Combined radiation pressure and thermal modelling of complex satellites: algorithms and on-orbit tests

In an era of high resolution gravity field modelling the dominant error sources in spacecraft orbit determination are non-conservative spacecraft surface forces. These forces include: solar radiation pressure, thermal re-radiation forces, the forces due to radiation both reflected and emitted by the Earth and atmospheric drag effects. All of these forces can be difficult to characterise a priori because they require detailed modelling of the spacecraft geometry and surface properties, its attitude behaviour, the incident flux spatial and temporal variations and the interaction of these fluxes with the surface. The conventional approach to overcoming these problems is to build simplified box-and-wing models of the satellites and to estimate empirically factors that account for the inevitable mis-modelling. Over the last five years the authors have developed a suite of software utilities that model analytically the first three effects in the list above: solar radiation pressure, thermal forces and the albedo/earthshine force. The techniques are designed specifically to deal with complex spacecraft structures, no structural simplifications are made and the method can be applied to any spacecraft. Substantial quality control measures are used during computation to both avoid and trap errors. The paper presents the broad basis of the modelling techniques for each of the effects. Two operational tests of the output models, using the medium earth orbit satellite GPS Block IIR and the low earth orbit Jason-1, are presented. Model tests for GPS IIR are based on predicting the satellite orbit using the dynamic models alone (with no empirical scaling or augmentation) and comparing the integrated trajectory with precise, post-processed orbits. Using one month's worth of precise orbits, and all available Block IIR satellites, the RMS difference between the predicted orbits and the precise orbits over 12 hours are: 0.14m (height), 0.07m across track and 0.51m (along track). The tests on the Jason-1 model were conducted by the Jet Propulsion Laboratory using 90 days of tracking data. They indicate that the model solar scale factor is consistently at the level of 1% over the 90 day period (whereas previous models were at the level of 8-20%). Moreover, the model implementation shows strongly improved overlap statistics in the dynamic orbits and better stability in estimated drag parameters. Finally the group's current work on atmospheric drag modelling is outlined.