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NASA NTRSDate not supplied

A New Statistical Estimate of the Radar Coverage of the Low Earth Orbit Debris Environment

For over three decades, the NASA Orbital Debris Program Office (ODPO) has used the Goldstone Orbital Debris Radar, Haystack Ultrawideband Satellite Imaging Radar (HUSIR), and Haystack Auxiliary (HAX) radar assets to collect data on the low Earth orbit (LEO) debris environment. Each radar, with its unique beamwidth, altitude and inclination coverage, and limiting size threshold, operates in a beam park mode to statistically sample the orbital debris population in LEO. Provided that these assets are shared with other users, the orbital debris data collection is not continuous; rather, intermittent data collects are acquired and sent to the NASA ODPO. To understand the sampling process conducted by each radar over time and any related observational biases, a Statistical Confirmation of Radar Uniformity or Bias (SCRUB) code has been implemented to model the coverage of these assets for informing future operations, as well as usage of the data collected from these ground-based sensors. For this analysis, Right Ascension of the Ascending Node (RAAN) is used as a metric to measure statistical coverage. A complete survey of the LEO environment is understood to be measurements that sufficiently sample all values of RAAN for each altitude-inclination pair visible from the radar asset. Regions of incompleteness or statistical bias can help inform future observation campaigns. The SCRUB tool evaluates the coverage of the LEO environment, not by examining individual objects that may pass through a sensor’s field of view (FOV), but by determining which orbit planes pass through the FOV. Once a pointing geometry for a radar site, observation time, and range extent are configured by the user, SCRUB computes the inclinations and altitudes that are visible by the sensor. For each inclination-altitude pair, there is a distinct pair of possible RAAN values, corresponding to the ascending and descending orbit passing through that point in the sensor cone. Repeating this process for all points in the beam, and for multiple time periods during an observation window, creates a matrix of all inclination-altitude-RAAN combinations that are visible during a sensor run. This process can then be repeated for all observations within a year (for an annual survey), propagating all the RAAN values to a common epoch, typically the start of a calendar year, and combining the observations to assemble a full estimate of the RAAN coverage of the LEO environment. This RAAN coverage can then be analyzed for uniformity of sampling, within a certain inclination-altitude pair, or between larger regions of the space environment. This paper provides a general overview of the radar assets utilized by ODPO, typical analysis data products assuming circular orbits, and a discussion of the algorithms that feed between modeling and measurement operations. Following the description of the algorithm, estimates of coverage using HUSIR radar data collected from multiple years are developed and compared.

Chris L Ostrom↗
NASA NTRS1990

Summary of the AIAA/NASA/DOD Orbital Debris Conference - Technical issues and future directions

An international conference on orbital debris was held on April 16-19, 1990, in Baltimore, Maryland. Topics of the conference included the implications of orbital debris for space flight, orbital debris measurements, modeling of the orbital debris environment, and methods to reduce the growth of the orbital debris population. Significant results from this meeting are summarized.

Potter, A.↗
NASA NTRS1994

Conceptual design of an Orbital Debris Defense System

Man made orbital debris has become a serious problem. Currently NORAD tracks over 7000 objects in orbit and less than 10 percent of these are active payloads. Common estimates are that the amount of debris will increase at a rate of 10 percent per year. Impacts of space debris with operational payloads or vehicles is a serious risk to human safety and mission success. For example, the impact of a 0.2 mm diameter paint fleck with the Space Shuttle Challenger window created a 2 mm wide by 0.6 mm deep pit. The cost to replace the window was over $50,000. A conceptual design for a Orbital Debris Defense System (ODDS) is presented which considers a wide range of debris sizes, orbits and velocities. Two vehicles were designed to collect and remove space debris. The first would attach a re-entry package to de-orbit very large debris, e.g. inactive satellites and spent upper stages that tend to break up and form small debris. This vehicle was designed to contain several re-entry packages, and be refueled and resupplied with more re-entry packages as needed. The second vehicle was designed to rendezvous with and capture debris ranging from 10 cm to 2 m. Due to tracking limitations, no technically feasible method for collecting debris below 10 cm in size could be devised; it must be accomplished through international regulations which reduce the accumulation of space debris.

