Fast computation of satellite gravitational gradient

The computation of the Earth's potential function at high order and degree with the method of reference [1], causes overflow most of the time. The nor malized method [2-6] can eliminate the overflows, but leads to formulae muc h more involved than those in reference [1]; besides, the programming is mo re complex and the computer time required larger. The method presented in this paper has the following features: each compone nt of the satellite gravitational gradient can be computed; the formulae ar e short and easy to be programmed; the method is much quicker than the norm alization method and can be carried out with a microcomputer, without overf low even in the case of Earth's spherical harmonics of order and degree as high as 1025 or higher. This method satisfies the present demand to compute satellite gravitational gradient with high accuracy. Furthermore, we present formulae for the fast computation, without overflow , of the gravitational gradient corresponding to Earth's spherical harmonic s up to order and degree of 3170 x 3170 or higher.