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  • 1
    Electronic Resource
    Electronic Resource
    Collision Probabilities for Keplerian Orbits (2000)
    Springer
    Space debris 2 (2000), S. 161-198 
    Details
    ISSN: 1572-9664
    Keywords: impact risk analysis ; orbital debris environment ; probability of collision
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We present a new derivation of the probability of collisions between spherical satellites occupying Keplerian orbits. The equations follow from the central concept of the instantaneous collision rate, an expression that describes the occurrence of collisions by using a Dirac δ-function. The derivation proceeds by showing how this instantaneous collision rate can be averaged over orbital mean anomaly angles and, additionally, over orbital precession angles to generate expressions appropriate for intermediate and long time scales. Collision rates averaged over mean anomalies tend to be non-zero during relatively brief collision seasons, when the peak collision probability may exceed the long-term average by several orders of magnitude. Derived precession-angle averages have a functional form similar but not identical to the collision probability expression derived using the spatial density approach of Kessler (Icarus, 48: 39–48, 1981), and the two methods have been found to yield numerical results to within 1% for all cases examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022916401768
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    Paper (German National Licenses)
    Fulltext
  • 2
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    Survey and chase: A new method of observations for the Michigan Orbital DEbris Survey Telescope (MODEST) (2009)
    Elsevier
    Details
    Publication Date: 2009-07-01
    Print ISSN: 0094-5765
    Electronic ISSN: 1879-2030
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Published by Elsevier
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  • 3
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    The Use of the Satellite Breakup Risk Assessment Model (SBRAM) to Characterize Collision Risk to Manned Spacecraft (1999)
    In:  Other Sources
    Details
    Publication Date: 2019-07-17
    Description: NASA uses environment models such as ORDEM96 to characterize the long-term orbital debris collision hazard for spacecraft in LEO. Occasionally, however, there are breakups of satellites or rocket bodies that create enhanced collision hazard for a period of time. This enhanced collision hazard can pose increased risks to space operations - especially those involving manned missions where the tolerance for risk is very low. NASA has developed SBRAM to simulate the enhanced debris environment in the days and weeks that follow such a breakup. This simulation provides the kind of risk probabilities that can be used by mission planners to consider if changes are warranted for the mission. Announcements of breakups come to NASA from US Space Command as soon as they are identified. The pre-breakup orbit and time of breakup are used to determine the initial conditions of the explosion. SBRAM uses the latest explosion models developed at NASA to simulate a debris cloud for the breakup. The model uses a Monte Carlo technique to create a random debris cloud from the probability distributions in the breakup model. Each piece of debris randomly created in the cloud is propagated in a deterministic manner to include the effects of drag and other orbital perturbations. The detailed geometry of each simulated close approach to the target spacecraft is noted and logged and the collision probability is computed using an estimated probability density in down-range and cross-range positions of both the target spacecraft and debris object. The collision probability is computed from the overlap of these probability densities for each close-approach geometry and summed over all computed conjunctions. Cloud propagation runs over the desired time interval are then repeated until the scale of the collision risk can be estimated to a desired precision. This paper presents an overview of the SBRAM model and a number of examples, both real and hypothetical, to demonstrate its use. In addition, a number of different examples are shown how the data can be used by decision makers on issues such as spacecraft orientation and timing of EVAs.
    Keywords: Spacecraft Design, Testing and Performance
    Type: IAA-99-IAA.6.5.09 , International Astronautical Congress; Oct 04, 1999 - Oct 08, 1999; Amsterdam; Netherlands
    Format: text
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  • 4
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    Oblate-Earth Effects on the Calculation of Ec During Spacecraft Reentry (2017)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The bulge in the Earth at its equator has been shown to lead to a clustering of natural decays biased to occur towards the equator and away from the orbit's extreme latitudes. Such clustering must be considered when predicting the Expectation of Casualty (Ec) during a natural decay because of the clustering of the human population in the same lower latitudes. This study expands upon prior work, and formalizes the correction that must be made to the calculation of the average exposed population density as a result of this effect. Although a generic equation can be derived from this work to approximate the effects of gravitational and atmospheric perturbations on a final decay, such an equation averages certain important subtleties in achieving a best fit over all conditions. The authors recommend that direct simulation be used to calculate the true Ec for any specific entry as a more accurate method. A generic equation is provided, represented as a function of ballistic number and inclination of the entering spacecraft over the credible range of ballistic numbers.
