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Analytical solutions to the four post-Newtonian effects in a near-Earth satellite orbit
Authors:Cheng Huang  Lin Liu
Institution:(1) Shanghai Observatory, Chinese Academy of Sciences, 200030 Shanghai, China;(2) Astronomy Department, Nanjing University, 210008 Nanjing, China
Abstract:On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J 2) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.
Keywords:Post-Newtonian perturbations  quasi-mean orbital element method  full analytical solutions
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