %; however, they are also seen at mean motions as small as 0.9 and as high 

as 1.08. Because of this variance, it is believed the ACO calculation is inducing an error into the 

calculation of mean motion for these objects. 
26

Figure 27. Mean motion distribution for CT and UCT objects. 

4.6 Inclination Distribution 

As expected, the INC distribution for functional CTs aligns with near 0° INC, with 87% of the detected 

objects showing in that bin, as shown in Figure 28. Nonfunctional CTs are seen through all INC bins up 

to 15° to 16°, as is expected due to the propagation of INC with orbital age (see Section 3.2 for a detailed 

discussion). The UCTs have a similar spread in INC bins. In the 2002–2003 data, two peaks were located 

near 6° and 12° INC. This does not seem to be the case for the 2004–2006 data. One could argue a peak 

near 11° INC, but there is no evidence to support the two peaks seen in previous years. Again, this can be 

attributed to lack of data in previous years. The nonfunctional CTs do not seem to have a peak, as three INC 

bins show similar percentages (5°, 6°, and 10°). The indication of a peak in the UCT data could signal the 

location of a breakup; however, clustering is easier to see when a comparison of INC versus RAAN is 

calculated. Those data are shown in Section 4.9. 

4.7 RAAN Distribution 

The distribution of RAAN in the functional CT, nonfunctional CT, and UCT populations is shown in 

Figure 29. Three peaks of UCTs are seen in these data as well, with the first peak located near 10°, the 

second peak located near 80°, and the third peak located near 330°. Previous data sets have shown only 

two peaks at the near 80° and near 330° locations. One peak is seen with the nonfunctional CTs near 80°, 

a similar location to that of one of the UCT peaks. 
27

Figure 28. Distribution of INC for CTs and UCTs. 

Figure 29. Distribution of RAAN for CT and UCT. The location of the data found 

is biased by the field center selection and the DOY. 

4.8 Absolute Magnitude Distribution and Derived Diameters 

As discussed in previous sections, the derived diameters stem from assuming an albedo of 0.175 and a 

diffuse Lambertian phase function.6

 A mean distance of 36,000 km is also used. As a reminder, the 

absolute magnitude is a log calculation (unitless); the smaller the number, the brighter and, likely, larger 

the object. The distribution of absolute magnitudes is shown in Figure 30. Overlaid on the distribution are 
28

the diameters associated with a few of the bins. The peak in absolute magnitude for functional CTs is seen 

at 10, corresponding to a size of 8 m. The peak of the nonfunctional objects is seen near 12.5, which is a 

size of 2.5 m. The catalog is said to be complete down to 1 m at GEO; using the assumptions above, this 

corresponds to an absolute magnitude of 14.4. The peak of the UCTs is an artificial one due to the 

detection capabilities of the telescope. It is believed that the UCT population will continue on the same 

slope throughout the smaller magnitudes. The smallest detected object to be seen with MODEST, using 

the albedo and phase function assumptions, is 6 cm.6

Figure 30. Absolute magnitude and derived size distribution, assuming an albedo of 0.175 and 

a diffuse Lambertian phase function. 

4.9 RAAN vs. INC Distribution 

The INC and RAAN distributions for the detected objects are shown in Figure 31. The top figure shows 

the data collected in 2004, the middle figure the 2005 data, and the bottom figure the data collected in 

2006. The data show a collection of UCTs near 330° RAAN and 11° INC. The first clumping is believed 

to be the location of the Titan breakup. Similar clustering is seen near 70° RAAN and 5° INC as well as 

near 10° RAAN and 14° INC. However, as no known breakups have occurred in those areas, the clusters 

may indicate locations of unknown breakups. More data need to be collected to confirm these findings. The 

data in these plots show the expected climb toward 15° INC for the UCTs and nonfunctional CTs as well 

as for the functional CTs at various RAANs with 0° INC. Figure 32 presents all the data together. Only two 

of the clusters of UCTs are still visible: the one near 330° RAAN and the one near 10° RAAN. 
29

Figure 31. RAAN vs. INC for CT and UCT objects. 

Figure 32. RAAN vs. INC for CT and UCT data for all 3 years. 

5.0 Conclusions 

This JSC report provides details of observational and data-reduction processes for the entire MODEST 

dataset acquired in CYs 2004, 2005, and 2006. Specifically, this report describes the collection and anal-
30

ysis of 42 nights of data collected in CY 2004, 23 nights of data collected in CY 2005 and 35 nights of 

data collected in CY 2006. 

The average number of detections each night over all 3 years was 18. On average in CY 2004, 72% of the 

detections were CTs and 27% were UCTs; in CY 2005, 74% of the detections were CTs and 26% were 

UCTs; and in 2006, 76% of the detections were CTs and 24% were UCTs. This variation in percentages 

between the years may be due to observations that were made in different locations with respect to the 

GEO belt. 