Bedillion, Erik↗
NASA NTRSDate not supplied

A Historical Overview of the NASA Orbital Debris Program Office’s Laboratory Optical Measurements

The NASA Orbital Debris Program Office (ODPO) has used laboratory measurements to help bring ground-based measurements together with models to ascertain Earth-orbiting target parameters of interest to support various orbital debris models. In 2005, the Optical Measurement Center (OMC) was established to simulate space-based illumination conditions using equipment and techniques that recreate telescopic observations, particularly source-target-sensor orientations. The intent was to recreate light curves using known aspect angles of known targets and phase angles (angle is defined by the vertex between illumination source-object-detector) to complement telescopic observations that could be used to update the current optical size estimation model (OSEM) – a model that converts object brightness into size for orbital debris models. To support the above goals, the laboratory has undergone several equipment upgrades to increase capabilities over almost 20 years of operation. The primary instrumentation acquires reflectance measurements and includes a solar-like light source, CCD camera with astrometric filters, and robotic arm. A rotary arm was added approximately five years after full operation to allow acquisition through a full 360° range of phase angles. Another part of the OMC instrumentation is a field spectrometer, predominately used for field operations to acquire pre- and post-flight spacecraft material spectral measurements. Additionally, reflectance spectroscopy of various materials is also of interest resulting from hypervelocity impact tests, pristine spacecraft materials, or samples of materials that are used in spacecraft design. These measurements are stored in NASA’s Spectral Material Database, a resource that is still being populated today. The study of spectral measurements also enabled the development of spectral unmixing routines to support the identification of spacecraft materials from spectral data gathered by ground based telescopes. Preliminary OMC investigations focused on feasibility studies to acquire 360° rotation light curves of simple shapes at a single-phase angle and extended to measurements of representative fragments from ground-based explosion tests. To correlate the light curves with ground-based optical measurements, a focused study on high area to mass materials was conducted in support of a newly identified population (at the time) in geosynchronous orbit (GEO) consisting of multi-layered insulation. To further characterize orbital debris, a larger selection of materials was analyzed using laboratory photometric measurements that included representative targets from pristine spacecraft materials and ground-based impact tests. Around 2012, an initiative was requested to understand the feasibility of active debris removal (ADR) of larger targets using grappling methods for spent rocket bodies. Using a priori information on selected targets, scaled-down versions of rocket bodies were generated thanks to improvements in 3D printing technology and machining. These targets were studied in the OMC to understand rotation characteristics. These were compared with telescopic data to determine if the tumble and rotation angles would allow ADR. In 2013, the OMC focused on combining spectral measurements with photometric data to characterize GEO orbital debris. Several years later, NASA acquired a Titan III Transtage test article from “The Boneyard” with a high-resemblance to on-orbit Titan III Transtage rocket bodies, allowing physical access to a representative rocket body that suffered fragmentations in GEO. This prompted the creation of 3D models using lidar technology and spectral measurements of the materials. Focused research also transitioned to specific materials (i.e., solar cells) when telescopic surveys requested characterization of specific GEO targets. In the different research products presented, the focus has been to understand the various parameters that influence optical size estimation, including albedo, phase functions, and brightness variations. Work in this area continues with newer sources of data, including DebriSat, a high-fidelity 56-kg spacecraft replica representative of a modern low Earth orbit (LEO) satellite subjected to a laboratory hypervelocity impact test to understand fragmentation events and to support updates to satellite breakup models and size estimation models. Utilizing the vast population of fragments from DebriSat and prior laboratory impact experiments, the ODPO has focused on acquiring bidirectional reflectance distribution function (BRDF) data to characterize targets in the laboratory, thus removing aspect angle dependencies. Additionally, the DebriSat project has provided improved processes for measuring size via image acquisition, such that a true fragment size can be directly compared to the derived size using the OSEM. The team continues to assess BRDFs and use spectral measurement data to investigate the parameters used in the OSEM, specifically magnitudes, albedo, and phase functions.

