Umbra prediction algorithms for LEO satellite

The traditional umbra prediction algorithms are of huge computational effort, and not suitable for the on-board computer to predict the shadow moments autonomously. Therefore, a on-board algorithm for shadow prediction is proposed in this paper. By constructing a reduced dimension coordinate system, the process of satellites' entering or leaving the shadow is transformed into the geometry problem occurring in the plane containing the satellite, the Earth and the Sun. The implicit analytical formula of the shadow conditions can be derived based on the constant variation method, namely the coefficients of the equation are given by the real-time orbit parameters. The spaceborne algorithm is designed into two-layer structure to simplify calculations. The shadow moments of satellites at every node are precisely predicted by constructing an iteration algorithm according to the real-time orbit parameters, and the analytical algorithm can be used to approximatively predict the shadow moments between nodes. Numerical simulations have shown that the spaceborne algorithm is of high predicting accuracy and small computational effort, and is suitable for the on-board computer to predict the shadow moments autonomously.