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Feasibility for Orbital Life Extension of a CubeSat in the Lower Thermosphere

Orbital flight of CubeSats at altitudes between 150 and 250 km has the potential to enable a new class of scientific, commercial, and defense-related missions. A study is presented to demonstrate the feasibility of extending the orbital lifetime of a CubeSat in a 210 km orbit. Propulsion consists of an electrospray thruster operating at a 2 W, 0.175 mN thrust, and an specific impulse (Isp) of 500 s. The mission consists of two phases. In phase 1, the CubeSat is deployed from a 414 km orbit and uses the thruster to deorbit to the target altitude of 210 km. In phase 2, the propulsion system is used to extend the mission lifetime until propellant is fully expended. A control algorithm based on maintaining a target orbital energy is presented that uses an extended Kalman filter to generate estimates of the orbital dynamic state, which are periodically updated by Global Positioning System measurements. For phase 1, the spacecraft requires 25.21 days to descend from 414 to 210 km, corresponding to a delta V = 96.25 m/s and a propellant consumption of 77.8 g. Phase 2 lasts 57.83 days, corresponding to a delta V = 119.15 m/s, during which the remaining 94.2 g of propellant are consumed.

Blandino, John J.↗

Direct Imaging of a Cold Jovian Exoplanet in Orbit around the Sun-Like Star GJ 504

Several exoplanets have recently been imaged at wide separations of >10 AU from their parent stars. These span a limited range of ages (<50 Myr) and atmospheric properties, with temperatures of 800-1800 K and very red colors (J −H > 0.5 mag), implying thick cloud covers. Furthermore, substantial model uncertainties exist at these young ages due to the unknown initial conditions at formation, which can lead to an order of magnitude of uncertainty in the modeled planet mass. Here, we report the direct imaging discovery of a Jovian exoplanet around the Sun-like star GJ 504, detected as part of the SEEDS survey. The system is older than all other known directly-imaged planets; as a result, its estimated mass remains in the planetary regime independent of uncertainties related to choices of initial conditions in the exoplanet modeling. Using the most common exoplanet cooling model, and given the system age of 160(+350/−60) Myr, GJ 504 b has an estimated mass of 4(+4.5/−1.0) Jupiter masses, among the lowest of directly imaged planets. Its projected separation of 43.5 AU exceeds the typical outer boundary of approx.. 30 AU predicted for the core accretion mechanism. GJ 504 b is also significantly cooler (510(+30/−20) K)) and has a bluer color (J − H = −0.23 mag) than previously imaged exoplanets, suggesting a largely cloud-free atmosphere accessible to spectroscopic characterization. Thus, it has the potential of providing novel insights into the origins of giant planets, as well as their atmospheric properties.

exoplanets↗

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 2: User's manual for earth orbital MAPSEP

The trajectory simulation mode (SIMSEP) requires the namelist SIMSEP to follow TRAJ. The SIMSEP contains parameters which describe the scope of the simulation, expected dynamic errors, and cumulative statistics from previous SIMSEP runs. Following SIMSEP are a set of GUID namelists, one for each guidance correction maneuver. The GUID describes the strategy, knowledge or estimation uncertainties and cumulative statistics for that particular maneuver. The trajectory display mode (REFSEP) requires only the namelist TRAJ followed by scheduling cards, similar to those used in GODSEP. The fixed field schedule cards define: types of data displayed, span of interest, and frequency of printout. For those users who can vary the amount of blank common storage in their runs, a guideline to estimate the total MAPSEP core requirements is given. Blank common length is related directly to the dimension of the dynamic state (NDIM) used in transition matrix (STM) computation, and, the total augmented (knowledge) state (NAUG). The values of program and blank common must be added to compute the total decimal core for a CDC 6500. Other operating systems must scale these requirements appropriately.