    Keywords: Spacecraft Design, Testing and Performance
    Type: JSC-CN39730-1 , International Association for the Advancement of Space Safety (IAASS); Oct 18, 2017 - Oct 20, 2017; Toulouse; France
    Format: application/pdf
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  • 5
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    Gravitational Focusing and the Computation of an Accurate Moon/Mars Cratering Ratio (2006)
    In:  Other Sources
    Details
    Publication Date: 2019-07-19
    Description: There have been a number of attempts to use asteroid populations to simultaneously compute cratering rates on the Moon and bodies elsewhere in the Solar System to establish the cratering ratio (e.g., [1],[2]). These works use current asteroid orbit population databases combined with collision rate calculations based on orbit intersections alone. As recent work on meteoroid fluxes [3] have highlighted, however, collision rates alone are insufficient to describe the cratering rates on planetary surfaces - especially planets with stronger gravitational fields than the Moon, such as Earth and Mars. Such calculations also need to include the effects of gravitational focusing, whereby the spatial density of the slower-moving impactors is preferentially "focused" by the gravity of the body. This leads overall to higher fluxes and cratering rates, and is highly dependent on the detailed velocity distributions of the impactors. In this paper, a comprehensive gravitational focusing algorithm originally developed to describe fluxes of interplanetary meteoroids [3] is applied to the collision rates and cratering rates of populations of asteroids and long-period comets to compute better cratering ratios for terrestrial bodies in the Solar System. These results are compared to the calculations of other researchers.
    Keywords: Astrophysics
    Format: text
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  • 6
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    Space Debris Symposium (A6.) Measurements and Space Surveillance (1.): Measurements of the Small Particle Debris Cloud from the 11 January, 2007 Chinese Anti-satellite Test (2008)
    In:  Other Sources
    Details
    Publication Date: 2019-07-19
    Description: On January 11, 2007, the Chinese military conducted a test of an anti-satellite (ASAT) system, destroying their own Fengyun-1C spacecraft with an interceptor missile. The resulting hypervelocity collision created an unprecedented number of tracked debris - more than 2500 objects. These objects represent only those large enough for the US Space Surveillance Network (SSN) to track - typically objects larger than about 5-10 cm in diameter. There are expected to be even more debris objects at sizes too small to be seen and tracked by the SSN. Because of the altitude of the target satellite (865 x 845 km orbit), many of the debris are expected to have long orbital lifetimes and contribute to the orbital debris environment for decades to come. In the days and weeks following the ASAT test, NASA was able to use Lincoln Laboratory s Haystack radar on several occasions to observe portions of the ASAT debris cloud. Haystack has the capability of detecting objects down to less than one centimeter in diameter, and a large number of centimeter-sized particles corresponding to the ASAT cloud were clearly seen in the data. While Haystack cannot track these objects, the statistical sampling procedures NASA uses can give an accurate statistical picture of the characteristics of the debris from a breakup event. For years computer models based on data from ground hypervelocity collision tests (e.g., the SOCIT test) and orbital collision experiments (e.g., the P-78 and Delta-180 on-orbit collisions) have been used to predict the extent and characteristics of such hypervelocity collision debris clouds, but until now there have not been good ways to verify these models in the centimeter size regime. It is believed that unplanned collisions of objects in space similar to ASAT tests will drive the long-term future evolution of the debris environment in near-Earth space. Therefore, the Chinese ASAT test provides an excellent opportunity to test the models used to predict the future debris environment. For this study, Haystack detection events are compared to model predictions to test the model assumptions, including debris size distribution, velocity distribution, and assumptions about momentum transfer between the target and interceptor. In this paper we will present the results of these and other measurements on the size and extent of collisional breakup debris clouds.
