Fast computation of satellite gravitational gradient.

Statistics – Computation

Scientific paper

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Geopotential: Astrodynamics, Geopotential: Computing

Scientific paper

The computation of the Earth's potential function at high order and degree with the method of Cunningham (1970) causes overflow most of the time. The normalized method can eliminate the overflows, but leads to formulae much more involved than those in Cunningham's method; besides, the programming is more complex and the computer time required larger. The method presented has the following features: each component of the satellite gravitational gradient can be computed; the formulae are short and easy to be programmed; the method is much quicker than the normalization method and can be carried out with a microcomputer, without overflow 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 the satellite gravitational gradient with high accuracy. Furthermore, the authors present formulae for the fast computation, without overflow, of the gravitational gradient corresponding to Earth's spherical harmonics up to order and degree of 3170×3170 or higher.

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