Source record↗

Fires and Smoke Observed from the Earth Observing System MODIS Instrument: Products, Validation, and Operational Use

The MODIS sensor, launched on NASA's Terra satellite at the end of 1999, was designed with 36 spectral channels for a wide array of land, ocean, and atmospheric investigations. MODIS has a unique ability to observe fires, smoke, and burn scars globally. Its main fire detection channels saturate at high brightness temperatures: 500 K at 4 microns and 400 K at 11 microns, which can only be attained in rare circumstances at the I kin fire detection spatial resolution. Thus, unlike other polar orbiting satellite sensors with similar thermal and spatial resolutions, but much lower saturation temperatures (e.g. AVHRR and ATSR), MODIS can distinguish between low intensity ground surface fires and high intensity crown forest fires. Smoke column concentration over land is for the first time being derived from the MOMS solar channels, extending from 0.41 microns to 2.1 microns. The smoke product has been provisionally validated both globally and regionally over southern Africa and central and south America. Burn scars are observed from MODIS even in the presence of smoke, using the 1.2 to 2.1 micron channels. MODIS burned area information is used to estimate pyrogenic emissions. A wide range of these fire and related products and validation are demonstrated for the wild fires that occurred in northwestern United States in the summer of 2000. The MODIS rapid response system and direct broadcast capability is being developed to enable users to obtain and generate data in near real time. It is expected that health and land management organizations will use these systems for monitoring the occurrence of fires and the dispersion of smoke within two to six hours after data acquisition.

Kaufman, Y. J.↗

Deriving Mercury Geodetic Parameters with Altimetric Crossovers from the Mercury Laser Altimeter (MLA)

Based on the previous applications of laser altimetry to planetary geodesy at GSFC, we use the recently developed PyXover software package to analyze altimetric crossovers from the Mercury Laser Altimeter (MLA). Using PyXover, we place new constraints on Mercury's geodetic parameters via least squares minimization of crossover discrepancies. We simultaneously solve for orbital corrections for each MLA ground track, for the geodetic parameters of the International Astronomical Union-recommended orientation model for Mercury (pole right-ascension and declination coordinates, prime meridian rotation rate, and librations), and for the Mercury's Love number h2. We calibrate the formal errors of our solution based on closed-loop simulations and on the level of robustness against a priori values, data selection, and parametrization. Our solution of the Mercury's rotational parameters is consistent with published values. In particular, our new estimate for the orientation of the pole places Mercury in a Cassini state, with an obliquity ϵ = 2.031 ± 0.03 arcmin compatible with previous “surface” related measurements. Moreover, we provide a first data-based estimate of the Love number h_(2) = 1.55 ± 0.65. The latter is consistent with expectations from models of Mercury's interior, although its precision does not enable their refinement.

S. Bertone↗

A Numerical Approach to Estimate the Ballistic Coefficient of Space Debris from TLE Orbital Data

Low Earth Orbit (LEO) is full of space debris, which consist of spent rocket stages, old satellites and fragments from explosions and collisions. As of 2009, more than 21,000 orbital debris larger than 10 cm are known to exist], and while it is hard to track anything smaller than that, the estimated population of particles between 1 and 10 cm in diameter is approximately 500,000, whereas small as 1 cm exceeds 100 million. These objects orbit Earth with huge kinetic energies speeds usually exceed 7 kms. The shape of their orbit varies from almost circular to highly elliptical and covers all LEO, a region in space between 160 and 2,000 km above sea level. Unfortunately, LEO is also the place where most of our active satellites are situated, as well as, International Space Station (ISS) and Hubble Space Telescope, whose orbits are around 400 and 550 km above sea level, respectively.This poses a real threat as debris can collide with satellites and deal substantial damage or even destroy them.Collisions between two or more debris create clouds of smaller debris, which are harder to track and increase overall object density and collision probability. At some point, the debris density couldthen reach a critical value, which would start a chain reaction and the number of space debris would grow exponentially. This phenomenon was first described by Kessler in 1978 and he concluded that it would lead to creation of debris belt, which would vastly complicate satellite operations in LEO. The debris density is already relatively high, as seen from several necessary debris avoidance maneuvers done by Shuttle, before it was discontinued, and ISS. But not all satellites have a propulsion system to avoid collision, hence different methods need to be applied. One of the proposed collision avoidance concepts is called LightForce and it suggests using photon pressure to induce small orbital corrections to deflect debris from colliding. This method is very efficient as seen from theoretical simulations, even few continuous mode 10 kW ground-based lasers, focused by 1.5 m telescopes with adaptive optics, were enough to prevent significant amount of the debris collisions. Simulations were done by propagating all space objects in LEO by 1 year into the future and checking whether the probability of collision was high. For those space objects different ground-based lasers were used to divert them, afterwards collision probabilities were reevaluated. However, the actual accuracy of the LightForce software, which has been developed at NASA AmesResearch Center, depends on the veracity of the input parameters, one of which is the objects ballistic coefficient. It is a measure of bodys ability to overcome air resistance, which has a significant impact on the debris in LEO, and thus it is responsible for the shape of the trajectory of the debris. Having the exact values of the ballistic coefficient would make significantly better collision predictions, unfortunately, we do not know what are the values for most of the objects.In this research, we were working with part of LightForce code, which estimates the ballistic coefficient from ephemerides. Previously used method gave highly inaccurate values, when compared to known objects, and it needed to be changed. The goal of this work was to try out a different method of estimating the ballistic coefficient and to check whether or not it gives noticeable improvements.

