Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-term evolution of orbits about a precessing oblate planet. 3. A
  semianalytical and a purely numerical approach   Construction of a theory of orbits about a precessing oblate planet, in terms
of osculating elements defined in a frame of the equator of date, was started
in Efroimsky and Goldreich (2004) and Efroimsky (2005, 2006). We now combine
that analytical machinery with numerics. The resulting semianalytical theory is
then applied to Deimos over long time scales. In parallel, we carry out a
purely numerical integration in an inertial Cartesian frame. The results agree
to within a small margin, for over 10 Myr, demonstrating the applicability of
our semianalytical model over long timescales. This will enable us to employ it
at the further steps of the project, enriching the model with the tides, the
pull of the Sun, and the planet's triaxiality. Another goal of our work was to
check if the equinoctial precession predicted for a rigid Mars could have been
sufficient to repel the orbits away from the equator. We show that for low
initial inclinations, the orbit inclination reckoned from the precessing
equator of date is subject only to small variations. This is an extension, to
non-uniform precession given by the Colombo model, of an old result obtained by
Goldreich (1965) for the case of uniform precession and a low initial
inclination. However, near-polar initial inclinations may exhibit considerable
variations for up to +/- 10 deg in magnitude. Nevertheless, the analysis
confirms that an oblate planet can, indeed, afford large variations of the
equinoctial precession over hundreds of millions of years, without repelling
its near-equatorial satellites away from the equator of date: the satellite
inclination oscillates but does not show a secular increase. Nor does it show
secular decrease, a fact that is relevant to the discussion of the possibility
of high-inclination capture of Phobos and Deimos.

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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol