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Beamed-Energy Propulsion (BEP) Study

The scope of this study was to (1) review and analyze the state-of-art in beamed-energy propulsion (BEP) by identifying potential game-changing applications, (2) formulate a roadmap of technology development, and (3) identify key near-term technology demonstrations to rapidly advance elements of BEP technology to Technology Readiness Level (TRL) 6. The two major areas of interest were launching payloads and space propulsion. More generally, the study was requested and structured to address basic mission feasibility. The attraction of beamed-energy propulsion (BEP) is the potential for high specific impulse while removing the power-generation mass. The rapid advancements in high-energy beamed-power systems and optics over the past 20 years warranted a fresh look at the technology. For launching payloads, the study concluded that using BEP to propel vehicles into space is technically feasible if a commitment to develop new technologies and large investments can be made over long periods of time. From a commercial competitive standpoint, if an advantage of beamed energy for Earth-to-orbit (ETO) is to be found, it will rest with smaller, frequently launched payloads. For space propulsion, the study concluded that using beamed energy to propel vehicles from low Earth orbit to geosynchronous Earth orbit (LEO-GEO) and into deep space is definitely feasible and showed distinct advantages and greater potential over current propulsion technologies. However, this conclusion also assumes that upfront infrastructure investments and commitments to critical technologies will be made over long periods of time. The chief issue, similar to that for payloads, is high infrastructure costs.

Patrick George↗

Searching for Optically Faint GEO Debris

We report on results from a search for optically faint debris (defined as R > 20th magnitude, or smaller than 10 cm assuming an albedo of 0.175)) at geosynchronous orbit (GEO) using the 6.5-m Magellan telescope "Walter Baade" at Las Campanas Observatory in Chile. Our goal is to characterize the brightness distribution of debris to the faintest limiting magnitude possible. Our data was obtained during 6 hours of observing time during the photometric nights of 26 and 27 March 2011 with the IMACS f/2 instrument, which has a field of view (fov) of 0.5 degrees in diameter. All observations were obtained through a Sloan r filter, and calibrated by observations of Landolt standard stars. Our primary objective was to search for optically faint objects from one of the few known fragmentations at GEO: the Titan 3C Transtage (1968-081) fragmentation in 1992. Eight debris pieces and the parent rocket body are in the Space Surveillance Network public catalog. We successfully tracked two cataloged pieces of Titan debris with the 6.5-m telescope, followed by a survey for unknown objects on similar orbits but with different mean anomalies. To establish the bright end of the debris population, calibrated observations were acquired on the same field centers, telescope rates, and time period with a similar filter on the 0.6-m MODEST (Michigan Orbital DEbris Survey Telescope), located 100 km to the south of Magellan at Cerro Tololo Inter-American Observatory, Chile. We will show the calibrated brightness distributions from both telescopes, and compare the observed brightness distributions with that predicted for various population models of debris of different sizes.

Seitzer, Patrick↗

Visible Light Spectroscopy of GEO Debris

Our goal is to understand the physical characteristics of debris at geosynchronous orbit (GEO). Our approach is to compare the observed reflectance as a function of wavelength with laboratory measurements of typical spacecraft surfaces to understand what the materials are likely to be. Because debris could be irregular in shape and tumbling at an unknown rate, rapid simultaneous measurements over a range of wavelengths are required. Acquiring spectra of optically faint objects with short exposure times to minimize these effects requires a large telescope. We describe optical spectroscopy obtained during 12-14 March 2012 with the IMACS imaging spectrograph on the 6.5-m 'Walter Baade' Magellan telescope at Las Campanas Observatory in Chile. When used in f/2 imaging mode for acquisition, this instrument has a field of view of 30 arc-minutes in diameter. After acquisition and centering of a GEO object, a 2.5 arc-second wide slit and a grism are moved into the beam for spectroscopy. We used a 200 l/mm grism blazed at 660 nm for wavelength coverage in the 500-900 nm region. Typical exposure times for spectra were 15-30 seconds. Spectra were obtained for five objects in the GEO regime listed as debris in the US Space Command public catalog, and one high area to mass ratio GEO object. In addition spectra were obtained of three cataloged IDCSP (Initial Defense Communications Satellite Program) satellites with known initial properties just below the GEO regime. All spectra were calibrated using white dwarf flux standards and solar analog stars. We will describe our experiences using Magellan, a telescope never used previously for orbital debris spectroscopy, and our initial results.