Errors associated with the derived quantities of range, INC, and RAAN were derived by comparing 

values calculated using an ACO and those known values seen in the TLE. The average INC RMS error is 

0.06 for functional CTs and 0.13 for nonfunctional CTs. Due to the fact that RAAN is ill-defined at 

values near 0 INC, the RMS error for RAAN is calculated only for objects with an INC greater than 1. 

The average RAAN RMS error is 10 for functional objects and 6 for nonfunctional objects in CY 2004; 

29 for functional objects and 8 for nonfunctional objects in CY 2005; and 14 for functional objects and 

12 for nonfunctional objects in CY 2006. The mean motion error is 0.0014 rev/day for functional objects 

and 0.010 rev/day for nonfunctional objects in CY 2004; 0.0008 rev/day for functional objects and 0.0068 

rev/day for nonfunctional objects in CY 2005; and 0.0015 rev/day for functional CTs and 0.0096 rev/day 

for nonfunctional CTs in CY 2006. This error analysis of CT values for INC, RAAN, and mean motion 

lends credibility to the determination of the UCT orbital distributions. 

The distribution of objects found UCTs clustering in three locations, with only one corresponding to the 

breakup of Titan. More data are needed to confirm whether the other two clusters could be from unknown 

breakups. 

The absolute magnitude distribution showed a peak for the functional CTs at 10th magnitude. An absolute 

magnitude of 10.5 corresponds to objects having average diameters of 8 m, assuming an albedo of 0.175 

and a diffuse Lambertian phase function. This result generally agrees with the known sizes of intact 

satellites. The absolute magnitude distribution for the UCTs is broad, but starts to roll off near a diameter 

of 25 cm or 17.5 magnitude. The roll off in the distribution reflects the detection capability of MODEST 

and does not reflect the true nature of the population. The true population is believed to continue at the 

same slope through fainter magnitudes, as was shown when the statistical population was compared to the 

power-law distribution of low-Earth orbit breakups. 

6.0 References 

1

Johnson, N.L., et al. “History of On-Orbit Satellite Fragmentations.” JSC-29517, Houston, TX, 2001. 

2

Pensa, A. F., et al. “Debris in Geosynchronous Orbit.” SPACE FORUM, Vol. 1, pp. 23 – 27, 1996. 

3

Talent, D. L. et al. “A Search for Debris in GEO.” Proceedings of the Second European Conference on 

Space Debris, Darmstadt, Germany, 1997. 

4

Friesen, L. et al. “Results in Orbital Evolution of Objects in the Geosynchronous Region.” AIAA 90-

1362, AIAA/NASA/DOD Orbital Debris Conference: Technical Issues and Future Directions,

Baltimore, MD, 1990. 
31

5

Vaughan, S. H. and Mullikin, T. L. “Long Term Behavior of Inactive Satellites and Debris Near 

Geosynchronous Orbits.” AIAA 95-200, AAS/AIAA Spaceflight Mechanics Meeting, Albuquerque, 

NM, 1995. 

6

Mulrooney, M.K., Matney, M.J., and Barker, E.S. “A New Bond Albedo for Performing Orbital Debris 

Brightness to Size Transformations.” International Astronautical Congress, Glasgow, Scotland, 

2008. 

7

Press, W.H., Teukolsky, S.A, Vetterling, W.T., and Flannery, B.P. Numerical Recipes in Fortran 90. 

Cambridge University Press. Volume 2. January 1996. 

8

Hoots, F.R. and Roehrich, R.L. “Spacetrack Report #3: Models for Propagation of the NORAD Element 

Sets.” U.S. Air Force Aerospace Defense Command, Colorado Springs, CO. 

9

Johnson, N.L., Krisko, P.H., Liou, J.C., Anz-Meador, P.D.: “NASA’s New Breakup Model of EVOLVE 

4.0.”, Adv. Space Res., Vol. 28, No. 9, pp 1377-1384, 2001. 
32

Appendix A: 

Fields File Example 

(This is a representative sample of the file) 

 DEC RA Time Frame 

4.842 124.306 10368.1 19 

4.842 124.306 10406.0 20 

4.842 124.306 10443.9 21 

4.842 124.306 10481.8 22 

4.842 124.306 10519.7 23 

4.842 124.306 10557.6 24 

4.842 124.306 10595.5 25 

4.842 124.306 10633.4 26 

4.842 124.306 10671.3 27 

4.842 124.306 10709.2 28 

4.842 124.306 10747.1 29 

4.842 124.306 10785.1 30 

4.842 124.306 10822.9 31 

4.842 124.306 10860.8 32 

4.842 124.306 10898.7 33 

4.842 124.306 10936.6 34 

4.842 124.306 10974.6 35 

4.842 124.306 11012.5 36 

4.842 124.306 11050.4 37 

4.842 124.306 11088.3 38 

4.842 124.306 11126.2 39 

4.842 124.306 11164.1 40 

4.842 124.306 11202.0 41 

4.842 124.306 11239.9 42 

4.842 124.306 11277.8 43 

4.842 124.306 11315.7 44 

4.842 124.306 11353.6 45 

4.842 124.306 11391.5 46 

4.842 124.306 11429.4 47 

4.842 124.306 11467.3 48 

4.842 124.306 11505.2 49 
33

Appendix B: 

Output File Example 

The columns are frame number, RA, DEC, epoch, magnitude, date, and time. Two objects are shown, both 

with nine detections. This output is what NASA receives from the telescope. 

