e-mail: Valery.Lainey @ imcce.fr,
نویسندگان
چکیده
Construction of an accurate theory of orbits about a precessing and nutating oblate planet, in terms of osculating elements defined in a frame associated with the equator of date, was started in Efroimsky & Goldreich (2004) and Efroimsky (2004b, 2005, 2006). Here we continue this line of research by combining that analytical machinery with numerical tools. Our model includes three factors: the J2 of the planet, its nonuniform equinoctial precession described by the Colombo formalism, and the gravitational pull of the Sun. This semianalytical and seminumerical theory, based on the Lagrange-type planetary equations for the Keplerian elements, is then applied to Deimos on very long time scales (up to 1 billion of years). In parallel with the said semianalytical theory for the Keplerian elements defined in the co-precessing equatorial frame, we have also carried out a completely independent, purely numerical, integration in a fixed inertial Cartesian frame. The results agree to within 10−3 − 10−2 (from 0.3%, for near-polar orbits, through 1.3% for near-equatorial ones), for over 20 Myr, thus demonstrating the applicability of our semianalytical model over long ∗ We use the term “precession” in its general meaning, which includes any change of the instantaneous spin axis. So generally defined precession embraces the entire spectrum of spin-axis variations – from the polar wander and nutations through the Chandler wobble through the equinoctial precession.
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تاریخ انتشار 2008