Collisions↗

Geologic analysis of averaged magnetic satellite anomalies

To investigate relative advantages and limitations for quantitative geologic analysis of magnetic satellite scalar anomalies derived from arithmetic averaging of orbital profiles within equal-angle or equal-area parallelograms, the anomaly averaging process was simulated by orbital profiles computed from spherical-earth crustal magnetic anomaly modeling experiments using Gauss-Legendre quadrature integration. The results indicate that averaging can provide reasonable values at satellite elevations, where contributing error factors within a given parallelogram include the elevation distribution of the data, and orbital noise and geomagnetic field attributes. Various inversion schemes including the use of equivalent point dipoles are also investigated as an alternative to arithmetic averaging. Although inversion can provide improved spherical grid anomaly estimates, these procedures are problematic in practice where computer scaling difficulties frequently arise due to a combination of factors including large source-to-observation distances ( 400 km), high geographic latitudes, and low geomagnetic field inclinations.

Goyal, H. K.↗

Shuttle rendezvous radar performance evaluation and simulation

The US Space Shuttle's Ku-band system was specifically designed for communications and tracking functions which are required during on-orbit operations with other spacecraft. Operating modes permit search and acquisition to be accomplished by computer designation or under manual control by the astronaut. Ku-band system data channels drive on-board dedicated displays and are incorporated into state vector updates by Shuttle guidance and navigation computers. Radar-cross-section estimates were used in computer simulations to predict the range at which radar detection and acquisition can be expected. Validity of the simulationi model and the radar design and performance were verified by flight tests on the White Sands test range. It is concluded that results of the testing established confidence in the capability of the system to provide the relative position and rate information which is needed for Shuttle work involving other spacecraft.

Griffin, John W.↗

Attitude Ground System (AGS) For The Magnetospheric Multi-Scale (MMS) Mission

The Magnetospheric Multiscale (MMS) mission is a Solar-Terrestrial Probe mission consisting of four identically instrumented spin-stabilized spacecraft flying in an adjustable pyramid-like formation around the Earth. The formation of the MMS spacecraft allows for three-dimensional study of the phenomenon of magnetic reconnection, which is the primary objective of the mission. The MMS spacecraft were launched early on March 13, 2015 GMT. Due to the challenging and very constricted attitude and orbit requirements for performing the science, as well as the need to maintain the spacecraft formation, multiple ground functionalities were designed to support the mission. These functionalities were incorporated into a ground system known as the Attitude Ground System (AGS). Various AGS configurations have been used widely to support a variety of three-axis-stabilized and spin-stabilized spacecraft missions within the NASA Goddard Space Flight Center (GSFC). The original MMS operational concept required the AGS to perform highly accurate predictions of the effects of environmental disturbances on the spacecraft orientation and to plan the attitude maneuvers necessary to stay within the science attitude tolerance. The orbit adjustment requirements for formation control drove the need also to perform calibrations that have never been done before in support of NASA GSFC missions. The MMS mission required support analysts to provide fast and accurately calibrated values of the inertia tensor, center of mass, and accelerometer bias for each MMS spacecraft. During early design of the AGS functionalities, a Kalman filter for estimating the attitude, body rates, center of mass, and accelerometer bias, using only star tracker and accelerometer measurements, was heavily analyzed. A set of six distinct filters was evaluated and considered for estimating the spacecraft attitude and body rates using star tracker data only. Four of the six filters are closely related and were compared during support of the Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Space Technology-5 (ST-5) missions. These analyses exposed high dependency and sensitivity on the knowledge of the spacecraft inertia tensor for both body rates and accelerometer bias estimation. The conclusion of the analysis led to the design of an inertia tensor calibration technique using only star tracker data. The second most important result of the analysis was the design of two separate Kalman filters to estimate the spacecraft attitude and body rates and the accelerometer bias instead of a single combined filter. In this paper, the calibration results of the mass properties, as well as the performance of the spacecraft attitude and body rates filters using flight data are presented and compared against the mission requirements.