Seitzer, Patrick↗

What Properties of CMEs are Most Important for Space Weather?

Severe space weather is characterized by intense particle radiation from the Sun and major geomagnetic storm caused by magnetized solar plasmas arriving at Earth. Coronal mass ejections (CMEs) are key players in both these aspects. CMEs traveling at super-Alfv nic speeds drive fast-mode MHD shocks that create the high levels of particle radiation. When a CME arrives at Earth, the CME-associated magnetic fields reconnect with Earth s magnetopause fields resulting in solar plasma entry into the magnetosphere and a geomagnetic storm depending on the magnetic structure of the CME. Particle radiation starts affecting geospace as soon as the CMEs leave the Sun and the geospace may be immersed in the radiation for several days. On the other hand, the geomagnetic storm happens only upon CME arrival at Earth. The requirements for the production of particles and magnetic storms by CMEs are different in a number of respects: solar source location, CME magnetic structure, conditions in the ambient solar wind, and shock-driving ability of CMEs. Intense shocks arriving at Earth have additional space weather effects such as sudden impulse that shrinks the magnetosphere often exposing satellites in geosynchronous orbit to the solar wind and energetic storm particle events. This paper highlights these space weather effects using CME observations space and ground based instruments during of solar cycles 23 and 24.

Gopalswamy, Nat↗

The Role of Cis-Lunar Space in Future Global Space Exploration

Cis-lunar space offers affordable near-term opportunities to help pave the way for future global human exploration of deep space, acting as a bridge between present missions and future deep space missions. While missions in cis-lunar space have value unto themselves, they can also play an important role in enabling and reducing risk for future human missions to the Moon, Near-Earth Asteroids (NEAs), Mars, and other deep space destinations. The Cis-Lunar Destination Team of NASA's Human Spaceflight Architecture Team (HAT) has been analyzing cis-lunar destination activities and developing notional missions (or "destination Design Reference Missions" [DRMs]) for cis-lunar locations to inform roadmap and architecture development, transportation and destination elements definition, operations, and strategic knowledge gaps. The cis-lunar domain is defined as that area of deep space under the gravitational influence of the earth-moon system. This includes a set of earth-centered orbital locations in low earth orbit (LEO), geosynchronous earth orbit (GEO), highly elliptical and high earth orbits (HEO), earth-moon libration or "Lagrange" points (E-ML1 through E-ML5, and in particular, E-ML1 and E-ML2), and low lunar orbit (LLO). To help explore this large possibility space, we developed a set of high level cis-lunar mission concepts in the form of a large mission tree, defined primarily by mission duration, pre-deployment, type of mission, and location. The mission tree has provided an overall analytical context and has helped in developing more detailed design reference missions that are then intended to inform capabilities, operations, and architectures. With the mission tree as context, we will describe two destination DRMs to LEO and GEO, based on present human space exploration architectural considerations, as well as our recent work on defining mission activities that could be conducted with an EML1 or EML2 facility, the latter of which will be an emphasis of this paper, motivated in part by recent interest expressed at the Global Exploration Roadmap Stakeholder meeting. This paper will also explore the links between this HAT Cis-Lunar Destination Team analysis and the recently released ISECG Global Exploration Roadmap and other potential international considerations, such as preventing harmful interference to radio astronomy observations in the shielded zone of the moon.

Bobskill, Marianne R.↗

Solar Wind Charge Exchange During Geomagnetic Storms

On March 31st. 2001, a coronal mass ejection pushed the subsolar magnetopause to the vicinity of geosynchronous orbit at 6.6 RE. The NASA/GSFC Community Coordinated Modeling Center (CCMe) employed a global magnetohydrodynamic (MHD) model to simulate the solar wind-magnetosphere interaction during the peak of this geomagnetic storm. Robertson et aL then modeled the expected 50ft X-ray emission due to solar wind charge exchange with geocoronal neutrals in the dayside cusp and magnetosheath. The locations of the bow shock, magnetopause and cusps were clearly evident in their simulations. Another geomagnetic storm took place on July 14, 2000 (Bastille Day). We again modeled X-ray emission due to solar wind charge exchange, but this time as observed from a moving spacecraft. This paper discusses the impact of spacecraft location on observed X-ray emission and the degree to which the locations of the bow shock and magnetopause can be detected in images.

