Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression

Ting-Lei Zhu; Chang-Yin Zhao; Ming-Jiang Zhang

doi:10.1007/s10509-017-3052-9

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arXiv · 1703.00655

Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression

Ting-Lei Zhu·Chang-Yin Zhao·Ming-Jiang Zhang

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Abstract

This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's $J_2$ and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane, Allan and Cook (1964) derived an analytic solution to the orbital plane evolution of circular orbits. Using their result as an intermediate solution, we establish an approximate analytic model with lunar orbital inclination and its node regression be taken into account. Finally, an approximate analytic expression is derived, which is accurate compared to the numerical results except for the resonant cases when the period of the reference orbit approximately equals the integer multiples (especially 1 or 2 times) of lunar node regression period.

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Ting-Lei Zhu, Chang-Yin Zhao, Ming-Jiang Zhang. 2017-03-02. Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression. https://doi.org/10.1007/s10509-017-3052-9

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