Heather Cowardin↗
NASA NTRS1991

The effect of ionospheric reflected noise on the performance of an orbital-debris radar system

An orbital-debris radar system was designed to detect the presence of small objects in low earth orbit by reflecting radio waves off the objects. The author provides a rigorous derivation of the ionospheric reflected noise power and provides an integration over the complete pulse period. Free electrons and ions contained in the ionosphere cause incoherent scatter of the radar signal. This ionospheric reflection tends to increase the noise at the terrestrial radar receiver. A parameter called the ionospheric scattering cross section per unit volume, which is a function of altitude, is useful for computing the power of the ionospheric reflection signal. The Doppler frequency speed of the ionospheric reflected signal is a function of altitude also. The ionospheric noise of a 9-GHz orbital-debris radar receiver is computed using these concepts. Annual and diurnal variations of the noise are included.

Bishop, Dennis F.↗
NASA NTRS2019

Experimentally-Derived Phase Function Approximations in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and elevation angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper presents the initial BRDF and phase function approximations for various fragments/targets acquired in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is used as a baseline for initial size estimation calculations and phase function comparisons. Spacecraft materials and fragments from hypervelocity laboratory impact tests are also presented to compare against the current assumed Lambertian phase function used for size estimates. This paper presents the preliminary phase function analysis and plan forward to utilize a laboratory-based phase function to improve the current optical size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Hostetler, J.↗
NASA NTRS2016

Orbital Debris Program

The attached is a presentation outlining an overview of the orbital debris problem, the NASA Orbital Debris Program Office, and Orbital debris mitigation policy.

Orbital↗
NASA NTRS2025

Time-Dependent Satellite Explosion Probabilities for Long-Term Orbital Debris Environment Modeling

On-orbit accidental explosions are a significant contributor to the growth of the orbital debris population. Certain types of satellites have been seen to exhibit different behaviors and timelines of explosions. Recent assessments of on-orbit explosions for three categories of satellites – Russian Sistema Obespecheniya Zapuska (SOZ, Proton 4th stage attitude and ullage motors) units, spacecraft, and rocket bodies – suggest that on-orbit explosions can be modeled using a continuous, time-dependent probability of explosion. This paper discusses the methodology for developing a time-dependent probability of explosion as a function of the satellite’s orbital lifetime based on historical explosions. The SOZ units are found to be best modeled by a modified Gaussian probability distribution, with the peak probability of explosion occurring around 10.4 years on-orbit. Spacecraft and rocket bodies both exhibit exponentially decaying explosion probabilities, with rocket bodies showing fast-, medium-, and slow-time modes of decay. Total cumulative probabilities of explosion are approximately 57% for SOZ units, 4% for spacecraft, and 2% for rocket bodies. Examples of implementation in a simulation of the orbital debris environment using NASA's long-term evolutionary model are given, showing the overall explosion behavior over two centuries is significantly different from that using a previously implemented constant-probability type-dependent explosion rate model and provides a better representation of the historical explosion record.

Alyssa P Manis↗
NASA NTRS1992

Radar detection of centimeter-sized orbital debris - Preliminary Arecibo observations at 12.5-cm wavelength

Orbital debris objects with sizes of 6 mm and larger were detected when they passed through the main beam of the high-power, 12.6-cm wavelength radar at the Arecibo Observatory. The number of objects detected at altitudes below 1000 km in the size range of 6 mm to 2 cm agreed with orbital debris model predictions to better than a factor of two. Radar detections of larger orbital debris (10-cm diameter and above) were also compared with the objects in the U.S. Space Command catalog (the cataloged objects have UHF radar cross-sections larger than 0.01 sq m). This experiment demonstrated that the large, earth-based radar telescopes normally used for planetary studies can provide useful data about the near-earth orbital debris populations.

