Impact of the time span selected to calibrate the ballistic parameter on spacecraft re-entry predictions

Abstract

The trajectory modeling of satellites that are re-entering the Earth’s atmosphere, as a result of natural orbital decay, has always been a challenging task. Residual lifetime estimations and re-entry predictions are affected by substantial uncertainties, associated with atmospheric density models, with the forecasts of the relevant solar and geomagnetic activity indices and with tracking data, which for uncontrolled re-entries are usually sparse and not particularly accurate. Furthermore, modeling the aerodynamic forces that act on low altitude satellites is a formidable task, especially for objects of a complex shape and unknown attitude evolution. The ballistic parameter, defined as B = C D A/M, where C D, A and M are, respectively, the satellite drag coefficient, cross-sectional area and mass, incorporates the uncertainties related to the physical characteristics and attitude of the satellite, as well as the complicated interaction between air molecules and satellite surface. Since the uncertainties affecting the drag force computation are driven mainly by the product of air density and ballistic parameter, the latter may be adjusted so as to force the atmospheric density model to agree with the air drag revealed by the tracking data. Thus, the value of B that gives the best numerical fit between the estimated and the observed orbit, in a given time/data span, can be used to propagate the last available state vector, so as to calculate the satellite’s residual lifetime. However, the value of B may fluctuate from one data fit span to another, depending both on how the true density differs from the modeled one and on the possible changes in the satellite’s attitude. Of course, different values of B can be seen in different estimations of the satellite’s lifetime and re-entry epoch. Therefore, the choice of any suitable time/data span to calibrate the ballistic parameter is very tricky during a re-entry campaign. In an attempt to assess the impact of the aforementioned time/data span on satellite re-entry predictions, the past seven Inter-Agency Space Debris (IADC) re-entry test campaigns, covering a substantial fraction of a solar activity cycle, from 1998 to 2005, were re-examined in a post-event analysis. For each satellite, atmospheric density model and observed solar and geomagnetic activity, various time/data spans were investigated to find the ballistic parameter best suited for re-entry predictions, as a function of the residual lifetime.