The fifth-order analytical solution of the equations of motion of a satellite in orbit around a non-spherical planet |
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Authors: | Sergey M. Kudryavtsev |
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Affiliation: | 1. Mission Control Centre, Russian Space Agency, Pionerskaya St. 4, 141070, Moscow Region, Kaliningrad, Russia
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Abstract: | A high-precise analytical theory of a satellite in orbit around a non-spherical planet has been developed. The Poisson's small parameter method has been used. All secular and short-periodic perturbations proportional up to and including a product of five arbitrary harmonic coefficients of the planetary potential expansion are calculated. Long-periodic perturbations are derived with the accuracy of up to the fourth-order, inclusive. The influence of the high-order perturbations on the motion of ETALON-1 satellite has been investigated. The results of comparison of the numerical and analytical integration of the equations of its motion over a five year interval are as follows: | - the r.m.s. difference between the positions is 1.1 cm; | | - the r.m.s. difference between the ranges is 0.5 cm. | The theory is intended to be used for processing precise laser range measurements of the Earth geodynamical satellites over long-term intervals. |
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Keywords: | Satellite motion perturbations due to the central body analytical theory |
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