SETI bioastro: Long-term evolution of orbits about a precessing oblate planet - 3 papers

Date: Thu Jul 27 2006 - 13:47:54 PDT

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    Astrophysics, abstract

    From: Michael Efroimsky [view email]

    Date: Sun, 23 Jul 2006 23:16:05 GMT (40kb)

    Long-term evolution of orbits about a precessing oblate planet. 2. The case
    of variable precession

    Authors: Michael Efroimsky

    Comments: Extended version of a paper to be published in ``Celestial
    Mechanics and Dynamical Astronomy."

    We continue the study undertaken in Efroimsky (2005a) where we explored the
    influence of spin-axis variations of an oblate planet on satellite orbits.
    Near-equatorial satellites had long been believed to keep up with the oblate
    primary's equator in the cause of its spin-axis variations. As demonstrated
    by Efroimsky and Goldreich (2004), this opinion had stemmed from an inexact
    interpretation of a correct result by Goldreich (1965). Though Goldreich
    (1965) mentioned that his result (preservation of the initial inclination,
    up to small oscillations about the moving equatorial plane) was obtained for
    non-osculating inclination, his admonition has been persistently ignored for
    forty years.

    It was explained in Efroimsky and Goldreich (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 (2005a) that the secular part of the inclination is affected only
    in the second order. This fact, anticipated by Goldreich (1965), remains
    valid for a constant rate of the precession. It turns out that non-uniform
    variations of the planetary spin state generate changes in the osculating
    elements, that are linear in the planetary equator's total precession rate,
    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.

    Astrophysics, abstract

    From: Michael Efroimsky [view email]

    Date: Sun, 23 Jul 2006 22:57:29 GMT (425kb)

    Long-term evolution of orbits about a precessing oblate planet. 3. A
    semianalytical and a purely numerical approach

    Authors: Valery Lainey, Pini Gurfil, Michael Efroimsky

    Comments: Submitted to "Celestial Mechanics and Dynamical Astronomy."

    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 20
    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, both for high and
    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 and to an arbitrary
    initial inclination, of an old result obtained by Goldreich (1965) for the
    case of uniform precession and a low initial inclination. Such "inclination
    locking" confirms that an oblate planet can, indeed, afford a large
    equinoctial precession for dozens of millions of years, without repelling
    its near-equatorial satellites away from the equator of date: the
    inclination oscillates but does not show a secular increase. Nor does it
    show a secular decrease, a fact that is relevant to the discussion of the
    possibility of high-inclination capture of Phobos and Deimos.

    Astrophysics, abstract

    From: Michael Efroimsky [view email]

    Date (v1): Mon, 9 Aug 2004 22:28:03 GMT (48kb)

    Date (revised v2): Wed, 25 Aug 2004 01:24:31 GMT (47kb)

    Long-term evolution of orbits about a precessing oblate planet: 1. The case
    of uniform precession

    Authors: Michael Efroimsky

    Subj-class: Astrophysics; Classical Physics; Dynamical Systems; Exactly
    Solvable and Integrable Systems

    Journal-ref: Celest.Mech.Dyn.Astron. 91 (2005) 75-108

    It was believed until very recently that a near-equatorial satellite would
    always keep up with the planet's equator (with oscillations in inclination,
    but without a secular drift). As explained in Efroimsky and Goldreich
    (2004), this misconception originated from a wrong interpretation of a
    (mathematically correct) result obtained in terms of non-osculating orbital
    elements. A similar analysis carried out in the language of osculating
    elements will endow the planetary equations with some extra terms caused by
    the planet's obliquity change. Some of these terms will be nontrivial, in
    that they will not be amendments to the disturbing function. Due to the
    extra terms, the variations of a planet's obliquity may cause a secular
    drift of its satellite orbit inclination. In this article we set out the
    analytical formalism for our study of this drift. We demonstrate that, in
    the case of uniform precession, the drift will be extremely slow, because
    the first-order terms responsible for the drift will be short-period and,
    thus, will have vanishing orbital averages (as anticipated 40 years ago by
    Peter Goldreich), while the secular terms will be of the second order only.
    However, it turns out that variations of the planetary precession make the
    first-order terms secular. For example, the planetary nutations will
    resonate with the satellite's orbital frequency and, thereby, may instigate
    a secular drift. A detailed study of this process will be offered in the
    subsequent publication, while here we work out the required mathematical
    formalism and point out the key aspects of the dynamics.

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