Estimation↗

Advanced space system concepts and their orbital support needs (1980 - 2000). Volume 3: Detailed data. Part 1: Catalog of initiatives, functional options, and future environments and goals

The following areas were discussed in relation to a study of the commonality of space vehicle applications to future national needs: (1) index of initiatives (civilian observation, communication, support), brief illustrated description of each initiative, time periods (from 1980 to 2000+) for implementation of these initiatives; (2) data bank of functional system options, presented in the form of data sheets, one for each of the major functions, with the system option for near-term, midterm, and far-term space projects applicable to each subcategory of functions to be fulfilled; (3) table relating initiatives and desired goals (public service and humanistic, materialistic, scientific and intellectual); and (4) data on size, weight and cost estimations.

Bekey, I.↗

An Investigation of Multipath Effects on the GPS System During Auto-Rendezvous and Capture

The proposed use of a Cargo Transport Vehicle (CTV) to carry hardware to the Space Station Freedom (SSF) during the construction phase of the SSF project requires remote maneuvering of the CTV. The CTV is not a manned vehicle. Obtaining the relative positions of the CTV and SSF for remote auto-rendezvous and capture (AR&C) scenarios will rely heavily on the Global Positioning System (GPS). The GPS system is expected to guide the CTV up to a distance of 100 to 300 meters from the SSF. At some point within this range, an optical docking system will take over the remote guidance for capture. During any remote guidance by GPS it is possible that significant multipath signals may be caused by large objects in the vicinity of the module being remotely guided. This could alter the position obtained by the GPS system from the actual position. Due to the nature of the GPS signals, it has been estimated that if the difference in distance between the Line of Sight (LOS) path and the multipath is greater than 300 meters, the GPS system is capable of discriminating between the direct signal and the reflected (or multipath) signal. However, if the path difference is less than 300 meters, one must be concerned. This report details the work accomplished by the Electromagnetic Simulations Laboratory at Marquette University over the period December 1993 to May 1995. This work is an investigation of the strength and phase of a multipath signal arriving at the CTV relative to the direct or line of sight (LOS) signal. The signal originates at a GPS satellite in half geo-stationary orbit and takes two paths to the CTV: (1) the direct or LOS path from the GPS satellite to the CTV; and (2) a scattered path from the GPS satellite to the SSF module and then to the CTV. The scattering from a cylinder has been computed using the physical optics approximation for the current. No other approximations or assumptions have been made including no assumptions regarding the far field or Fresnel field approximations. The integrations required to obtain the scattered field have been computed numerically using an N dimensional Romberg integration. The total scattered electric field is then projected onto the RCP component in the direction of propagation only. The direct or line of sight signal is then used to compute the relative strength and phase of the scattered field. The trajectory of the CTV has been parameterized into 4,214 points that are calculated for each of the geometries investigated. The motion of the CTV between points is small enough for the magnitude data (dB down from direct signal) to appear very smooth; however, because of the distances and wavelengths involved, the phase of the scattered field relative to the direct signal varies very rapidly.

Richie, James E.↗

Analysis of normalized radar cross section (sigma-O) signature of Amazon rain forest using SEASAT scatterometer data

The normalized radar cross section (NRCS) signature of the Amazon rain forest was SEASAT scatterometer data. Statistics of the measured (NRCS) values were determined from multiple orbit passes for three local time periods. Plots of mean normalized radar cross section, dB against incidence angle as a function of beam and polarization show that less than 0.3 dB relative bias exists between all beams over a range of incidence angle from 30 deg to 53 deg. The backscattered measurements analyzed show the Amazon rain forest to be relatively homogeneous, azimuthally isotropic and insensitive to polarization. The return from the rain forest target appears relatively consistent and stable, except for the small diurnal variation (0.75 dB) that occurs at sunrise. Because of the relative stability of the rain forest target and the scatterometer instrument, the response of versus incidence angle was able to detect errors in the estimated yaw altitude angle. Also, small instrument gain biases in some of the processing channels were detected. This led to the development of an improved NRCS algorithm, which uses a more accurate method for estimating the system noise power.

