Frozen orbits at high eccentricity and inclination: application to Mercury orbiter

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• 作者：N. Delsate ; P. Robutel ; A. Lema卯tre and T. Carletti
• 关键词：Planetary probes ; Stability ; Long ; term evolution ; Kozai resonances ; Frozen orbit equilibria ; Lidov ; Kozai effect ; BepiColombo
• 刊名：Celestial Mechanics and Dynamical Astronomy
• 出版时间：November 2010
• 出版年：2010
• 期刊代码：7_09232958
• 类别：soc
• 卷：108
• 期：3
• 页码：275-300
• 数据来源：sp

摘要

We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lay in the equatorial plane (Sun or Jupiter for example) using a Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient J ₂ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect and the coefficient J ₃ determines a shift of the equilibria.