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NASA NTRS2012

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↗
NASA NTRS2013

Oxygen Assessments Ensure Safer Medical Devices

A team at White Sands Test Facility developed a test method to evaluate fire hazards in oxygen-enriched environments. Wendell Hull and Associates, located in Las Cruces, New Mexico, entered a Space Act Agreement with NASA and now provides services including fire and explosion investigations, oxygen testing and training, and accident reconstruction and forensic engineering.

Source record↗
NASA NTRS2013

Optical Reflection Spectroscopy of GEO Objects

We report on optical reflection spectroscopy of geosynchronous (GEO) objects in the US Space Surveillance Network (SSN) catalog. These observations were obtained using imaging spectrographs on the 6.5-m Magellan telescopes at the Las Campanas Observatory in Chile. Our goal is to determine the composition of these objects by comparing these spectral observations with ground-based laboratory measurements of spacecraft materials. The observations are all low resolution (1 nm after smoothing) obtained through a 5 arcsecond wide slit and using a grism as the dispersing element. The spectral range covered was from 450 nm to 800 nm. All spectra were flux calibrated using observations of standard stars with the exact same instrumental setup. An effort was made to obtain all observations within a limited range of topocentric phase angle, although the solar incident angle is unknown due to the lack of any knowledge of the attitude of the observed surface at the time of observation.

Seitzer, Patrick↗
NASA NTRS2013

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.↗
NASA NTRS2013

International Space Station (ISS) Soyuz Vehicle Descent Module Evaluation of Thermal Protection System (TPS) Penetration Characteristics

The descent module (DM) of the ISS Soyuz vehicle is covered by thermal protection system (TPS) materials that provide protection from heating conditions experienced during reentry. Damage and penetration of these materials by micrometeoroid and orbital debris (MMOD) impacts could result in loss of vehicle during return phases of the mission. The descent module heat shield has relatively thick TPS and is protected by the instrument-service module. The TPS materials on the conical sides of the descent module (referred to as backshell in this test plan) are exposed to more MMOD impacts and are relatively thin compared to the heat shield. This test program provides hypervelocity impact (HVI) data on materials similar in composition and density to the Soyuz TPS on the backshell of the vehicle. Data from this test program was used to update ballistic limit equations used in Soyuz TPS penetration risk assessments. The impact testing was coordinated by the NASA Johnson Space Center (JSC) Hypervelocity Impact Technology (HVIT) Group [1] in Houston, Texas. The HVI testing was conducted at the NASA-JSC White Sands Hypervelocity Impact Test Facility (WSTF) at Las Cruces, New Mexico. Figure

Davis, Bruce A.↗
NASA NTRS2013

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↗
NASA NTRS2013

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↗
NASA NTRS2012

Soil Carbon and Nutrient Changes Associated with Deforestation for Pasture in Southern Costa Rica

We assessed the effects of deforestation on soil carbon (C) and nutrient stocks in the premontane landscape near Las Cruces Biological Station in southern Costa Rica, where forests were cleared for pasture in the mid-1960s. We excavated six soil pits to a depth of 1 m in both pasture and primary forest, and found that C stocks were ~20 kg C per square meters in both settings. Nevertheless, soil delta C-13 suggests ~50 percent of the forest-derived soil C above 40 cm depth has turned over since deforestation. Soil nitrogen (N) and phosphorus (P) stocks derived from the soil pits were not significantly different between land uses (P = 0.43 and 0.61, respectively). At a larger spatial scale, however, the ubiquity of ruts produced by cattle-induced erosion indicates that there are substantial soil effects of grazing in this steep landscape. Ruts averaged 13 cm deep and covered ~45 percent of the landscape, and thus are evidence of the removal of 0.7 Mg C/ ha/yr, and 70, 9 and 40 kg/ha/yr of N, P and potassium (K), respectively. Subsoils in this region are ~10 times less C- and N-rich, and ~2 times less P- and K-rich than the topsoil. Thus, rapid topsoil loss may lead to a decline in pasture productivity in the coming decades. These data also suggest that the soil C footprint of deforestation in this landscape may be determined by the fate of soil C as it is transported downstream, rather than C turnover in situ.

soil carbon↗
NASA NTRS2014

Advanced Sine Wave Modulation of Continuous Wave Laser System for Atmospheric CO2 Differential Absorption Measurements

