Astrophysics and Space Science

, Volume 339, Issue 2, pp 295–304

Long-term perturbations due to a disturbing body in elliptic inclined orbit

Original Article


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.


Third-body perturbations Restricted problem of three bodies Obliquity Averaged model Earth-Moon system Mars-Sun system 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of AerospaceTsinghua UniversityBeijingChina

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