LongTerm Evolution of Orbits About A Precessing Oblate Planet: 1. The Case of Uniform Precession
 Michael Efroimsky
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Abstract
It was believed until very recently that a nearequatorial satellite would always keep up with the planet’s equator (with oscillations in inclination, but without a secular drift). As explained in Efroimsky and Goldreich [Astronomy & Astrophysics (2004) Vol. 415, pp. 1187–1199], this misconception originated from a wrong interpretation of a (mathematically correct) result obtained in terms of nonosculating orbital elements. A similar analysis carried out in the language of osculating elements will endow the planetary equations with some extra terms caused by the planet’s obliquity change. Some of these terms will be nontrivial, in that they will not be amendments to the disturbing function. Due to the extra terms, the variations of a planet’s obliquity may cause a secular drift of its satellite orbit inclination. In this article we set out the analytical formalism for our study of this drift. We demonstrate that, in the case of uniform precession, the drift will be extremely slow, because the firstorder terms responsible for the drift will be shortperiod and, thus, will have vanishing orbital averages (as anticipated 40 years ago by Peter Goldreich), while the secular terms will be of the second order only. However, it turns out that variations of the planetary precession make the firstorder terms secular. For example, the planetary nutations will resonate with the satellite’s orbital frequency and, thereby, may instigate a secular drift. A detailed study of this process will be offered in a subsequent publication, while here we work out the required mathematical formalism and point out the key aspects of the dynamics.
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 Title
 LongTerm Evolution of Orbits About A Precessing Oblate Planet: 1. The Case of Uniform Precession
 Journal

Celestial Mechanics and Dynamical Astronomy
Volume 91, Issue 12 , pp 75108
 Cover Date
 20050101
 DOI
 10.1007/s105690042415z
 Print ISSN
 09232958
 Online ISSN
 15729478
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 nearequatorial satellites of oblate planets
 contact orbital elements
 Industry Sectors
 Authors

 Michael Efroimsky ^{(1)}
 Author Affiliations

 1. US Naval Observatory, 20392, Washington, DC, USA