Refining space object radiation pressure modeling with bidirectional reflectance distribution functions

High-fidelity orbit propagation requires detailed knowledge of the solar radiation pressure on a space object. The solar radiation pressure depends not only on the space object's shape and attitude, but also on the absorption and reflectance properties of each surface on the object. These properties are typically modeled in a simplistic fashion, but are here described by a surface bidirectional reflectance distribution function. Several analytic bidirectional reflectance distribution function models exist, and are typically complicated functions of illumination angle and material properties represented by parameters within the model. In general, the resulting calculation of the solar radiation pressure would require a time-consuming numerical integration. This might be impractical if multiple solar radiation pressure calculations are required for a variety of material properties in real time; for example, in a filter where the particular surface parameters are being estimated. This paper develops a method to make accurate and precise solar radiation pressure calculations quickly for some commonly used analytic bidirectional reflectance distribution functions. In addition, other radiation pressures exist, including Earth albedo/Earth infrared radiation pressure, and thermal radiation pressure from the space object itself, and are influenced by the specific bidirectional reflectance distribution function. A description of these various radiation pressures and a comparison of the magnitude of the resulting accelerations at various orbital heights and the degree to which they affect the space object's orbit are also presented. Significantly, this study suggests that, for space debris whose interactions with electro-magnetic radiation are described accurately with a bidirectional reflectance distribution function, then hitherto unmodeled torques would account for rotational characteristics affecting both tracking signatures and the ability to predict the orbital evolution of the objects.