NASA/TP-2010-216128 

Michigan Orbit

Observations of

Debris Environ

Observing Years: 2

K. J. Abercromby1, P. Seitzer2, E. S.

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 

2002–2003

. Barker

3

, H. M. Cowardin1, M. J. Matney3, and T. L

escope 

Orbital 

L. Parr-Thumm1 
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NASA/TP-2010-216128 

Michigan Orbit

Observations of

Debris Environ

Observing Years: 2

K. J. Abercromby1, P. Seitzer2, E. S.

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 

2002–2003

. Barker

3

, H. M. Cowardin1, M. J. Matney3, and T. L

escope 

Orbital 

L. Parr-Thumm1 
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/ 
iii 

Contents 

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

1.0 Introduction ......................................................................................................................... 2 

2.0 Background ......................................................................................................................... 2 

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

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

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

3.3 Data Collection ................................................................................................................... 6 

3.4 Data Processing ................................................................................................................... 7 

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

3.5.1 Correlation of detections ..................................................................................................... 8 

3.5.2 Orbital elements calculation................................................................................................ 8 

3.5.3 Comparison of derived orbital quantities with orbital parameters of known objects ......... 9 

3.5.3.1 Inclination ........................................................................................................................... 10 

3.5.3.2 Mean Motion Determination ............................................................................................... 14 

3.5.3.3 RAAN Determination ......................................................................................................... 16 

3.6 Summary of Data Processing .............................................................................................. 18 

4 Results ................................................................................................................................. 18 

4.1 Detection Rates ................................................................................................................... 18 

4.2 Location of Field Centers and Detections ........................................................................... 18 

4.3 Angular Momentum Vector ................................................................................................ 20 

4.4 No-sees ................................................................................................................................ 23 

4.5 Mean Motion Distribution .................................................................................................. 23 

4.6 Inclination Distribution ....................................................................................................... 23 

4.7 RAAN Distribution ............................................................................................................. 24 

4.8 Absolute Magnitude Distribution and Derived Diameters .................................................. 25 

4.9 RAAN vs. INC Distribution................................................................................................ 25 

5.0 Conclusions ......................................................................................................................... 27 

6.0 References ........................................................................................................................... 27 

Appendix A: Fields File Example ......................................................................................................... 29 

Appendix B: Output File Example........................................................................................................ 30 

Appendix C: Correlation Output ........................................................................................................... 31 
iv 

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 ..................................................................................................... 3

3 Inclination vs. launch date .................................................................................................... 4 

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 for a given date ........................................................ 5 

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

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 ........................................................................................ 7

8 Geometry for computing orbital parameters ......................................................................... 10 

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

(NF) categories. CY 2002 is on the left and CY 2003 is on the right ................................... 11 

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

(NF) categories, concise range. CY 2002 is on the left and CY 2003 is on the right ........... 12 

11 INC error as a function of INC, entire range ........................................................................ 13 

12 INC error as a function of INC, concise range ..................................................................... 13 

13 Comparison of inferred and known mean motion ................................................................ 14 

14 Comparison of inferred and known mean motion, concise range ........................................ 15 

15 Mean motion error vs. ACO mean motion ........................................................................... 15 

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

17 RAAN error as a function of INC ......................................................................................... 17 

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

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

20 Probability of finding specific orbits based on field center locations ................................... 19 

21 Angular momentum vector of an orbit ................................................................................. 20 

22 Polar coordinates for objects, CY 2002 ................................................................................ 21 

23 Polar coordinates for objects, CY 2003 ................................................................................ 22 

24 Polar coordinates with probability and detections overlaid .................................................. 22 

25 Mean motion distribution for CT and UCT objects .............................................................. 24 

26 Distribution of INCs for CTs and UCTs ............................................................................... 24 

27 Distribution of RAAN for CTs and UCTs. The location of the data found is biased 

by the field center selection and the DOY ............................................................................ 25 

