Longterm evolution of orbits about a precessing oblate planet. 2. The case of variable precession
 Michael Efroimsky
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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.
 Brouwer, D., van Woerkom, A.J.J.: The secular variations of the orbital elements of the principal planets. Astronomical papers prepared for the use of the American Ephemeris and Nautical Almanac, vol. 13 (Part 2), pp. 81–107. US Government Printing Office, Washington DC, 1950
 Brumberg, V.A. (1992) Essential Relativistic Celestial Mechanics. Adam Hilger, Bristol
 Colombo, G. (1996) Cassini’s second and third laws. Astron. J. 71: pp. 891896 CrossRef
 Efroimsky, M., Goldreich, P. (2003) Gauge symmetry of the Nbody problem in the Hamilton–Jacobi approach. J. Math. Phys. 44: pp. 59585977 CrossRef
 Efroimsky, M., Goldreich, P. (2004) Gauge freedom in the Nbody problem of celestial mechanics. Astron. Astrophys. 415: pp. 11871199 CrossRef
 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: pp. 75108 CrossRef
 Efroimsky, M. (2005b) Gauge freedom in orbital mechanics. Ann. NY Acad. Sci. 1065: pp. 346374 CrossRef
 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)
 Goldreich, P. (1965) Inclination of satellite orbits about an oblate precessing planet. Astron. J. 70: pp. 59 CrossRef
 Gurfil, P., Elipe, A., Tangren, W., Efroimsky, M.: The SerretAndoyer Formalism in RigidBody Dynamics: I. Symmetries and Perturbations. Submitted to Regular and Chaotic Dynamics (2007) (astroph/0607201)
 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)
 Kinoshita, T. (1993) Motion of the orbital plane of a satellite due to a secular change of the obliquity of its mother planet. Celest. Mech. Dyn. Astron. 57: pp. 359368 CrossRef
 Laskar, J. (1988) Secular evolution of the solar system over 10 million years. Astron. Astrophy. 198: pp. 341362
 Laskar, J. (1990) The chaotic motion of the solar system. A numerical estimate of the size of the chaotic zones. Icarus 88: pp. 26691 CrossRef
 Laskar, J. (2004) A comment on “accurate spin axes and solar system dynamics: climatic variations for the Earth and Mars”. Astron. Astrophys. 416: pp. 799800 CrossRef
 Laskar, J., Robutel, J. (1993) The chaotic obliquity of the planets. Nature 361: pp. 608612 CrossRef
 Murray, B.C., Ward, W.R., Yeung, S.C. (1973) Periodic insolation variations on Mars. Science 180: pp. 638640 CrossRef
 Touma, J., Wisdom, J. (1994) LiePoisson integrators for rigid body dynamics in the solar system. Astron. J. 107: pp. 11891202 CrossRef
 Ward, W. (1973) Largescale variations in the obliquity of Mars. Science 181: pp. 260262 CrossRef
 Ward, W. (1974) Climatic variations of Mars. Astronomical theory of insolation. J. Geophys. Res. 79: pp. 33753386 CrossRef
 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