NASA Langley Research Center in collaboration with ITT Exelis have been experimenting with Continuous Wave (CW) laser absorption spectrometer (LAS) as a means of performing atmospheric CO2 column measurements from space to support the Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) mission.Because range resolving Intensity Modulated (IM) CW lidar techniques presented here rely on matched filter correlations, autocorrelation properties without side lobes or other artifacts are highly desirable since the autocorrelation function is critical for the measurements of lidar return powers, laser path lengths, and CO2 column amounts. In this paper modulation techniques are investigated that improve autocorrelation properties. The modulation techniques investigated in this paper include sine waves modulated by maximum length (ML) sequences in various hardware configurations. A CW lidar system using sine waves modulated by ML pseudo random noise codes is described, which uses a time shifting approach to separate channels and make multiple, simultaneous online/offline differential absorption measurements. Unlike the pure ML sequence, this technique is useful in hardware that is band pass filtered as the IM sine wave carrier shifts the main power band. Both amplitude and Phase Shift Keying (PSK) modulated IM carriers are investigated that exibit perfect autocorrelation properties down to one cycle per code bit. In addition, a method is presented to bandwidth limit the ML sequence based on a Gaussian filter implemented in terms of Jacobi theta functions that does not seriously degrade the resolution or introduce side lobes as a means of reducing aliasing and IM carrier bandwidth.

Campbell, Joel F.↗
NASA NTRS2013

Analysis and Results from a Flush Airdata Sensing (FADS) System in Close Proximity to Firing Rocket Nozzles

This presentation presents information regarding the nose-cap flush airdata sensing (FADS) system on Orion's Pad Abort 1 (PA-1) vehicle. The purpose of the nose-cap FADS system was to test whether or not useful data could be obtained from a FADS system if it was placed in close proximity to firing rockets nozzles like the attitude control motor (ACM) nozzles on the PA-1 launch abort system (LAS). The nose-cap FADS systems use pressure measurements from a series of pressure ports which are arranged in a cruciform pattern and flush with the surface of the vehicle to estimate values of angle of attack, angle of side-slip, Mach number, impact pressure and free-stream static pressure.

Pad Abort 1↗
NASA NTRS2013

Stellar Populations in Compact Galaxy Groups: a Multi-wavelength Study of HCGs 16, 22, and 42, Their Star Clusters, and Dwarf Galaxies

We present a multi-wavelength analysis of three compact galaxy groups, Hickson compact groups (HCGs) 16, 22, and 42, which describe a sequence in terms of gas richness, from space- (Swift, Hubble Space Telescope (HST), and Spitzer) and ground-based (Las Campanas Observatory and Cerro Tololo Inter-American Observatory) imaging and spectroscopy.We study various signs of past interactions including a faint, dusty tidal feature about HCG 16A, which we tentatively age-date at <1 Gyr. This represents the possible detection of a tidal feature at the end of its phase of optical observability. Our HST images also resolve what were thought to be double nuclei in HCG 16C and D into multiple, distinct sources, likely to be star clusters. Beyond our phenomenological treatment, we focus primarily on contrasting the stellar populations across these three groups. The star clusters show a remarkable intermediate-age population in HCG 22, and identify the time at which star formation was quenched in HCG 42. We also search for dwarf galaxies at accordant redshifts. The inclusion of 33 members and 27 "associates" (possible members) radically changes group dynamical masses, which in turn may affect previous evolutionary classifications. The extended membership paints a picture of relative isolation in HCGs 16 and 22, but shows HCG 42 to be part of a larger structure, following a dichotomy expected from recent studies. We conclude that (1) star cluster populations provide an excellent metric of evolutionary state, as they can age-date the past epochs of star formation; and (2) the extended dwarf galaxy population must be considered in assessing the dynamical state of a compact group.