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

a diffuse Lambertian phase function ..................................................................................... 26 

29 RAAN vs. INC for CT and UCT objects .............................................................................. 26 
v 

Tables 

1 Inclination Errors for CY 2002 and CY 2003....................................................................... 11 

2 Mean Motion Errors ............................................................................................................. 14 

3 RAAN Errors ........................................................................................................................ 16 

4 Statistics on CY 2002 and CY 2003 Data Collection ........................................................... 18 

 
vi 

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 [only used 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 [only used 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 

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) 2002 and 2003. Specifically, this report describes 

the collection and analysis of 35 nights of data collected in CY 2002 and 16 nights collected in CY 2003. 

MODEST is equipped with a 2.0482.048-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. For both years, averages of 23 objects were detected each night. On average 

in CY 2002, 76% of the detections were CTs and 24% were UCTs, whereas in CY 2003 the percentages 

were 66% and 34% for CTs and UCTs, respectively. The differences may be due to observing in different 

locations. 

From the correlated objects, estimates can be made as to the errors associated with the derived quantities 

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

determined using an assumed circular orbit. The average INC root mean square (RMS) error is 0.1 for 

functional CTs and 0.3 for nonfunctional CTs. Since RAAN is ill-defined at small values of INC (those 

less than 1), the RMS error for RAAN is calculated for only objects with INC greater than 1. The 

average RAAN RMS error is 20 for functional objects and 11 for nonfunctional objects in CY 2002, 

and 57 for functional objects and 16 for nonfunctional objects in CY 2003. For CY 2002, the mean 

motion error is 0.0005 for functional and 0.0070 for nonfunctional objects and 0.0071 and 0.0091 for 

functional CTs and nonfunctional CTs, respectively. 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 1,137 objects detected in the data processed for CY 2002 and CY 

2003. The actual peak of the absolute magnitude distribution for the functional correlated targets is 11th

magnitude. An absolute magnitude of 11.5 corresponds to objects having average diameters of 4.6 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 29 cm or 17.5 magnitude. The roll off in distribution reflects the detection 

capability of MODEST, and 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 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 (CTIO) 

in Chile, to help characterize the debris 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 consisting of dead satellites, rocket body upper stages, deployment hardware, small debris, etc., has been placed into GEO. 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,1,2 SSN 3432, 

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

telescopes tracked these objects for a few days after the event, but 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 this 

survey indicated that, to a limiting apparent magnitudes 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 as 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 2,048 

2,048 pixels, each of which is 24 microns square. This provides a sampling of 2.318 arc-seconds/pixel, 

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) that is equal to 10 on a point source detection of 18th R magnitude under typical dark sky conditions at CTIO. 

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 that are 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 for a given date. 

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 this envelope, most debris will be found near or inside the envelope. 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 the debris 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 can be seen from 25°W to 135°W. Each night, MODEST 

observers determine a specific right ascension (RA) and a 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 Earth’s 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 at the sidereal rate in RA and a fixed DEC. The CCD chip is aligned on the telescope 

such that the RA vector is parallel to the shift registers. During the 5-s exposure, the charge on the CCD is 

shifted in reverse so that objects are seen as a point source and 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. 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 that a possible target is 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 that 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, 

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

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

False positives (largely due to cosmic rays and the end of star streaks) are rejected by the operator. 

Experience demonstrates that 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 is carried out to 

correlate all satellites within a 1 radius of the center of the FOV with any detected object. The results are 

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

subset of that 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 one 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 then 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 year-to-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 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 an ascending node 

and an 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 

each of the observation times for that orbit, and these positions are compared to the positions that are ac-
10 

tually 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 the departures from the 

circular orbit approximation used in calculating 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 it moves 

along the arc AB during the exposure sequence and by assuming it 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 termed a functional CT; 

if not, it 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 observation of the object. 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 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 both calendar years (CYs), 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 believed to be actively stationkeeping, whereas nonfunctional objects appear not to be station-kept. 
12 

Table 1. Inclination Errors for CY 2002 and CY 2003 

Types of Error

(reported in degrees) Functional Objects Nonfunctional Objects 

RMS 2002 0.1 0.3 

RMS 2003 0.2 0.1 

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

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

result. There are some outliers on the 2002 data above a predicted INC of 10° and one outlier near 6°. 