    Keywords: Astronautics (General)
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  • 7
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    A New Bond Albedo for Performing Orbital Debris Brightness to Size Transformations (2008)
    In:  Other Sources
    Details
    Publication Date: 2019-07-19
    Description: We have developed a technique for estimating the intrinsic size distribution of orbital debris objects via optical measurements alone. The process is predicated on the empirically observed power-law size distribution of debris (as indicated by radar RCS measurements) and the log-normal probability distribution of optical albedos as ascertained from phase (Lambertian) and range-corrected telescopic brightness measurements. Since the observed distribution of optical brightness is the product integral of the size distribution of the parent [debris] population with the albedo probability distribution, it is a straightforward matter to transform a given distribution of optical brightness back to a size distribution by the appropriate choice of a single albedo value. This is true because the integration of a powerlaw with a log-normal distribution (Fredholm Integral of the First Kind) yields a Gaussian-blurred power-law distribution with identical power-law exponent. Application of a single albedo to this distribution recovers a simple power-law [in size] which is linearly offset from the original distribution by a constant whose value depends on the choice of the albedo. Significantly, there exists a unique Bond albedo which, when applied to an observed brightness distribution, yields zero offset and therefore recovers the original size distribution. For physically realistic powerlaws of negative slope, the proper choice of albedo recovers the parent size distribution by compensating for the observational bias caused by the large number of small objects that appear anomalously large (bright) - and thereby skew the small population upward by rising above the detection threshold - and the lower number of large objects that appear anomalously small (dim). Based on this comprehensive analysis, a value of 0.13 should be applied to all orbital debris albedo-based brightness-to-size transformations regardless of data source. Its prima fascia genesis, derived and constructed from the current RCS to size conversion methodology (SiBAM Size-Based Estimation Model) and optical data reduction standards, assures consistency in application with the prior canonical value of 0.1. Herein we present the empirical and mathematical arguments for this approach and by example apply it to a comprehensive set of photometric data acquired via NASA's Liquid Mirror Telescopes during the 2000-2001 observing season.
    Keywords: Lunar and Planetary Science and Exploration
    Format: text
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  • 8
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    The New NASA Orbital Debris Engineering Model ORDEM2000 (2002)
    In:  CASI
    Details
    Publication Date: 2019-07-10
    Description: The NASA Orbital Debris Program Office at Johnson Space Center has developed a new computer-based orbital debris engineering model, ORDEM2000, which describes the orbital debris environment in the low Earth orbit region between 200 and 2000 km altitude. The model is appropriate for those engineering solutions requiring knowledge and estimates of the orbital debris environment (debris spatial density, flux, etc.). ORDEM2000 can also be used as a benchmark for ground-based debris measurements and observations. We incorporated a large set of observational data, covering the object size range from 10 mm to 10 m, into the ORDEM2000 debris database, utilizing a maximum likelihood estimator to convert observations into debris population probability distribution functions. These functions then form the basis of debris populations. We developed a finite element model to process the debris populations to form the debris environment. A more capable input and output structure and a user-friendly graphical user interface are also implemented in the model. ORDEM2000 has been subjected to a significant verification and validation effort. This document describes ORDEM2000, which supersedes the previous model, ORDEM96. The availability of new sensor and in situ data, as well as new analytical techniques, has enabled the construction of this new model. Section 1 describes the general requirements and scope of an engineering model. Data analyses and the theoretical formulation of the model are described in Sections 2 and 3. Section 4 describes the verification and validation effort and the sensitivity and uncertainty analyses. Finally, Section 5 describes the graphical user interface, software installation, and test cases for the user.
