Modeling satellite drag coefficients with response surfaces

Abstract

Satellite drag coefficients are a major source of uncertainty in predicting the drag force on satellites in low Earth orbit. Among other things, accurately predicting the orbit requires detailed knowledge of the satellite drag coefficient. Computational methods are an important tool in computing the drag coefficient but are too intensive for real-time and predictive applications. Therefore, analytic or empirical models that can accurately predict drag coefficients are desired. This work uses response surfaces to model drag coefficients. The response surface methodology is validated by developing a response surface model for the drag coefficient of a sphere where the closed-form solution is known. The response surface model performs well in predicting the drag coefficient of a sphere with a root mean square percentage error less than 0.3% over the entire parameter space. For more complex geometries, such as the GRACE satellite, the Hubble Space Telescope, and the International Space Station, the model errors are only slightly larger at about 0.9%, 0.6%, and 1.0%, respectively.