Thompson, T. W.↗
NASA NTRS2008

Optical Studies of Orbital Debris at GEO Using Two Telescopes

Beginning in March, 2007, optical observations of debris at geosynchronous orbit (GEO) were commenced using two telescopes simultaneously at the Cerro Tololo Inter-American Observatory (CTIO) in Chile. The University of Michigan's 0.6/0.9-m Schmidt telescope MODEST (for Michigan Orbital DEbris Survey Telescope) was used in survey mode to find objects that potentially could be at GEO. Because GEO objects only appear in this telescope's field of view for an average of 5 minutes, a full six-parameter orbit can not be determined. Interrupting the survey for follow-up observations leads to incompleteness in the survey results. Instead, as objects are detected on MODEST, initial predictions assuming a circular orbit are done for where the object will be for the next hour, and the objects are reacquired as quickly as possible on the CTIO 0.9-m telescope. This second telescope then follows-up during the first night and, if possible, over several more nights to obtain the maximum time arc possible, and the best six parameter orbit. Our goal is to obtain an initial orbit for all detected objects fainter than R = 15th in order to estimate the orbital distribution of objects selected on the basis of two observational criteria: magnitude and angular rate. Objects fainter than 15th are largely uncataloged and have a completely different angular rate distribution than brighter objects. Combining the information obtained for both faint and bright objects yields a more complete picture of the debris environment rather than just concentrating on the faint debris. One objective is to estimate what fraction of objects selected on the basis of angular rate are not at GEO. A second objective is to obtain magnitudes and colors in standard astronomical filters (BVRI) for comparison with reflectance spectra of likely spacecraft materials. This paper reports on results from two 14 night runs with both telescopes: in March and November 2007: (1) A significant fraction of objects fainter than R = 15th have eccentric orbits (e > 0.1) (2) Virtually all objects selected on the basis of angular rate are in the GEO and GTO regimes. (3) Calibrated magnitudes and colors in BVRI were obtained for many objects fainter than R = 15th magnitude. This work is supported by NASA's Orbital Debris Program Office, Johnson Space Center, Houston, Texas, USA.

Seitzer, P.↗
NASA NTRSDate not supplied

Laboratory Radar Measurements in Support of the NASA Orbital Debris Program Office’s Size Estimation Model

The NASA Orbital Debris Program Office (ODPO) relies on ground-based radar measurements from both the Haystack Ultrawideband Satellite Imaging Radar (HUSIR) and the Goldstone Solar System Radar (Goldstone) to characterize mm to cm debris population in low Earth orbit (LEO). Radar measurements help characterize the size of orbital debris objects, particularly fragmentation debris. However, debris size is not directly measured by radar but inferred from the measured radar cross section (RCS) which depends on several parameters in addition to physical size including electrical conductivity and polarization. To interpret the observed RCS of orbital debris objects detected by radar measurements as physical sizes, NASA uses an empirical size estimation model (SEM) based on laboratory RCS measurements of breakup fragments generated during hypervelocity impact tests as well as some pieces of non-impact-generated “artificial” debris-like objects expected to be representative of the debris population. Since the development of the ODPO SEM, many new materials have been introduced to spacecraft construction. Consequently, ODPO plans to update the radar SEM based on planned laboratory RCS measurements of debris fragments from DebriSat, a ground-based hypervelocity impact experiment conducted in 2014 that consisted of a high-fidelity spacecraft model characteristic of a modern LEO spacecraft. Prior to measuring DebriSat fragments, a set of calibration targets with well-defined geometries and material compositions were measured at The Ohio State University’s ElectroScience Laboratory (OSU-ESL) compact radar range. These calibration measurements help to validate, and understand any limitations of, laboratory measurements of RCS. Calibration targets include idealizations of typical shape categories seen in DebriSat fragments such as nuggets, flat plates, and cylinders. As with DebriSat, calibration target materials were chosen to represent typical modern-day spacecraft components and include stainless steel, aluminum, printed circuit board (PCB) substrate, and carbon fiber-reinforced polymer (CFRP). These materials also represent a wide range of electrical conductivities, which strongly influences measured RCS and inferred target size. The RCS calibration measurements were collected over a frequency sweep from 2 to 18 GHz and stepping through different azimuth angles from 0 to 360 degrees at an elevation of 0 degrees. A second set of calibration measurements is in work consisting of more complex shapes such as bent rods and plates as well as different mounting options including epoxy and a 3D printed holder. These further measurements along with our initial calibration set will inform selection of representative DebriSat fragments for laboratory RCS measurements that will contribute to the planned update to the ODPO radar SEM. An appropriate subset of both the radar calibration and DebriSat samples will also be measured in the ODPO Optical Measurements Center to cross-calibrate size estimates over these different wavelength regimes.

