Thermal re-radiation (TRR) affects spacecraft orbits when a net recoil force results from the uneven emission of radiation from the spacecraft surface these forces can perturb spacecraft trajectories by several metres over a few hours. The mis-modelling of TRR limits the accuracy with which some spacecraft orbits can be computed, and in turn limits capabilities of applications where satellite positioning is key. These range from real-time navigation to geodetic measurements using low earth orbiting spacecraft. Approaches for the precise analytical modelling of TRR forces are presented. These include methods for the treatment of spacecraft multilayer insulation (MLI), solar panels and other spacecraft components. Techniques for determining eclipse boundary crossing times for an oblate earth and modelling penumbral fluxes are also described. These affect both the thermal force and the considerably larger solar radiation pressure (SRP) force. These methods are implemented for the Global Positioning System (GPS) Block IIR spacecraft and the altimetry satellite Jason-1. For GPS Block IIR, model accuracy is assessed by orbit prediction through numerical integration of the spacecraft force model. Orbits were predicted over 12 hours and compared to precise orbits before and after thermal and eclipse-related models were included. When the solar panel model was included, mean orbit prediction errors dropped from 3.3m to 3.0m over one orbit inclusion of the MLI model reduced errors further to 0.6m. For eclipsing satellites, the penumbral flux model reduced errors from 0.7 m to 0.56m. The Jason-1 models were tested by incorporation into GIPSY-OASIS II, the Jet Propulsion Laboratory's (JPL) orbit determination software. A combined SRP and TRR model yielded significant improvements in orbit determination over all other existing models and is now used routinely by JPL in the operational orbit determination of Jason-1