These objects were investigated and 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 2002 is on the left and CY 2003 is on the right. 

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

investigated. As seen in the figure, the ACO INC is overestimating the INC as referenced to the TLEs in 

all cases for both years. Measures currently are being taken to correct this offset, including correcting any 

possible pointing errors from the telescope. However, the error is still very small and may not be significant compared to other sources of error. 
Figure 10. INC comparison for corre

concise rang

An examination of the error in INC 

11 and Figure 12 for both the entir

this point forward, the more concise

in one part of the figure. This exam

any specific INC or within function

from previous charts. The function

the INC. The nonfunctional objects

throughout all INC ranges. However

as one would expect, but the nonfu

examined but no correlation could 

way inclination is calculated. Invest

13 

lated targets separated into functional (F) and nonfunctional 

ge. CY 2002 is on the left and CY 2003 is on the right. 

vs. the ACO INC was investigated, and the results a

re range and a more concise range of inclinations, r

e range is used when the X- or Y-axis is changed to s

mination was conducted to determine whether large e

nal or nonfunctional objects. The 2002 data showed w

nal objects gather near 0° and have errors showing u

s have an equal spread between over- and underesti

r, the 2003 data were slightly different. The function

unctional data were almost all underdetermined. A 

be found near the observational area, the objects 

tigations are still underway. 

(NF) categories, 

are shown in Figure 

respectively. From 

show greater detail 

errors were seen at 

what was expected 

underestimation of 

imation of the INC 

nal objects behaved

cause for this was 

themselves, or the 
Figure 

Figure 1

14 

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

2. INC error as a function of INC, concise range. 
3.5.3.2 Mean Motion Determinatio

The usual mean motion for geostatio

is shown in Table 2. The errors ar

observed, the errors are consistent. 

functional objects; but again, the err

Types of Error

RMS 2002 

RMS 2003 

The data for mean motion are plot

comparison of the ACO mean moti

more concise range of mean motion

13 center around the mean motion 

these data, meaning that the data w

objects. Figure 14, where the data 

through a predicted value of 1.0027

mean motion. No reason can be fo

examining the range in values it is s

The data in Figure 15 show the erro

spaced equally between negative an

upper left to the lower right. No rea

Figure 13

15 

on 

onary objects is near 1.0027 revs/day. The RMS erro

re very small for both years, meaning that regardle

The errors for nonfunctional objects are slightly lar

rors for both cases are very small. 

Table 2. Mean Motion Errors 

Functional Objects Nonfunctional O

0.0005 0.0070 

0.0071 0.0091 

tted in a similar fashion to that seen in the section

ion vs. the predicted (TLE) mean motion is shown i

ns using the same data is shown in Figure 14. The da

of 1, which is to be expected. Some of the data fal

were collected on both sub-synchronous and superare shown in a more concise range of values, sho

7 revs/day, but that value has a range of possible v

ound to explain the results. Although this looks lik

seen that this error is very small. 

or in mean motion vs. the ACO mean motion. The sp

nd positive values in error. However, there is a slig

son for this slope could be obtained. 

. Comparison of inferred and known mean motion. 

or for mean motion 

ss of the locations 

rger than those for 

Objects 

n for inclination. A 

in Figure 13, and a 

ata shown in Figure 

ll above and below 

-synchronous GEO 

ows a straight line 

alues for the ACO 

ke a large error, by 

pread in the error is 

ght slope from the 
Figure 14. Compa

Figure

16 

rison of inferred and known mean motion, concise range. 