Bracalente, E. M.↗

Comparison of Southern Hemisphere radiosonde and LIMS temperatures at 100 mb

Radiosonde (RS)and satellite-derived (Nimbus-7 LIMS) 100-mb temperatures over New Zealand at 12 GMT are compared for the 1978-79 summer. The colocated LIMS temperature information consists of synoptically mapped values (for 12 GMT), as well as the primary nighttime orbital retrievals valid at about 1030 GMT. The RS time series of temperature is dominated by temporal fluctuations associated mainly with the eastward passage of waves which have characteristic periods of 4-5 and 11-12 days and peak-to-peak amplitudes of 10-15 K. The LIMS temperatures and the corresponding temperature time series are also found to exhibit quite close agreement (in terms of temporal phase for the latter) with the RS data. However, the LIMS-mapped temperature fluctuations suffer from a noticeable attenuation in amplitude (approaching 50 percent for higher-frequency fluctuations), which will affect the accuracy of LIMS-derived estimates of dynamical quantities such as wind velocity and relative vorticity in the lower stratosphere.

Miles, T.↗

Determination of GPS orbits to submeter accuracy

Orbits for satellites of the Global Positioning System (GPS) were determined with submeter accuracy. Tests used to assess orbital accuracy include orbit comparisons from independent data sets, orbit prediction, ground baseline determination, and formal errors. One satellite tracked 8 hours each day shows rms error below 1 m even when predicted more than 3 days outside of a 1-week data arc. Differential tracking of the GPS satellites in high Earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the full GPS constellation. To demonstrate this capability, baselines of up to 2000 km in North America were also determined with the GPS orbits. The 2000 km baselines show rms daily repeatability of 0.3 to 2 parts in 10 to the 8th power and agree with very long base interferometry (VLBI) solutions at the level of 1.5 parts in 10 to the 8th power. This GPS demonstration provides an opportunity to test different techniques for high-accuracy orbit determination for high Earth orbiters. The best GPS orbit strategies included data arcs of at least 1 week, process noise models for tropospheric fluctuations, estimation of GPS solar pressure coefficients, and combine processing of GPS carrier phase and pseudorange data. For data arc of 2 weeks, constrained process noise models for GPS dynamic parameters significantly improved the situation.

Bertiger, W. I.↗

Calibration of TOPEX/POSEIDON at Platform Harvest

We present estimates for the mean bias of the TOPEX/POSEIDON NASA altimeter (ALT) and the Centre National d'Etudes Spatiales altimeter (SSALT) using in-situ data gathered at Platform Harvest during the first 36 cycles of the mission. Data for 21 overflights of the ALT and six overflights of the SSALT have been analyzed. The analysis includes an independent assessment of in-situ measurements of sea level, the radial component of the orbit, wet tropospheric path delay, and ionospheric path delay. (The sign convention used is such that, to correct the geophysical data record values for sea level, add the bias algebraically. Unless otherwise stated, the uncertainty in a given parameter is depicted by +/- sigma(sub x), where sigma(sub x) is the sample standard deviation of x about the mean.) Tide gauges at Harvest provide estimates of sea level with an uncertainty of +/- 1.5 cm. The uncertainty in the radial component of the orbit is estimated to be +/- 1.3 cm. In-situ measurements of tropopsheric path delay at Harvest compare to within +/- 1.3 cm of the TOPEX/POSEIDON microwave radiometer, and in-situ measurements of the ionospheric path delay compare to within -0.4 +/- 0.7 cm of the dual-frequency ALT and 1.1 +/- 0.6 cm of Doppler orbitography and radiopositioning integrated by satellite. We obtain mean bias estimates of -14.5 +/- 2.9 cm for the ALT and +0.9 +/- 3.1 cm for the SSALT (where the uncertainties are based on the standard deviation of the estimated mean (sigma(sub bar x/y), which is derived from sample statistics and estimates for errors that cannot be observed). These results are consistent with independent estimates for the relative bias between the two altimeters. A linear regression applied to the complete set of data shows that there is a discernable secular trend in the time series for the ALT bias estimates. A preliminary analysis of data obtained through cycle 48 suggests that the apparent secular drift may be the result of a poorly sampled annual signal.

