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27 Oct 2006
Longterm evolution of orbits about a precessing oblate planet. 2. The case of variable precession
 Michael Efroimsky
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We continue the study undertaken in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] where we explored the influence of spinaxis variations of an oblate planet on satellite orbits. Nearequatorial satellites had long been believed to keep up with the oblate primary’s equator in the cause of its spinaxis variations. As demonstrated by Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)], this opinion had stemmed from an inexact interpretation of a correct result by Goldreich [Astron. J. 70, 5–9 (1965)]. Although Goldreich [Astron. J. 70, 5–9 (1965)] mentioned that his result (preservation of the initial inclination, up to small oscillations about the moving equatorial plane) was obtained for nonosculating inclination, his admonition had been persistently ignored for forty years. It was explained in Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)] that the equator precession influences the osculating inclination of a satellite orbit already in the first order over the perturbation caused by a transition from an inertial to an equatorial coordinate system. It was later shown in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] that the secular part of the inclination is affected only in the second order. This fact, anticipated by Goldreich [Astron. J. 70, 5–9 (1965)], remains valid for a constant rate of the precession. It turns out that nonuniform variations of the planetary spin state generate changes in the osculating elements, that are linear in \( \varvec{\dot{\vec{\mu}}} \), where \(\varvec{\vec{\mu}}\) is the planetary equator’s total precession rate that includes the equinoctial precession, nutation, the Chandler wobble, and the polar wander. We work out a formalism which will help us to determine if these factors cause a drift of a satellite orbit away from the evolving planetary equator.
By “precession,” in its most general sense, we mean any change of the direction of the spin axis of the planet—from its longterm variations down to nutations down to the Chandler wobble and polar wander.
References
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Efroimsky, M.: Longterm evolution of orbits about a precessing oblate planet. 1. The case of uniform precession. (2004) (astroph/0408168) This preprint is an extended version of Efroimsky (2005a). It contains a lengthy Appendix where all calculations are explained in every detail
Efroimsky M. (2005a) Longterm evolution of orbits about a precessing oblate planet. 1. The case of uniform precession. Celest. Mech. Dyn. Astron. 91, 75–108MathSciNetCrossRefADSMATH
Efroimsky, M.: Longterm evolution of orbits about a precessing oblate planet. 2. The case of variable precession. (2006) (astroph/0607522) This preprint is a very extended version of the present paper. It contains all calculations in every detail
Efroimsky, M.: The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables. Submitted to Celestial Mechanics and Dynamical Astronomy (2007) (astroph/0506427)
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Gurfil, P., Lainey, V., Efroimsky, M.: Longterm evolution of orbits about a precessing oblate planet. 3. A semianalytical and a purely numerical approach. Submitted to Celestial Mechanics and Dynamical Astronomy (2007) (astroph/0607530)
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 Title
 Longterm evolution of orbits about a precessing oblate planet. 2. The case of variable precession
 Journal

Celestial Mechanics and Dynamical Astronomy
Volume 96, Issue 34 , pp 259288
 Cover Date
 20061101
 DOI
 10.1007/s1056900690465
 Print ISSN
 09232958
 Online ISSN
 15729478
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Equinoctial precession
 Satellite orbits
 Orbital elements
 Osculating elements
 Nonosculating elements
 Industry Sectors
 Authors

 Michael Efroimsky ^{(1)}
 Author Affiliations

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