 15. Mean motion error vs. ACO mean motion. 
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 as well as 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; an even smaller error is seen with the nonfunctional objects. 

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

the RAAN calculation for functional CTs, which nominally have 0 inclination, are erroneous. The nonfunctional CTs have good agreement with the predicted value of RAAN, showing that the calculation of 

RAAN is a valid calculation. 

Table 3. RAAN Errors 

Type of Error 

(reported in degrees) All objects All objects

INCs > 1

Nonfunctional 

objects 

Nonfunctional 

objects INCs > 1

RMS 2002 81 6 3 2 

RMS 2003 80 4 25 2 

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. Two sets of arcs are seen 

in the nonfunctional CT data, and the trends are seen in both years of data. Errors in the RAAN calculation 

are small for these objects; however, the arcing shape seen in the figure is puzzling. Objects found along 
18 

this arc do not have anything in common in regards to date of collection, time of year, object number, or 

eccentricity. The only factor they have in common is that the lower the INC, the higher the error. 

Figure 17. RAAN error as a function of INC. 

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

3.6 Summary of Data Processing 

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

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 a 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 

Thirty-five nights of data were reduced for CY 2002, starting with day of year (DOY) 009 and ending 

with DOY 315. For CY 2003, there were 16 nights of data, starting with DOY 032 and ending with DOY 

272. 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. those for the UCTs. 

Table 4. Statistics on CY 2002 and CY 2003 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 

2002 76% 24% 17 7 11 6 

2003 67% 33% 15 8 11 8 

4.2 Location of Field Centers and Detections 

During a normal 2-week telescope run for the 2002–2003 data collection period, the strategy was to keep 

the RA unchanged while offsetting in declination by ±1.2 degrees each night. In addition to this, the RA 

was chosen based on the location of the anti-solar point and closest proximity to that point possible 

without being in the shadow of the Earth. The data in Figure 19 show, using dots, a snapshot view of where 

objects are expected to be, 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 2002; the blue squares show the locations for 2003. There is some overlap of 

field centers in 2002 and 2003 near 9° DEC. Note: The size of the square on the plot does not depict the 

size of the FOV for the telescope. 

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, as 

shown in Figure 20, has different colors representing 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 2 years of data, for which the CTs are solid 

diamonds and the UCTs are open circles. With a larger number of nights collected, it would be possible to 

assess a population from these probability data. This is done in subsequent MODEST reports in which 
20 

more data were collected over the time frame reported. Once the probability chart was created, it was 

determined that FOV locations for future telescope runs could be predetermined by filling in areas of the 

probability chart. In future years, the goal is to have all areas covered with at least some color and to have 

all inclinations less than 15° have a probability of detection of at least 0.6. If this can be achieved, there is 

an excellent rationale for conducting a population assessment. 

Figure 19. Location of field centers. 

Figure 20. Probability of finding specific orbits based on field center locations. 
21 

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 the 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 the north pole, as shown in 

Figure 21. 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 21. 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 

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

from this idealized path, depending on how strong the delta-velocity was they received at breakup. 
22 

The data collected in 2002 and 2003 are shown in Figure 22 and Figure 23, respectively. The plot has four 

subplots, which are termed polar plots due to the coordinate system shown. The upper left images show 

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 and 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 (see the lower right plot), there appears to be an 

inner circle of data in all three data types; however, it is more apparent in the UCT data. The data shown 

for CY 2002 and CY 2003 have similar trends.

Figure 22. Polar coordinates for objects, CY 2002. 
23 

Figure 23. Polar coordinates for objects, CY 2003. 

Figure 24 shows the probability of detection data converted into the polar data and overlaid with the 2002 

and 2003 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 24. Polar coordinates with probability and detections overlaid. 
24 

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 the object 

having too faint a visual magnitude or being outside of the rate box. In addition, the TLE used to predict 

an object’s location could be bad due to an old epoch date or station-keeping maneuvers. It is important to 

understand why an object is not seen, as it aids in understanding 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. However, if a reason cannot be obtained for the no-see, it is labeled as a true no-see. 

