Abstract
In the current study, a double-averaged analytical model including the action of the perturbing body’s inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body’s inclination, and illustrate that the lunar obliquity with the value 6.68∘ is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.
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This work was supported by National Basic Research Program of China (973 Program) (2012CB720000) and the National Natural Science Foundation of China (No. 11072122).
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Liu, X., Baoyin, H. & Ma, X. Long-term perturbations due to a disturbing body in elliptic inclined orbit. Astrophys Space Sci 339, 295–304 (2012). https://doi.org/10.1007/s10509-012-1015-8
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DOI: https://doi.org/10.1007/s10509-012-1015-8