Extrapolation of the gravity acceleration by means of taylor series expansion

Details Extrapolation of the gravity acceleration by means of taylor series expansion Extrapolation of the gravity acceleration by means of taylor series expansion

Jan 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999adspr..23..689m&link_type=abstract

Advances in Space Research, Volume 23, Issue 4, p. 689-692.

Computer Science

Scientific paper

We have recently derived very general formulas expressing the derivatives of a potential of arbitrary order with respect to rectangular coordinates. In this formulation, each derivative has the form of a spherical harmonic expansion similar to that of the potential. In this paper, we use the derivatives for evaluating the gravity acceleration by means of Taylor series expansion. Such an algorithm proves to be very efficient for computing satellite orbits strongly perturbed by the gravity potential. For example, we have achieved a speed up factor of about 200 to compute a 5 days arc at an altitude of 300 km for a potential truncated to degree and order 140. In the same time, the estimated accuracy is better than 2 mm in position and 2 μm/s in velocity.

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