A Drag Coefficient Modeling Approach Using Spatial and Temporal Fourier Expansions for Orbit Determination

The estimation and modeling of drag effects on low altitude satellites and debris is a limiting problem in the prediction of their orbits over time. Independent of the stochastic variations in atmospheric density, which drive the magnitude of the drag force, there are systematic variations in the drag coefficient due to satellite specific factors and atmospheric conditions. These include satellite attitude shifts, variations in ambient atmospheric parameters such as temperature, molecular composition, and the satellite wall temperature. Thus, even with accurate empirical models for the atmospheric density, there remain systematic model uncertainties and time variations in the effective coefficient of drag that affect the satellite's motion, which are not captured using the standard constant drag coefficient model. We report on our recent research on developing Fourier expansion based models of an arbitrary object's coefficient of drag with the overall purpose to develop corrections to the standard model. If the attitude profile of a satellite or object is known, a Fourier series expansion of the overall coefficient of drag as a function of wind vector direction in the body-frame can be introduced. For bodies with unknown or more complex attitude profiles, we introduce a periodically varying drag coefficient tied to a satellite's position in orbit. This model enables the estimation of higher-order temporal variations in drag that would be correlated with variations in altitude, temperature and density. An improved prediction capability over the standard cannonball model is shown and the formulation of how it can be incorporated into standard filtering techniques is presented.