Robertson, Ina P.↗

Simultaneous Multi-Filter Optical Photometry of GEO Debris

Information on the physical characteristics of unresolved pieces of debris comes from an object's brightness, and how it changes with time and wavelength. True colors of tumbling, irregularly shaped objects can be accurately determined only if the intensity at all wavelengths is measured at the same time. In this paper we report on simultaneous photometric observations of objects at geosynchronous orbit (GEO) using two telescopes at Cerro Tololo Inter-American Observatory (CTIO). The CTIO/SMARTS 0.9-m observes in a Johnson B filter, while the 0.6-m MODEST (Michigan Orbital DEbris Survey Telescope) observes in a Cousins R filter. The two CCD cameras are electronically synchronized so that the exposure start time and duration are the same for both telescopes. Thus we obtain the brightness as a function of time in two passbands simultaneously, and can determine the true color of the object at any time. We will report here on such calibrated measurements made on a sample of GEO objects and what is the distribution of the observed B-R colors. In addition, using this data set, we will show what colors would be observed if the observations in different filters were obtained sequentially, as would be the case for conventional imaging observations with a single detector on a single telescope. Finally, we will compare our calibrated colors of GEO debris with colors determined in the laboratory of selected materials actually used in spacecraft construction.

Seitzer, Patrick↗

Observations of GEO Debris with the Magellan 6.5-m Telescopes

Optical observations of geosynchronous orbit (GEO) debris are important to address two questions: 1. What is the distribution function of objects at GEO as a function of brightness? With some assumptions, this can be used to infer a size distribution. 2. Can we determine what the likely composition of individual GEO debris pieces is from studies of the spectral reflectance of these objects? In this paper we report on optical observations with the 6.5-m Magellan telescopes at Las Campanas Observatory in Chile that attempt to answer both questions. Imaging observations over a 0.5 degree diameter field-of-view have detected a significant population of optically faint debris candidates with R > 19th magnitude, corresponding to a size smaller than 20 cm assuming an albedo of 0.175. Many of these objects show brightness variations larger than a factor of 2, suggesting either irregular shapes or albedo variations or both. The object detection rate (per square degree per hour) shows an increase over the rate measured in the 0.6-m MODEST observations, implying an increase in the population at optically fainter levels. Assuming that the albedo distribution is the same for both samples, this corresponds to an increase in the population of smaller size debris. To study the second issue, calibrated reflectance spectroscopy has been obtained of a sample of GEO and near GEO objects with orbits in the public U.S. Space Surveillance Network catalog. With a 6.5-m telescope, the exposures times are short (30 seconds or less), and provide simultaneous wavelength coverage from 4500 to 8000 Angstroms. If the observed objects are tumbling, then simultaneous coverage and short exposure times are essential for a realistic assessment of the object fs spectral signature. We will compare the calibrated spectra with lab-based measurements of simple spacecraft surfaces composed of a single material.

Seitzer, Patrick↗

Comparisons of a Constrained Least Squares Model Versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

Spectral reflectance data through the visible regime was collected at Las Campanas Observatory in Chile using an imaging spectrograph on one of the twin 6.5-m Magellan telescopes. The data were obtained on 1-2 May 2012 on the 'Landon Clay' telescope with the LDSS3 (Low Dispersion Survey Spectrograph 3). Five pieces of Geosynchronous Orbit (GEO) or near-GEO debris were identified and observed with an exposure time of 30 seconds on average. In addition, laboratory spectral reflectance data was collected using an Analytical Spectral Device (ASD) field spectrometer at California Polytechnic State University in San Luis Obispo on several typical common spacecraft materials including solar cells, circuit boards, various Kapton materials used for multi-layer insulation, and various paints. The remotely collected data and the laboratory-acquired data were then incorporated in a newly developed model that uses a constrained least squares method to unmix the spectrum in specific material components. The results of this model are compared to the previous method of a human-in-the-loop (considered here the traditional method) that identifies possible material components by varying the materials and percentages until a spectral match is obtained. The traditional model was found to match the remotely collected spectral data after it had been divided by the continuum to remove the space weathering effects, or a "reddening" of the materials. The constrained least-squares model also used the de-reddened spectra as inputs and the results were consistent with those obtained through the traditional method. For comparison, a first-order examination of including reddening effects into the constrained least-squares model will be explored and comparisons to the remotely collected data will be examined. The identification of each object's suspected material component will be discussed herein.

