A Derivation of the Analytical Relationship between the Projected Albedo-Area Product of a Space Object and its Aggregate Photometric Measurements

摘要

In this paper, we present a method to directly convert the photometric measurements to the projected albedo-Area product of a resident space object. The derivation is based on Lambertian reflectance but is general in all other ways. Its most powerful attribute is that it is independent of sensor, space object geometry and other characteristics, as well as photometric waveband. The governing expression can be combined with specific geometries of different orbits and satellite attitude control methods to obtain a parent equation from which the component projected albedo-Area products can be calculated. First we develop the governing expression from first principals and provide its physical and mathematical foundations. Then we derive, for the specific case of a three-axis stabilized satellite with a nadir-pointing body and articulating solar panels, the parent equation for the unique geometries of this case. Then we show how to decompose the aggregate albedo-Area product of the satellite into the respective albedo-Area products of the body and the solar panels. The governing albedo-Area expression provides a baseline that can be utilized for the characterization of a variety of space objects irrespective of their geometry and attitude.