Long-term evolution of orbits about a precessing oblate planet: the likely history of Phobos and Deimos
Résumé
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 (2005a,b). Here we continue this line of research by combining those analytics with numerical tools. This semianalytical and seminumerical theory, based on the Lagrange-type planetary equations for the Keplerian elements, is then applied to Deimos at very large time scales. In parallel with the said semianalytical-seminumerical theory for the Keplerian elements, we have also carried out a completely independent, purely numerical, integration in a fixed inertial Cartesian frame. These parallel efforts were taken to make sure that the results are reliable and robust.