Rapp, Jason↗

Characterization of the 2012-044c Briz-M Upper Stage Breakup

On 6 August, 2012, Russia launched two commercial satellites aboard a Proton rocket, and attempted to place them in geosynchronous orbit using a Briz-M upper stage (2012-044C, SSN 38746). Unfortunately, the upper stage failed early in its burn and was left stranded in an elliptical orbit with a perigee in low Earth orbit (LEO). Because the stage failed with much of its fuel on board, it was deemed a significant breakup risk. These fears were confirmed when it broke up 16 October, creating a large cloud of debris with perigees below that of the International Space Station. The debris cloud was tracked by the US Space Surveillance Network (SSN), which can reliably detect and track objects down to about 10 cm in size. Because of the unusual geometry of the breakup, there was an opportunity for NASA Orbital Debris Program Office to request radar assets to characterize the extent of the debris cloud in sizes smaller than the standard debris tracked by the SSN. This paper will describe the observation campaign to measure the small particle distributions of this cloud, and presents the results of the analysis of the data. We shall compare the data to the modelled size distribution, number, and shape of the cloud, and what implications this may have for future breakup debris models. We shall conclude the paper with a discussion how this measurement process can be improved for future breakups.

Matney, M. J.↗

NASA Orbital Debris Baseline Populations

The NASA Orbital Debris Program Office has created high fidelity populations of the debris environment. The populations include objects of 1 cm and larger in Low Earth Orbit through Geosynchronous Transfer Orbit. They were designed for the purpose of assisting debris researchers and sensor developers in planning and testing. This environment is derived directly from the newest ORDEM model populations which include a background derived from LEGEND, as well as specific events such as the Chinese ASAT test, the Iridium 33/Cosmos 2251 accidental collision, the RORSAT sodium-potassium droplet releases, and other miscellaneous events. It is the most realistic ODPO debris population to date. In this paper we present the populations in chart form. We describe derivations of the background population and the specific populations added on. We validate our 1 cm and larger Low Earth Orbit population against SSN, Haystack, and HAX radar measurements.

Krisko, Paula H.↗

Comparisons of a Constrained Least Squares Model versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

Spectral reflectance data through the visible regime was collected at Las Campanas Observatory in Chile using an imaging spectrograph on one of the twin 6.5-m Magellan telescopes. The data were obtained on 1-2 May 2012 on the 'Landon Clay' telescope with the LDSS3 (Low Dispersion Survey Spectrograph 3). Five pieces of Geosynchronous Orbit (GEO) or near-GEO debris were identified and observed with an exposure time of 30 seconds on average. In addition, laboratory spectral reflectance data was collected using an Analytical Spectral Device (ASD) field spectrometer at California Polytechnic State University (Cal Poly) in San Luis Obispo on several typical common spacecraft materials including solar cells, circuit boards, various Kapton materials used for multi-layer insulation, and various paints. The remotely collected data and the laboratory-acquired data were then incorporated in a newly developed model that uses a constrained least squares method to unmix the spectrum in specific material components. The results of this model are compared to the previous method of a human-in-the-loop (considered here the traditional method) that identifies possible material components by varying the materials and percentages until a spectral match is obtained. The traditional model was found to match the remotely collected spectral data after it had been divided by the continuum to remove the space weathering effects, or a reddening of the materials. The constrained least-squares model also used the de-reddened spectra as inputs and the results were consistent with those obtained through the traditional method. For comparison, a first-order examination of including reddening effects into the constrained least-squares model will be explored and comparisons to the remotely collected data will be examined. The identification of each object s suspected material component will be discussed herein.