Compact Galaxy↗
NASA NTRS2014

NASA's Optical Measurement Program 2014

The Optical Measurements Group (OMG) within the NASA Orbital Debris Program Office (ODPO) addresses U.S. National Space Policy goals by monitoring and characterizing debris. Since 2001, the OMG has used the Michigan Orbital Debris Survey Telescope (MODEST) at Cerro Tololo Inter-American Observatory (CTIO) in Chile for general orbital debris survey. The 0.6-m Schmidt MODEST provides calibrated astronomical data of GEO targets, both catalogued and uncatalogued debris, with excellent image quality. The data are utilized by the ODPO modeling group and are included in the Orbital Debris Engineering Model (ORDEM) v. 3.0. MODEST and the CTIO/SMARTS (Small and Moderate Aperture Research Telescope System) 0.9 m both acquire filter photometric data, as well as synchronously observing targets in selected optical filters. This information provides data used in material composition studies as well as longer orbital arc data on the same target, without time delay or bias from a rotating, tumbling, or spinning target. NASA, in collaboration with the University of Michigan, began using the twin 6.5-m Magellan telescopes at Las Campanas Observatory in Chile for deep imaging (Baade) and spectroscopic data (Clay) in 2011. Through the data acquired on Baade, debris have been detected that are ~3 magnitudes fainter than detections with MODEST, while the data from Clay provide better resolved information used in material characterization analyses via selected bandpasses. To better characterize and model optical data, the Optical Measurements Center (OMC) at NASA/JSC has been in operation since 2005, resulting in a database of comparison laboratory data. The OMC is designed to emulate illumination conditions in space using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. Lastly, the OMG is building the Meter Class Autonomous Telescope (MCAT) at Ascension Island. The 1.3-m telescope is designed to observe GEO and LEO targets, using a modified Ritchey-Chrétien configuration on a double horseshoe equatorial mount to allow tracking objects at LEO rates through the dome's keyhole at zenith. Through the data collection techniques employed at these unique facilities, NASA's ODPO has developed a multi-faceted approach to characterize the orbital debris risk to satellites in various altitudes and provide material characterization of debris via photometric and spectroscopic measurements. Ultimately, the data are used in conjunction with in-situ and radar measurements to provide accurate data for models of our space environment and service spacecraft risk assessment.

Cowardin, H.↗
NASA NTRS2014

NASA's Optical Measurement Program 2014

The Optical Measurements Group (OMG) within the NASA Orbital Debris Program Office (ODPO) addresses U.S. National Space Policy goals by monitoring and characterizing debris. Since 2001, the OMG has used the Michigan Orbital Debris Survey Telescope (MODEST) at Cerro Tololo Inter-American Observatory (CTIO) in Chile for general orbital debris surveys. The 0.6-m Schmidt MODEST provides calibrated astronomical data of GEO targets, both catalogued and uncatalogued debris, with excellent image quality. The data are utilized by the ODPO modeling group and are included in the Orbital Debris Engineering Model (ORDEM) v. 3.0. MODEST and the CTIO/SMARTS (Small and Moderate Aperture Research Telescope System) 0.9 m are both employed to acquire filter photometry data as well as synchronously observe targets in selected optical filters. Obtaining data synchronously yields data for material composition studies as well as longer orbital arc data on the same target without time delay or bias from a rotating, tumbling, or spinning target. Observations of GEO orbital debris using the twin 6.5-m Magellan telescopes at Las Campanas Observatory in Chile for deep imaging (Baade) and spectroscopic data (Clay) began in 2011. Through the data acquired on Baade, debris has been detected that reaches approx. 3 magnitudes fainter than detections with MODEST, while the spectral data from Clay provide better resolved information used in material characterization analyses. To better characterize and model optical data, the Optical Measurements Center (OMC) at NASA/JSC has been in operation since 2005, resulting in a database of comparison laboratory data. The OMC is designed to emulate illumination conditions in space using equipment and techniques that parallel telescopic observations and sourcetarget- sensor orientations. Lastly, the OMG is building the Meter Class Autonomous Telescope (MCAT) at Ascension Island. The 1.3-m telescope is designed to observe GEO and LEO targets, using a modified Ritchey-Chrétien configuration on a double horseshoe equatorial mount to allow tracking objects at LEO rates through the dome's keyhole at zenith. Through the data collection techniques employed at these unique facilities, NASA's ODPO has developed a multifaceted approach to characterize the orbital debris risk to satellites in various altitudes and provide insight leading toward material characterization of debris via photometric and spectroscopic measurements. Ultimately, the data are used in conjunction with in-situ and radar measurements to provide accurate data for models of our space environment and for facilitating spacecraft risk assessment.

Cowardin, H.↗
NASA NTRS2014

Ka-Band Atmospheric Phase Stability Measurements in Goldstone, CA; White Sands, NM; and Guam

As spacecraft communication links are driven to higher frequencies (e.g. Ka-band) both by spectrum congestion and the appeal of higher data rates, the propagation phenomena at these frequencies must be well characterized for effective system design. In particular, the phase stability of a site at a given frequency will govern whether or not the site is a practical location for an antenna array, particularly if uplink capabilities are desired. Propagation studies to characterize such phenomena must be done on a site-by-site basis due to the wide variety of climates and weather conditions at each ground terminal. Accordingly, in order to statistically characterize the atmospheric effects on Ka-Band links, site test interferometers (STIs) have been deployed at three of NASA's operational sites to directly measure each site's tropospheric phase stability. Using three years of results from these experiments, this paper will statistically characterize the simultaneous atmospheric phase noise measurements recorded by the STIs deployed at the following ground station sites: the Goldstone Deep Space Communications Complex near Barstow, CA; the White Sands Ground Terminal near Las Cruces, NM; and the Guam Remote Ground Terminal on the island of Guam.

