Uncertainty analysis on direct solar radiation pressure modelling for GPS IIR and Galileo FOC satellites

Solar Radiation Pressure (SRP) is one of the main perturbations that needs to be carefully considered for space missions requiring great precision in satellite's orbit. The computation of SRP is related to both satellite's geometry and surface material. SRP model is usually used in the estimation of satellite's position in space. However, the quality of SRP model is not easy to be assessed in a straightforward way. In this study, we proposed an uncertainty analysis on satellite geometry and surface optical properties using GPS IIR and Galileo FOC spacecraft. We compared the SRP acceleration between simple box-wing and the detailed geometry model under the condition that the optical properties are set exactly the same. It showed that the average difference caused by satellite geometry is around 6.7% and 2% of the total SRP for GPS IIR and Galileo FOC. We also found that the irregular shape of satellites can be a source of the so-called “y-bias” in orbit modelling. In addition, the partial derivatives of SRP acceleration with respect to optical properties for complex satellite geometry are computed using ray tracing. The partials w.r.t optical properties on solar panels are larger than that on satellite bus due to the large area of solar panels. Furthermore, partials w.r.t reflectivity is about 10 times larger than that w.r.t specularity for both solar panels and satellite bus. For GPS IIR (mass 1100 kg) and Galileo FOC (mass 700 kg) satellites, if we require the uncertainty of SRP model be less than 0.1 nm·s^-2, the standard deviation of optical properties has to be less than 0.001 on solar panels and 0.01 on satellite bus.