Over the 2-year period of 51 nights, 422 nonunique objects were considered no-sees for various reasons. 

Some of these may have been categorized as no-sees multiple times over the 2-year time frame. Of these 

422 no-sees, 77% were due to rate box issues, 5% were due to bad TLE or 80,000s (80,000 objects are 

those that are in the catalog but have not been associated with a specific launch), 5% were due to bad/old 

epochs, and 12% were true no-sees. 

Although an object may not be seen on a certain night, this does not rule out its detection on a different 

night. Of the 349 unique no-see CTs, 50 of these objects were detected and correlated on different nights. 

Of these 50 objects, 66% were rate issues, 32% were true no-sees, and 2% were 80,000s. 

When the total number of detections over the 2-year time frame was compared to the total number of nosees, a rate of 6% was deduced. This means that roughly 50 CTs could have been added to the 838 detected CTs. Assuming this rate is the same for UCTs, approximately 10 UCTs were missed. However, 

assuming the no-see rates for CTs and UCTs are the same could be presumptuous, since UCTs are 

complicated with complex shapes, photometric variations, and generally tend to be fainter than CTs. 

There does not appear to be a difference between the no-see rate for functional vs. nonfunctional CTs due 

to the fact that nonfunctional objects usually had older epochs while functional objects are maneuvered. 

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 rev/day. The graph in Figure 25 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 (97% of the objects collected). In addition, a large percentage of the 

nonfunctional CTs are also seen near 1 (43% of the objects collected). However, more nonfunctional CTs 

are 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 17%; 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 that the ACO calculation is inducing an error 

into the calculation of mean motion for these objects. 

4.6 Inclination Distribution 

As expected, the INC distribution for functional CTs aligns with 0° INC with 94% of the detected objects 

showing in that bin, as seen in Figure 26. Nonfunctional CTs are seen through all INC bins up to 15° to 

16°, as expected due to the propagation of INC with orbital age; see Section 3.2 Search Strategy. The 

nonfunctional CTs have one peak near 5°. The UCTs have a similar spread in INC bins; however, two 

peaks appear to be located near 6° and 12° INC. Although the indication of two peaks could signal the 

location of a breakup, much more data would need to be collected prior to making a definitive statement. 

The data collected in the years following may prove useful in determining the reason for the two peaks. 
Figure 25.

Figu

4.7 RAAN Distribution 

Distribution of RAAN in the functio

As seen previously, the functional 

250°, whereas the nonfunctional C

UCTs are also seen in these data, w

could be an indication of the same t

INC distribution, one peak is locate

25 

. Mean motion distribution for CT and UCT objects. 

ure 26. Distribution of INCs for CTs and UCTs. 

onal CT, nonfunctional CT, and UCT populations is s

CT RAAN calculation concentrates on the region 

CT and UCT populations are seen at all RAAN valu

with the first located near 70° and the second locate

two breakups that were alluded to in the previous se

d with the nonfunctional CTs near 80°. 

shown in Figure 27. 

between 100° and 

ues. Two peaks of 

ed near 350°. This 

ection. As with the 
Figure 27. Distribution of RA

4.8 Absolute Magnitude D

As discussed in previous sections, 

diffuse Lambertian phase function

absolute magnitude is a log calcula

the object. The distribution of absol

the diameters associated with a few 

at 11, corresponding to a size of 4 

size of 2.5 m. The catalog is said to

corresponds to an absolute magnit

detection capabilities of the telescop

throughout the smaller magnitudes. 

MODEST, using the albedo and pha

4.9 RAAN vs. INC Distrib

INC and RAAN distributions for th

the data collected in 2002, and the 

collection of UCTs near 350° RAAN

Similar clustering is observed near 7

no known breakups have occurred in

but more data need to be collected 

climb toward 15° INC for the UCT

RAANs with 0° INC. 

