Obtaining the properly weighted average albedo of orbital debris from optical and radar data

Abstract

Like any average, the proper weighting to obtain an average albedo of orbital debris depends upon the application of this average and the limitations of the data used to obtain individual orbital debris albedos. The most frequent application of the average orbital debris albedo is to transform number or flux as a function of observed orbital debris brightness into number or flux as a function of debris diameter, mass, or radar cross-section. This paper will develop and use two methods to obtain the properly weighted average albedo for transforming flux as a function of observed brightness into flux as a function of radar cross-section using data obtained from the 3.0 m NASA Liquid Mirror Telescope (LMT) and the US Space Command sensors. One method uses plots of number of objects detected by the LMT as a function of both magnitude and radar cross-section, corrected by assumed limitations in the detection capabilities of both the LMT and US Space Command sensors. In this method, the “proper average albedo” is the albedo required to force these two plots to predict the same number of objects at the same size. The other method integrates over the albedo distribution. Simplified assumptions allow the integration to be performed analytically. Care must be taken to consistently obtain an albedo distribution data set to either a limiting radar cross-section or a limiting magnitude, with the former being preferred. Instrument characteristics or limitations must be considered or they can contradict these simplified assumptions, resulting in misleading averages. Both techniques illustrate that the proper average albedo is not only a function of the albedo distribution, but also a function of the relative number of small debris to large debris. When the relative number of small debris to large debris is as great as has been measured for uncatalogued debris, the frequency of specular reflections is found to increase the proper average albedo significantly.