Analytic Free-Molecular Aerodynamics for Rapid Propagation of Resident Space Objects

Abstract

Aerodynamic forces and moments are significant perturbations on low-Earth-orbiting objects, second in magnitude to the nonspherical gravity field. Traditionally, the aerodynamic perturbations are calculated using a direct simulation Monte Carlo method. Under certain assumptions, these forces and moments can be described analytically via free-molecular flow theory. Using symbolic manipulation techniques, exact expressions for the free-molecular aerodynamics of analytic shapes can be derived. In this investigation, analytic expressions for the aerodynamic force and moment coefficients of primitive and composite parametric surfaces are derived, then validated against industry-standard direct simulation Monte Carlo techniques. A framework for the rapid and accurate calculation of free-molecular aerodynamics of composite geometries based on superposition is described. This framework is applied to axisymmetric composite geometries. Results within 6% of direct simulation Monte Carlo calculations are obtained in 0.05% of the time. The analytic aerodynamics models enable rapid trajectory and uncertainty propagation for low-Earth-orbiting objects. A case study on aerodynamic perturbations of a low-Earth-orbit nanosatellite is included to demonstrate application of these analytic models. The case study shows that these derived analytical free-molecular aerodynamics produce results that are applicable to inclusion in rapid trajectory propagation tools for orbit prediction and conceptual mission design.