Abercromby, Kira J.↗

Characterization of the 2012-044C Briz-M Upper Stage Breakup

On 6 August, 2012, Russia launched two commercial satellites aboard a Proton rocket, and attempted to place them in geosynchronous orbit using a Briz-M upper stage (2012-044C, SSN 38746). Unfortunately, the upper stage failed early in its burn and was left stranded in an elliptical orbit with a perigee in low Earth orbit (LEO). Because the stage failed with much of its fuel on board, it was deemed a significant breakup risk. These fears were confirmed when it broke up 16 October, creating a large cloud of debris with perigees below that of the International Space Station. The debris cloud was tracked by the US Space Surveillance Network (SSN), which can reliably detect and track objects down to about 10 cm in size. Because of the unusual geometry of the breakup, there was an opportunity for NASA Orbital Debris Program Office to use specialized radar assets to characterize the extent of the debris cloud in sizes smaller than the standard debris tracked by the SSN. This paper will describe the observation campaign to measure the small particle distributions of this cloud, and presents the results of the analysis of the data. We shall compare the data to the modelled size distribution, number, and shape of the cloud, and what implications this may have for future breakup debris models. We shall conclude the paper with a discussion how this measurement process can be improved for future breakups.

Matney, M. J.↗

Observations of Titan IIIC Transtage Fragmentation Debris

The fragmentation of a Titan IIIC Transtage (1968-081) on 21 February 1992 is one of only two known break-ups in or near geosynchronous orbit. The original rocket body and 24 pieces of debris are currently being tracked by the U. S. Space Surveillance Network (SSN). The rocket body (SSN# 3432) and several of the original fragments (SSN# 25000, 25001, 30000, and 33511) were observed in survey mode during 2004-2010 using the 0.6-m Michigan Orbital DEbris Survey Telescope (MODEST) in Chile using a broad R filter. This paper presents a size distribution for all calibrated magnitude data acquired on MODEST. Size distribution plots are also shown using historical models for small fragmentation debris (down to 10 cm) thought to be associated with the Titan Transtage break-up. In November 2010, visible broadband photometry (Johnson/Kron-Cousins BVRI) was acquired with the 0.9-m Small and Moderate Aperture Research Telescope System (SMARTS) at the Cerro Tololo Inter-American Observatory (CTIO) in Chile on several Titan fragments (SSN 25001, 33509, and 33510) and the parent rocket body (SSN 3432). Color index data are used to determine the fragment brightness distribution and how the data compares to spacecraft materials measured in the laboratory using similar photometric measurement techniques. In order to better characterize the break-up fragments, spectral measurements were acquired on three Titan fragments (one fragment observed over two different time periods) using the 6.5-m Magellan telescopes at Las Campanas Observatory in Chile. The telescopic spectra of SSN 25000 (May 2012 and January 2013), SSN 38690, and SSN 38699 are compared with laboratory acquired spectra of materials (e.g., aluminum and various paints) to determine the surface material.

Cowardin, Heather↗

Observations of Titan 3C-4 Transtage Fragmentation Debris

The fragmentation of a Titan 3C-4 Transtage (1968-081) on 21 February 1992 is one of only two known break-ups in or near geosynchronous orbit. The original rocket body and 24 pieces of debris are currently being tracked by the US Space Surveillance Network (SSN). The rocket body (SSN# 3432) and several of the original fragments (SSN# 25000, 25001, 30000, and 33511) were observed in survey mode during 2004-2010 using the 0.6-m Michigan Orbital DEbris Survey Telescope (MODEST) in Chile using a broad R filter. This paper will present a size distribution for all calibrated magnitude data acquired on MODEST. Size distribution plots will also be shown using historical models for small fragmentation debris (down to 10 cm) believed to be associated with the Titan break-up. In November 2010, visible broadband photometry (Johnson/Kron-Cousins BVRI) was acquired with the 0.9-m Small and Moderate Aperture Research Telescope System (SMARTS) at the Cerro Tololo Inter-American Observatory (CTIO) in Chile on several Titan fragments (SSN# 25001, 33509, 33510) and the parent rocket body. Color index data will be used to determine the fragment brightness distribution and how the data compares to spacecraft materials measured in the laboratory using similar photometric measurement techniques. In 2012, the SSN added 16 additional fragments to the catalogue. MODEST acquired magnitude data on ten Titan fragments in late 2012 and early 2013. The magnitude distribution of all the observed fragments are analyzed as a function of time. In order to better characterize the breakup fragments spectral measurements were acquired on the original rocket body and five Titan fragments using the 6.5-m Magellan telescopes at Las Campanas Observatory in Chile. The telescopic spectra are compared with laboratory acquired spectra of materials (e.g., Aluminum and various paints) and categorized based on known absorption features for spacecraft materials.

