Fast computation of the spherical harmonic perturbation on an artificial satellite

Up till now, among the numerical computation methods of the spherical harmonic perturbation on an artificial satellite, the computation speed of Cunningham’s method is the fastest However, running programs based on this method easily causes overflow. A method is presented, which has a computation speed higher than that of any other methods, and can avoid overflow in operation, even when the order and degree of the Earth’s spherical harmonic perturbation are extended to 100 × 100 or more. It satisfies the requirements of the high-accuracy SLR, GPS, LLR, etc. This method has been programmed and used in practice Now a large-scale calculation related to the satellite precision ephemeris could be done just with a microcomputer.