Semi-Empirical Satellite Accommodation Model for Spherical and Randomly Tumbling Objects

Orbits of launch-vehicle upper stages and spheres were observed by U.S. Air Force Space Command, and the resulting observations were converted by the Space Analysis Office to fitted ballistic coefficients by comparing the observed orbit with an orbit predicted by an atmospheric-drag model. The ballistic coefficients contain signals that result from atmospheric variability not captured by the model as well as signals that correspond to changes in the satellite-drag coefficient. For objects in highly elliptical orbits with perigee altitudes below 200\ km a 50\% change in ballistic coefficient can be observed. This drastic change is associated with both changes in the energy accommodation coefficient driven by atomic-oxygen adsorption and entry into a transition flow region where a diffuse shock forms ahead of the satellite near perigee. Furthermore, the observed ballistic coefficients for objects in near-circular orbits (7.5 km/s speeds) do not match those of objects in highly eccentric orbits (10 km/s speeds near perigee). This difference is attributed to a decrease in adsorption efficiency postulated by previous researchers that is formalized in this work into a semi-empirical model. The model parameters suggest that the average binding energy of atomic oxygen on satellite surfaces is about 5.7\ eV.