Mark Mulrooney (NASA-JSC/MEI Tech), Mark J. Matney, Ph.D.(Mark J. Matney, Ph.D. (NASA Johnson Space Center)
Keywords: Orbital Debris
Abstract:
We have developed a technique for estimating the intrinsic size distribution of orbital debris objects via optical measurements alone. The process is predicated on apriori knowledge of the power-law size distribution of debris (as indicated by radar RCS measurements) and the log-normal distribution of optical albedos. Since the observed distribution of optical brightness is the convolution of the parent [size] population with the albedo distribution, it is a straightforward matter to transform a given distribution of optical brightness back to a size distribution by appropriate choice of a single albedo value. This is true because the integration of a power-law with a log-normal distribution 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 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 weighted-average albedo which when applied to an observed brightness distribution yields zero offset and therefore recovers the original size distribution. For physically realistic power-laws of negative slope, the proper choice of weighted albedo effectively removes the biases caused by the large number of small objects that look anomalously large (bright) and the lower number of large objects looking anomalously small (dim). Based on this comprehensive analysis a global value of 0.13 should be applied to all orbital debris albedo-based brightness-to-size transformations of debris objects regardless of data source. This represents a modification to the canonical value of 0.1 widely employed. 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 observing season.
Date of Conference: September 12-15, 2007
Track: Poster