2002009.0001 9 

 29 123.6621 4.8225 2000.0 11.3 2002-01-09 2.98532 

 30 123.8204 4.8225 2000.0 11.3 2002-01-09 2.99585 

 31 123.9782 4.8225 2000.0 11.3 2002-01-09 3.00637 

 32 124.1370 4.8225 2000.0 11.3 2002-01-09 3.01690 

 33 124.2953 4.8232 2000.0 11.3 2002-01-09 3.02743 

 34 124.4537 4.8243 2000.0 11.3 2002-01-09 3.03795 

 35 124.6126 4.8244 2000.0 11.3 2002-01-09 3.04849 

 36 124.7703 4.8244 2000.0 11.3 2002-01-09 3.05902 

 37 124.9286 4.8244 2000.0 11.3 2002-01-09 3.06955 

2002009.0002 9 

 50 123.6602 4.8534 2000.0 11.2 2002-01-09 3.20642 

 51 123.8191 4.8534 2000.0 11.2 2002-01-09 3.21695 

 52 123.9768 4.8534 2000.0 11.2 2002-01-09 3.22747 

 53 124.1358 4.8534 2000.0 11.2 2002-01-09 3.23800 

 54 124.2943 4.8543 2000.0 11.0 2002-01-09 3.24853 

 55 124.4524 4.8534 2000.0 11.2 2002-01-09 3.25907 

 56 124.6103 4.8539 2000.0 11.2 2002-01-09 3.26959 

 57 124.7690 4.8553 2000.0 11.2 2002-01-09 3.28012 

 58 124.9276 4.8553 2000.0 11.2 2002-01-09 3.29065 
34

Appendix C: 

Correlation Output 

These data are the correlation file for the two objects listed in Appendix B. The computer correlated one object; the other object was correlated by hand. 

REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and 

maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including 

suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, 

and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 

1. AGENCY USE ONLY (Leave Blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 

 August 2010 Technical Publication 

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Michigan Orbital DEbris Survey Telescope Observations of the Geosynchronous Orbital 

Debris Environment – Observing Years: 2004-2006 

 

6. AUTHOR(S) 

K. J. Abercromby*, P. Seitzer**, E. S. Barker***, H. M. Cowardin*, M. J. Matney*** 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

REPORT NUMBERS

Lyndon B. Johnson Space Center 

Houston, Texas 77058 

S-1074 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING 

AGENCY REPORT NUMBER

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

TP-2010-216129 

11. SUPPLEMENTARY NOTES 

*ESC Group/Jacobs, Houston; **University of Michigan, Ann Arbor; NASA Johnson Space Center, Houston 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

Unclassified/Unlimited 

Available from the NASA Center for AeroSpace Information (CASI) 

7115 Standard 

Hanover, MD 21076-1320 Category: 88

 

13. ABSTRACT (Maximum 200 words)

Orbital debris is a concern to nations using satellites or launch space vehicles. The debris field scattered near Earth’s geosynchronous 

orbit (GEO) poses a threat to anything residing in or passing through it. To mitigate risk and minimize this environment’s expansion, 

the environment must be understood. NASA uses the Michigan Orbital DEbris Survey Telescope (MODEST), a University of 

Michigan-owned 0.61-m aperture Schmidt telescope at Cerro Tololo Inter-American Observatory in Chile, to help characterize the 

GEO debris environment. Objectives for this survey are to determine the extent and character of debris in GEO, specifically by 

obtaining distributions for brightness, inclination (INC), right ascension of ascending node (RAAN), and mean motion for the debris. 

This report describes the collection and analysis of 42 nights of data in contract year (CY) 2004, 23 nights in CY 2005, and 35 nights 

in CY 2003. Eighteen objects on average were detected nightly: in CY 2004, 72% were correlated targets (CTs) and 27% were 

uncorrelated targets (UCTs); in CY 2005, 74% were CTs and 26% were UCTs; and in CY 2006, 76% were CTs and 24% were UCTs. 

Estimates can be made from correlated objects on errors associated with derived quantities of range, INC, and RAAN. 

14. SUBJECT TERMS 15. NUMBER OF 

PAGES 

16. PRICE CODE 

space debris; geosynchronous orbits; Earth orbital environments; brightness; inclination, 

orbits; targets; range, orbital position estimation; astronomical telescopes 46 

17. SECURITY CLASSIFICATION 

OF REPORT 

18. SECURITY CLASSIFICATION 

 OF THIS PAGE

19. SECURITY CLASSIFICATION 

OF ABSTRACT

20. LIMITATION OF ABSTRACT 

Unclassified Unclassified Unclassified Unlimited 

Standard Form 298 (Rev Feb 89) (MS Word Mar 97) 

Prescribed by ANSI Std. 239-18 

298-102 

NSN 7540-01-280-5500