Fast computation of satellite gravitational gradient |
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Authors: | Lin Qinchang Lin Yuan |
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Institution: | (1) Guangzhou Satellite Station, Chinese Academy ofSciences, Guangzhou, 510640, China;(2) L. C. Smith College of Engineering Computer Science, Syracuse University, NY 13210, USA |
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Abstract: | 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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | overflow high order and degree harmonics satellite gravitational gradient |
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