# Long-term evolution of orbits about a precessing oblate planet. 2. The case of variable precession

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## Abstract

We continue the study undertaken in Efroimsky [Celest. Mech. Dyn. Astron. **91**, 75–108 (2005a)] where we explored the influence of spin-axis variations of an oblate planet on satellite orbits. Near-equatorial satellites had long been believed to keep up with the oblate primary’s equator in the cause of its spin-axis 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 *non-osculating* 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 non-uniform 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.

## Keywords

Equinoctial precession Satellite orbits Orbital elements Osculating elements Nonosculating elements## Preview

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## References

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