    Keywords: Space Sciences (General)
    Type: NASA/TP-2002-210780 , S-890 , NAS 1.60:210780
    Format: application/pdf
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  • 9
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    GEO Population Estimates using Optical Survey Data (2007)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: Optical survey data taken using the NASA Michigan Orbital Debris Survey Telescope (MODEST) gives us an opportunity to statistically sample faint object population in the Geosynchronous (GEO) and near-GEO environment. This paper will summarize the MODEST survey work that has been conducted by NASA since 2002, and will outline the techniques employed to arrive at the current population estimates in the GEO environment for dim objects difficult to detect and track using current systems in the Space Surveillance Network (SSN). Some types of orbits have a higher detection rate based on what parts of the GEO belt is being observed, a straightforward statistical technique is used to debias these observations to arrive at an estimate of the total population potentially visible to the telescope. The size and magnitude distributions of these fainter debris objects are markedly different from the catalogued population. GEO debris consists of at least two different populations, one which follows the standard breakup power law and one which has anomalously high Area-to-Mass Ratios (1 to approx. 30 square meters per kilogram; a sheet of paper = approx. 13 square meters per kilogram). The Inter-Agency Space Debris Coordination Committee (IADC) is investigating objects in GEO orbits with anomalously high Area-to-Mass Ratios (AMRs). The ESA Space Debris Telescope discovered this population and has and its properties of inclinations (0 to 30 degrees), changing eccentricities (0 and 0.6), and mean motions (approx. 1 rev), will be presented. The accepted interpretation of this orbital behavior is that solar radiation pressure drives the perturbations causing time varying inclinations and eccentricities. The orbital parameters are unstable for this population and thus difficult to predict. Their dim visual magnitudes and photometric variability make observations a challenge. The IADC has enlisted a series of observatories (participating institutions: University of Michigan/CTIO, Astronomical Institute University of Bern, Boeing LTS / AMOS, Keldysh Institute of Applied Mathematics) at different longitudes. Complete observational coverage over periods of days to months will provide a better understanding of the properties, such as solar radiation pressure effects on orbital elements, size, shape, attitude, color variations, and spectral characteristics. Results from recent observational programs will be summarized, and includes a description of the orbit elements prediction processes, a summary of the metric tracking performance, and some photometric characteristics of this class of debris.
    Keywords: Optics
    Type: 2007 Space Control Conference; May 01, 2007 - May 03, 2007; Lexington, MA; United States
    Format: application/pdf
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  • 10
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    Survey and Chase: A New Method of Observations For The Michigan Orbital Debris Survey Telescope (MODEST) (2006)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: For more than 40 years astronauts have been observing Earth, taking photographs or digital images from their spacecraft. Today, a robust program of observation from the International Space Station (ISS) has yielded hundreds of thousands of images of the Earth s surface collected since 2001. Seeing Earth through the eyes of an astronaut is exciting to the general public, and the images are popular in classrooms. Because the ISS has an orbital inclination of 51.6 degrees (the north-south limits of the orbit are at 51.6 degrees latitude), high latitude observations are common. Some of the most striking images collected include views of polar phenomena. Astronauts routinely pass above brilliant red and green aurora; view high, wispy clouds at the top of the atmosphere; or look down on glaciers and floating ice rafts. These images, framed and captured by humans, are easily interpreted by students and teachers. Astronaut observations provide a way to visualize complicated polar phenomena and communicate about them to students of all ages. Over the next two years, astronauts aboard the ISS will formally focus their observations on polar phenomena as participants in the International Polar Year (IPY). Imagery acquisition from the ISS will be coordinated with other IPY scientists staging studies and field campaigns on the ground. The imagery collected from the ISS will be cataloged and served on NASA s web-based database of images, http://eol.jsc.nasa.gov . The website allows investigators, students and teachers to search through the imagery, assemble image datasets, and download the imagery and the metadata. We display some of the most spectacular examples of polar imagery and demonstrate NASA s database of astronaut images of Earth.
    Keywords: Space Sciences (General)
    Type: IAC-06-B6.1.2 , 57th International Astronautical Congress; Oct 02, 2006 - Oct 06, 2006; Valencia; Spain
    Format: application/pdf
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