26 

AAN for CTs and UCTs. The location of the data found is biase

field center selection and the DOY. 

Distribution and Derived Diameters 

the derived diameters stem from assuming an albe

n.

6

 A mean distance of 36,000 km is also used. A

ation (unitless); the smaller the number, the brighter

lute magnitudes is shown in Figure 28. Overlaid on t

of the bins. The peak in absolute magnitude for func

m. The peak of the nonfunctional objects is seen n

o be complete down to 1 m at GEO; using the assum

tude of 14.4. The peak of the UCTs is an artifici

pe. It is believed the UCT population will continue 

As described in this report, the smallest detected obj

ase function assumptions, is 10 cm.6

ution 

he detected objects are illustrated in Figure 29. The

bottom figure shows the data collected in 2003. Th

N and 12° INC. This is believed to be the location of

70° RAAN and 5° INC as well as near 90° RAAN and

n those areas. The clusters may indicate locations of 

to confirm these findings. The data in these plots 

Ts and nonfunctional CTs as well as for the functio

ed by the 

edo of 0.175 and a 

As a reminder, the 

r and, likely, larger 

the distribution are 

ctional CTs is seen 

near 12, which is a 

mptions above, this 

ial one due to the 

on the same slope 

ect to be seen with 

e top figure shows 

hese data present a 

f the Titan breakup. 

d 3° INC; however, 

unknown breakups 

show the expected 

nal CTs at various 
27 

Figure 28. Absolute magnitude and derived size distribution, assuming an albedo of 0.175 and 

a diffuse Lambertian phase function. 

Figure 29. RAAN vs. INC for CT and UCT objects. 
28 

5.0 Conclusions 

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

dataset acquired in CY 2002 and CY 2003. Specifically, this report describes the collection and analysis 

of 35 nights of data collected in CY 2002 and of 16 nights of data collected in CY 2003. 

For both years, averages of 22 objects were detected each night. On average in CY 2002, 76% of the 

detections were CTs and 24% were UCTs, whereas in CY 2003 the percentages were 67% and 33% for 

CTs and UCTs, respectively. The variation in percentages between the years may be due to observing 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 0.1

for functional CTs and 0.3 for nonfunctional CTs. Due to the fact that RAAN is ill-defined at values of 

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

RAAN RMS error is 20 for functional objects and 11 for nonfunctional objects in CY 2002, and 57 for 

functional objects and 16 for nonfunctional objects in CY 2003. For CY 2002, the mean motion error is 

0.0005 rev/day for functional and 0.0070 rev/day for nonfunctional objects, and 0.0071 rev/day and 

0.0091 rev/day for functional CTs and nonfunctional CTs, respectively. This error analysis of CT values 

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

distributions. 

The distribution of objects found UCTs clustering in three locations, with only one cluster 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 11th magnitude. An absolute 

magnitude of 11.5 corresponds to objects having 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 a diameter of 

29 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. 

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. 
29 

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. 
30 

Appendix A: 

Fields File Example 

(This is a representative sample of the file) 

 DEC RA Time (sec) 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 
31 

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 
32 

Appendix C 

Correlation Output 

These data are from the correlation file for the two objects listed in Appendix B. The computer program 

correlated one object, and 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: 2002-2003 

 

6. AUTHOR(S) 

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

Parr-Thumm* 

 

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

REPORT NUMBERS

Lyndon B. Johnson Space Center 

Houston, Texas 77058 

S-1073 

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-2010-216128 

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 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 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 (CTIO) 

in Chile, to help characterize the debris 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. This report describes the collection and analysis of 35 nights of data in contract year (CY) 

2002 and 16 nights in CY 2003. Twenty-three objects on average were detected nightly for both years: in CY 2002, 76% were 

correlated targets (CTs) and 24% were uncorrelated targets (UCTs); in CY 2003, 66% were CTs and 34% 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 44 

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