An efficient algorithm for the computation of the earth's gravitational potential and its first-order derivatives for solving satellite problems

Computer Science

Scientific paper

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Earth Gravitation, Geopotential, Gravitational Fields, Satellite Perturbation, Accuracy, Algorithms, Earth Orbits, Legendre Functions, Satellite Orbits

Scientific paper

An efficient algorithm has been developed for computing the earth's gravitational potential and its first order derivatives, which can be used in the construction of any satellite orbit, incuding polar orbits. The simple normalizing factors for the associated Legendre functions and the stable recursive relations of the algorithm result in a quadruple reduction in calculation time compared with Cunningham's algorithm. The proposed method permits the practical utilization of geopotential models of high degrees and orders when constructing satellite orbits with decimeter accuracy on computers of moderate efficiency.

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