Drag Coefficients of Satellites with Concave Geometries: Comparing Models and Observations

Predictions of satellite orbital perturbations often contain uncertainties due to the use of constant drag coefficients. While convex satellites may be analyzed using analytical solutions, concave geometry must be treated numerically, taking into account the effects of secondary reflections and flow shadowing. To evaluate these effects, the direct simulation Monte Carlo method was compared with analytical convex-shaped equations in free molecular flow with the measured drag of Starshine I, II, and III. The Starshine satellites were covered by hundreds of small mirrors, resulting in varying degrees of surface concavity. Ballistic coefficient measurements were collected by the United States Air Force Space Command and are adjusted herein for atmospheric model biases as well as new estimates of the Starshine cross-sectional areas. The addition of the mirrors was analyzed using two approaches. The first approach assumed that molecules were successively accommodated with each surface impact. The second method assumed that a molecule accommodates most during its first surface impact. The second model predicted an increase in the drag coefficients of concave objects, which is in agreement with drag observations of smooth and rough spherical satellites. The results indicate a 7-25% correction to the drag force and ballistic coefficient of the Starshine satellites.