Long-term evolution of orbits about a precessing oblate planet: the likely history of Phobos and Deimos

Details Long-term evolution of orbits about a precessing oblate planet: the likely history of Phobos and Deimos Long-term evolution of orbits about a precessing oblate planet: the likely history of Phobos and Deimos

Dec 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005dps....37.6803e&link_type=abstract

American Astronomical Society, DPS meeting #37, #68.03; Bulletin of the American Astronomical Society, Vol. 37, p.1570

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Scientific paper

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.
One goal of this work was to make an independent check of whether the equinoctial precession predicted for a rigid Mars could have been sufficient to repel the orbits away from the equator, on a billion-year time scale. The answer to this question, in combination with our knowledge of the current position of Phobos and Deimos, will help us to understand whether this precession could indeed be as large as predicted or whether it ought to have been less.
Another goal was to trace the history of a hypothetical satellite captured at a high inclination and to see if its inclination could decrease through aeons. The latter numerical experiment was motivated by the ongoing discussion on the possible scenarios of the Martian satellites capture.
It has turned out that, both for high and low initial inclinations, the orbit inclination, reckoned from the precessing equator of date, is subject only to extremely small variations. This is an extension, to non-uniform equinoctial precession given by the Colombo model, of an old result obtained by Goldreich (1965) for the case of uniform precession. Such ``inclination locking" confirms that an oblate planet can, indeed, afford a large equinoctial precession for billions of years, without repelling its near-equatorial satellites away from the equator of date. This also may be used as a potential argument against the theories of high-inclination capture of Phobos and Deimos (though a more rigorous exploration of the latter topic should incorporate more factors into the model -- the Sun, the tides, the planet's J3 ).

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