Christensen, E. J.↗

Spacecraft Charging and the Microwave Anisotropy Probe Spacecraft

The Microwave Anisotropy Probe (MAP), a MIDEX mission built in partnership between Princeton University and the NASA Goddard Space Flight Center (GSFC), will study the cosmic microwave background. It will be inserted into a highly elliptical earth orbit for several weeks and then use a lunar gravity assist to orbit around the second Lagrangian point (L2), 1.5 million kilometers, anti-sunward from the earth. The charging environment for the phasing loops and at L2 was evaluated. There is a limited set of data for L2; the GEOTAIL spacecraft measured relatively low spacecraft potentials (approx. 50 V maximum) near L2. The main area of concern for charging on the MAP spacecraft is the well-established threat posed by the "geosynchronous region" between 6-10 Re. The launch in the autumn of 2000 will coincide with the falling of the solar maximum, a period when the likelihood of a substorm is higher than usual. The likelihood of a substorm at that time has been roughly estimated to be on the order of 20% for a typical MAP mission profile. Because of the possibility of spacecraft charging, a requirement for conductive spacecraft surfaces was established early in the program. Subsequent NASCAP/GEO analyses for the MAP spacecraft demonstrated that a significant portion of the sunlit surface (solar cell cover glass and sunshade) could have nonconductive surfaces without significantly raising differential charging. The need for conductive materials on surfaces continually in eclipse has also been reinforced by NASCAP analyses.

Timothy, VanSant J.↗

Status of Validation Program for Tropical Rainfall Measuring Mission (TRMM)

The Tropical Rainfall Measuring Mission (TRMM) is in its sixth year of operation. This successful research mission, a joint U.S./Japan effort, has become-a key element in the routine monitoring of global precipitation. The package of rain measuring instrumentation, including the first meteorological radar in space, continues to function perfectly, and with the increase in orbital altitude (from 350 km to 400 km) the mission will hopefully continue for a number of years. The validation effort has been a combination of routine use of 1) ground-based radar and raingauge measurements for comparison with the satellite-based estimates, 2) the use of field experiment data for evaluation of the satellite data products and investigation of some of the assumptions in the satellite retrievals, and 3) use of other comparison data sets, including atoll and buoy gauges over ocean and research and operational gauge data sets over land. The status of the program will be described along with "lessons learned". Near term plans for improved validation products and new thrusts related to validation of TRMM-based multi-satellite products that extend into middle latitudes will be outlined.

Adler, Robert↗

Derivation and Application of a Global Albedo yielding an Optical Brightness To Physical Size Transformation Free of Systematic Errors

Orbital object data acquired via optical telescopes can play a crucial role in accurately defining the space environment. Radar systems probe the characteristics of small debris by measuring the reflected electromagnetic energy from an object of the same order of size as the wavelength of the radiation. This signal is affected by electrical conductivity of the bulk of the debris object, as well as its shape and orientation. Optical measurements use reflected solar radiation with wavelengths much smaller than the size of the objects. Just as with radar, the shape and orientation of an object are important, but we only need to consider the surface electrical properties of the debris material (i.e., the surface albedo), not the bulk electromagnetic properties. As a result, these two methods are complementary in that they measure somewhat independent physical properties to estimate the same thing, debris size. Short arc optical observations such as are typical of NASA's Liquid Mirror Telescope (LMT) give enough information to estimate an Assumed Circular Orbit (ACO) and an associated range. This information, combined with the apparent magnitude, can be used to estimate an "absolute" brightness (scaled to a fixed range and phase angle). This absolute magnitude is what is used to estimate debris size. However, the shape and surface albedo effects make the size estimates subject to systematic and random errors, such that it is impossible to ascertain the size of an individual object with any certainty. However, as has been shown with radar debris measurements, that does not preclude the ability to estimate the size distribution of a number of objects statistically. After systematic errors have been eliminated (range errors, phase function assumptions, photometry) there remains a random geometric albedo distribution that relates object size to absolute magnitude. Measurements by the LMT of a subset of tracked debris objects with sizes estimated from their radar cross sections indicate that the random variations in the albedo follow a log-normal distribution quite well. In addition, this distribution appears to be independent of object size over a considerable range in size. Note that this relation appears to hold for debris only, where the shapes and other properties are not primarily the result of human manufacture, but of random processes. With this information in hand, it now becomes possible to estimate the actual size distribution we are sampling from. We have identified two characteristics of the space debris population that make this process tractable and by extension have developed a methodology for performing the transformation.

Mulrooney, Dr. Mark K.↗