Radar↗
NASA NTRS2009

In Situ Measurement Activities at the NASA Orbital Debris Program Office

The NASA Orbital Debris Program Office has been involved in the development of several particle impact instruments since 2003. The main objective of this development is to eventually conduct in situ measurements to better characterize the small (millimeter or smaller) orbital debris and micrometeoroid populations in the near-Earth environment. In addition, the Office also supports similar instrument development to define the micrometeoroid and lunar secondary ejecta environment for future lunar exploration activities. The instruments include impact acoustic sensors, resistive grid sensors, fiber optic displacement sensors, and impact ionization sensors. They rely on different mechanisms and detection principles to identify particle impacts. A system consisting of these different sensors will provide data that are complimentary to each other, and will provide a better description of the physical and dynamical properties (e.g., size, mass, and impact speed) of the particles in the environment. Details of several systems being considered by the Office and their intended mission objectives are summarized in this paper.

Liou, J.-C.↗
NASA NTRS2014

The New NASA Orbital Debris Engineering Model ORDEM 3.0

The NASA Orbital Debris Program Office (ODPO) has released its latest Orbital Debris Engineering Model, ORDEM 3.0. It supersedes ORDEM 2.0. This newer model encompasses the Earth satellite and debris flux environment from altitudes of low Earth orbit (LEO) through geosynchronous orbit (GEO). Debris sizes of 10 microns through 1 m in non-GEO and 10 cm through 1 m in GEO are modeled. The inclusive years are 2010 through 2035. The ORDEM model series has always been data driven. ORDEM 3.0 has the benefit of many more hours from existing data sources and from new sources that weren't available to past versions. Returned surfaces, ground tests, and remote sensors all contribute data. The returned surface and ground test data reveal material characteristics of small particles. Densities of fragmentation debris particles smaller than 10 cm are grouped in ORDEM 3.0 in terms of high-, medium-, and lowdensities, along with RORSAT sodium-potassium droplets. Supporting models have advanced significantly. The LEO-to-GEO ENvironment Debris model (LEGEND) includes an historical and a future projection component with yearly populations that include launched and maneuvered intacts, mission related debris (MRD), and explosion and collision fragments. LEGEND propagates objects with ephemerides and physical characteristics down to 1 mm in size. The full LEGEND yearly population acts as an a priori condition for a Bayesian statistical model. Specific, well defined populations are added like the Radar Ocean Reconnaissance Satellite (RORSAT) sodium-potassium (NaK) droplets, recent major accidental and deliberate collision fragments, and known anomalous debris event fragments. For microdebris of sizes 10 microns to 1 mm the ODPO uses an in-house Degradation/Ejecta model in which a MLE technique is used with returned surface data to estimate populations. This paper elaborates on the upgrades of this model over previous versions highlighting the material density splits and consequences of that to the penetration risk to spacecraft.

Krisko, P. H.↗
NASA NTRS2014

The New NASA Orbital Debris Engineering Model ORDEM 3.0

The NASA Orbital Debris Program Office (ODPO) has released its latest Orbital Debris Engineering Model, ORDEM 3.0. It supersedes ORDEM 2000, now referred to as ORDEM 2.0. This newer model encompasses the Earth satellite and debris flux environment from altitudes of low Earth orbit (LEO) through geosynchronous orbit (GEO). Debris sizes of 10 micron through larger than 1 m in non-GEO and 10 cm through larger than 1 m in GEO are available. The inclusive years are 2010 through 2035. The ORDEM model series has always been data driven. ORDEM 3.0 has the benefit of many more hours of data from existing sources and from new sources than past ORDEM versions. The object data range in size from 10 μm to larger than 1 m, and include in situ and remote measurements. The in situ data reveals material characteristics of small particles. Mass densities are grouped in ORDEM 3.0 in terms of 'high-density', represented by 7.9 g/cc, 'medium-density' represented by 2.8 g/cc and 'low-density' represented by 1.4 g/cc. Supporting models have also advanced significantly. The LEO-to-GEO ENvironment Debris model (LEGEND) includes an historical and a future projection component with yearly populations that include launched and maneuvered intact spacecraft and rocket bodies, mission related debris, and explosion and collision event fragments. LEGEND propagates objects with ephemerides and physical characteristics down to 1 mm in size. The full LEGEND yearly population acts as an a priori condition for a Bayesian statistical model. Specific populations are added from sodium potassium droplet releases, recent major accidental and deliberate collisions, and known anomalous debris events. This paper elaborates on the upgrades of this model over previous versions. Sample validation results with remote and in situ measurements are shown, and the consequences of including material density are discussed as it relates to heightened risks to crewed and robotic spacecraft

