Celestial Mechanics and Dynamical Astronomy

, Volume 96, Issue 3, pp 259–288

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

Original Paper

DOI: 10.1007/s10569-006-9046-5

Cite this article as:
Efroimsky, M. Celestial Mech Dyn Astr (2006) 96: 259. doi:10.1007/s10569-006-9046-5


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.


Equinoctial precessionSatellite orbitsOrbital elementsOsculating elementsNonosculating elements

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.US Naval ObservatoryWashingtonUSA