A Wave Scattering Approach to Modelling Surface Roughness in Orbital Aerodynamics

Abstract

The increasing density of space objects in low-Earth orbit highlights the critical need for accurate orbit predictions to minimise operational disruptions. One significant challenge lies in accurately modelling the interaction of gas particles with the surfaces of these objects, as errors in aerodynamic coefficient modelling directly impact orbit prediction accuracy. Current approaches rely on empirical models, such as those by Sentman and Cercignani-Lampis-Lord, incorporating one or two adjustable parameters typically calibrated with orbital acceleration data. However, these models fall short in capturing essential gas-solid interaction processes, including multiple reflections, shadowing, and backscattering caused by surface roughness. We present a novel, physics-based gas-surface interaction model that utilises electromagnetic wave theory to account for macroscopic effects of surface roughness on gas particle scattering distributions. This approach not only offers a more accurate representation of gas-surface interactions but also allows parameter determination through a combination of ground-based surface roughness measurements and molecular dynamics simulations at the atomic scale. The model validity is tested across the entire parameter space using a test-particle Monte Carlo method on a simulated rough surface. Furthermore, it successfully reproduces experimental results from the literature on the scattering of Argon and Helium from smooth and rough Kapton and Aluminium surfaces. Finally, we demonstrate the model's impact on aerodynamic coefficients for simple geometric shapes, comparing the results with those from the Sentman and Cercignani-Lampis-Lord models. This comparison reveals that inconsistencies previously observed between these models and tracking data for spherical satellites can be attributed to surface roughness effects, which our model effectively accounts for.