**From:** LARRY KLAES (*ljk4_at_msn.com*)

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

**Previous message:**LARRY KLAES: "SETI bioastro: The Transit Light Curve (TLC) Project. I. Four Consecutive Transits of the Exopl"

Astrophysics, abstract

astro-ph/0607522

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.

http://arxiv.org/abs/astro-ph/0607522

Astrophysics, abstract

astro-ph/0607530

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.

http://arxiv.org/abs/astro-ph/0607530

Astrophysics, abstract

astro-ph/0408168

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.

http://arxiv.org/abs/astro-ph/0408168

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