Interferometry↗
NASA NTRS2014

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.↗
NASA NTRS2013

Methods for Retrievals of CO2 Mixing Ratios from JPL Laser Absorption Spectrometer Flights During a Summer 2011 Campaign

The JPL airborne Laser Absorption Spectrometer instrument has been flown several times in the 2007-2011 time frame for the purpose of measuring CO2 mixing ratios in the lower atmosphere. This instrument employs CW laser transmitters and coherent detection receivers in the 2.05- micro m spectral region. The Integrated Path Differential Absorption (IPDA) method is used to retrieve weighted CO2 column mixing ratios. We present key features of the evolving LAS signal processing and data analysis algorithms and the calibration/validation methodology. Results from 2011 flights in various U.S. locations include observed mid-day CO2 drawdown in the Midwest and high spatial resolution plume detection during a leg downwind of the Four Corners power plant in New Mexico.

laser remote sensing↗
NASA NTRS2015

Multi-Axis Independent Electromechanical Load Control for Docking System Actuation Development and Verification Using dSPACE

The development of highly complex and advanced actuation systems to meet customer demands has accelerated as the use of real-time testing technology expands into multiple markets at Moog. Systems developed for the autonomous docking of human rated spacecraft to the International Space Station (ISS), envelope multi-operational characteristics which place unique constraints on an actuation system. Real-time testing hardware has been used as a platform for incremental testing and development for the linear actuation system which controls initial capture and docking for vehicles visiting the ISS. This presentation will outline the role of dSPACE hardware as a platform for rapid control-algorithm prototyping as well as an Electromechanical Actuator (EMA) system dynamic loading simulator, both conducted at Moog to develop the safety critical Linear Actuator System (LAS) of the NASA Docking System (NDS).

Oesch, Christopher↗
NASA NTRS2016

NASA's Orbital Debris Optical and IR Ground-Based Observing Program Utilizing the MCAT, UKIRT, and Magellan Telescopes

Characterizing debris in Earth-orbit has become increasingly important as the population growth rises steadily, posing greater and greater threats to active satellites with each passing year. Currently, the Joint Space Operations is tracking over 23,000 pieces of debris, ranging in size from 1-meter and larger in geosychronous orbits (GEO) to 10-cm and larger at low-Earth orbits (LEO). Model estimates suggest that there may be more than 500,000 pieces of spacecraft debris larger than 1 cm currently in orbit around the Earth. With such a small fraction of the total population being tracked, and new break-ups occurring in LEO, GEO, and Geo Transfer Orbits, new assets, techniques, and approaches for characterizing this debris are needed. With this in mind, NASA's Orbital Debris Program Office has actively tasked a suite of telescopes around the world. In 2015, the newly-built 1.3m optical Meter Class Autonomous Telescope (MCAT) came on-line on Ascension Island in the South Atlantic Ocean and is currently in its commissioning phase. MCAT is designed to track Earth-orbiting objects above 200km, conduct surveys at GEO, and work in tandem with a newly-installed Raven-class commercial-off-the-shelf system, a 0.4-meter telescope co-located on Ascension with a field-of-view similar to MCAT's and research-grade instrumentation designed to complement MCAT for observations taken either simultaneously or in tandem. The 3.8m infrared UKIRT telescope on Mauna Kea, Hawaii, has been heavily tasked throughout 2015 and into 2016, collecting data on individual targets as well as in survey modes to study both the general GEO population as well as an individual break-up event of a BRIZ-M Rocket body that occurred in January 2016. Data collected include photometry and spectroscopy in the near-Infrared (0.85-2.5 m) and the mid-infrared (8-16 m). Finally, the 6.5-m Baade Magellan telescope at Las Campanas Observatory in Chile was used to collect optical photometric survey data in October 2015 of two GEO Titan breakups, focusing on locations of possible debris concentrations as indicated by the NASA standard break-up model.

Lederer, Susan↗