Cowardin, Heather↗

LEMUR: Large European Module for Solar Ultraviolet Research

The solar outer atmosphere is an extremely dynamic environment characterized by the continuous interplay between the plasma and the magnetic field that generates and permeates it. Such interactions play a fundamental role in hugely diverse astrophysical systems, but occur at scales that cannot be studied outside the solar system. Understanding this complex system requires concerted, simultaneous solar observations from the visible to the vacuum ultraviolet (VUV) and soft X-rays, at high spatial resolution (between 0.1′′ and 0.3′′), at high temporal resolution (on the order of 10 s, i.e., the time scale of chromospheric dynamics), with a wide temperature coverage (0.01 MK to 20 MK, from the chromosphere to the flaring corona), and the capability of measuring magnetic fields through spectropolarimetry at visible and near-infrared wavelengths. Simultaneous spectroscopic measurements sampling the entire temperature range are particularly important. These requirements are fulfilled by the Japanese Solar-C mission (Plan B), composed of a spacecraft in a geosynchronous orbit with a payload providing a significant improvement of imaging and spectropolarimetric capabilities in the UV, visible, and near-infrared with respect to what is available today and foreseen in the near future. The Large European Module for solar Ultraviolet Research (LEMUR), described in this paper, is a large VUV telescope feeding a scientific payload of high-resolution imaging spectrographs and cameras. LEMUR consists of two major components: a VUV solar telescope with a 30 cm diameter mirror and a focal length of 3.6 m, and a focal-plane package composed of VUV spectrometers covering six carefully chosen wavelength ranges between 170 Angstrom and 1270 Angstrom. The LEMUR slit covers 280′′ on the Sun with 0.14′′ per pixel sampling. In addition, LEMUR is capable of measuring mass flows velocities (line shifts) down to 2 km s − 1 or better. LEMUR has been proposed to ESA as the European contribution to the Solar C mission.

Magnetic↗

NIR Color vs Launch Date: A 20-Year Analysis of Space Weathering Effects on the Boeing 376 Spacecraft

The Boeing HS‐376 spin stabilized spacecraft was a popular design that was launched continuously into geosynchronous orbit starting in 1980 with the last launch occurring in 2002. Over 50 of the HS‐376 buses were produced to fulfill a variety of different communication missions for countries all over the world. The design of the bus is easily approximated as a telescoping cylinder that is covered with solar cells and an Earth facing antenna that is despun at the top of the cylinder. The similarity in design and the number of spacecraft launched over a long period of time make the HS‐376 a prime target for studying the effects of solar weathering on solar panels as a function of time. A selection of primarily non‐operational HS‐376 spacecraft launched over a 20 year time period were observed using the United Kingdom Infrared Telescope on Mauna Kea and multi‐band near‐infrared photometry produced. Each spacecraft was observed for an entire night cycling through ZYJHK filters and time‐varying colors produced to compare near‐infrared color as a function of launch date. The resulting analysis shown here may help in the future to set launch date constraints on the parent object of unidentified debris objects or other unknown spacecraft.

Frith, James↗

Detection of Optically Faint GEO Debris

There have been extensive optical surveys for debris at geosynchronous orbit (GEO) conducted with meter-class telescopes, such as those conducted with MODEST (the Michigan Orbital DEbris Survey Telescope, a 0.6-m telescope located at Cerro Tololo in Chile), and the European Space Agency's 1.0-m space debris telescope (SDT) in the Canary Islands. These surveys have detection limits in the range of 18th or 19th magnitude, which corresponds to sizes larger than 10 cm assuming an albedo of 0.175. All of these surveys reveal a substantial population of objects fainter than R = 15th magnitude that are not in the public U.S. Satellite Catalog. To detect objects fainter than 20th magnitude (and presumably smaller than 10 cm) in the visible requires a larger telescope and excellent imaging conditions. This combination is available in Chile. NASA's Orbital Debris Program Office has begun collecting orbital debris observations with the 6.5-m (21.3-ft diameter) "Walter Baade" Magellan telescope at Las Campanas Observatory. The goal is to detect objects as faint as possible from a ground-based observatory and begin to understand the brightness distribution of GEO debris fainter than R = 20th magnitude.

Seitzer, P.↗