Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998cemda..71..157q&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 71, Issue 3, p. 157-166 (1998).
Astronomy and Astrophysics
Astronomy
Overflow, High Order And Degree Harmonics, Satellite Gravitational Gradient
Scientific paper
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 normalized method [2-6] can eliminate the overflows, but leads to formulae much more involved than those in reference [1]; besides, the programming is more complex and the computer time required larger. The method presented in this paper has the following features: each component of the satellite gravitational gradient can be computed; the formulae are short and easy to be programme; the method is much quicker than the normalization method and can be carried out with a micro-computer, 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 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 harmonics up to order and degree of 3170 × 3170 or higher.
Qinchang Lin
Yuan Lin
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