Krisko, P. H.↗
NASA NTRS2024

The NASA Orbital Debris Program Office - In Service of Space Safety

Since the NASA Orbital Debris Program Office’s (ODPO) founding in 1979 at the Johnson Space Center in Houston, Texas, it has been at the forefront of orbital debris research, modeling, and policy development. The ODPO has worked in collaboration with NASA and other U.S. government missions since the 1980s to mitigate the growth of the orbital debris environment and protect the population of the Earth. Two main products from the ODPO, the Orbital Debris Engineering Model (ORDEM) and the Debris Assessment Software (DAS), are frequently among the top three most-downloaded software packages from the NASA Software Catalog. These products are provided free of charge to the public in furtherance of the goal to ensure that new space missions, in compliance with NASA’s orbital debris mitigation requirements, are developed, operated, and disposed of responsibly. In addition to these external-facing software tools, the ODPO maintains high-fidelity internal tools for reentry simulation (the Object Reentry Survival Analysis Tool, ORSAT), short-term risk assessment for robotic and human spaceflight missions (the Satellite Breakup Risk Assessment Module, SBRAM), among others. Using data from the ORDEM model, as well as using the Meteoroid Environment Model (MEM) developed by the Meteoroid Environment Office (MEO) at NASA’s Marshall Space Flight Center, the Hypervelocity Impact Technology (HVIT) team uses the BUMPER code to assess penetration risk to space vehicles in Earth orbit and beyond. This paper will discuss the services that the ODPO and HVIT provide, from mission concept development through end-of-mission, for NASA-related and commercial missions.

Chris Ostrom↗
NASA NTRS1993

Orbital debris and near-Earth environmental management: A chronology

This chronology covers the 32-year history of orbital debris and near-Earth environmental concerns. It tracks near-Earth environmental hazard creation, research, observation, experimentation, management, mitigation, protection, and policy-making, with emphasis on the orbital debris problem. Included are the Project West Ford experiments; Soviet ASAT tests and U.S. Delta upper stage explosions; the Ariane V16 explosion, U.N. treaties pertinent to near-Earth environmental problems, the PARCS tests; space nuclear power issues, the SPS/orbital debris link; Space Shuttle and space station orbital debris issues; the Solwind ASAT test; milestones in theory and modeling the Cosmos 954, Salyut 7, and Skylab reentries; the orbital debris/meteoroid research link; detection system development; orbital debris shielding development; popular culture and orbital debris; Solar Max results; LDEF results; orbital debris issues peculiar to geosynchronous orbit, including reboost policies and the stable plane; seminal papers, reports, and studies; the increasing effects of space activities on astronomy; and growing international awareness of the near-Earth environment.

Portree, David S. F.↗
NASA NTRS2006

Calculating Statistical Orbit Distributions Using GEO Optical Observations with the Michigan Orbital Debris Survey Telescope (MODEST)

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit suitable for tracking purposes. Telescopes operating in survey mode, however, randomly observe objects that pass through their field of view. Typically, these short-arc observation are inadequate to obtain detailed orbits, but can be used to estimate approximate circular orbit elements (semimajor axis, inclination, and ascending node). From this information, it should be possible to make statistical inferences about the orbital distributions of the GEO population bright enough to be observed by the system. The Michigan Orbital Debris Survey Telescope (MODEST) has been making such statistical surveys of the GEO region for four years. During that time, the telescope has made enough observations in enough areas of the GEO belt to have had nearly complete coverage. That means that almost all objects in all possible orbits in the GEO and near- GEO region had a non-zero chance of being observed. Some regions (such as those near zero inclination) have had good coverage, while others are poorly covered. Nevertheless, it is possible to remove these statistical biases and reconstruct the orbit populations within the limits of sampling error. In this paper, these statistical techniques and assumptions are described, and the techniques are applied to the current MODEST data set to arrive at our best estimate of the GEO orbit population distribution.

Matney, M.↗