Issue |
A&A
Volume 432, Number 3, March IV 2005
|
|
---|---|---|
Page(s) | 1101 - 1113 | |
Section | Celestial mechanics and astrometry | |
DOI | https://doi.org/10.1051/0004-6361:20041312 | |
Published online | 07 March 2005 |
Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars
1
Instituto de Astronomía y Geodesia (UCM – CSIC), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid, Spain e-mail: martafl@mat.ucm.es
2
Observatoire de Paris, SYRTE, UMR 8630 du CNRS, 61 avenue de l'Observatoire, 75014 Paris, France e-mail: Jean.Souchay@obspm.fr
Received:
18
May
2004
Accepted:
25
October
2004
The purpose of this paper is to show how to solve in
Hamiltonian formalism the equations of the polar motion of any
arbitrarily shaped elastic celestial body, i.e. the motion of its
rotation axis (or angular momentum) with respect to its figure
axis. With this aim, we deduce from canonical equations related to
the rotational Hamiltonian of the body, the analytical solution
for its free polar motion which depends both on the elasticity and
on its moments of inertia. In particular, we study the influence
of the phase angle δ, responsible for the dissipation, on
the damping of the polar motion. In order to validate our
analytical equations, we show that, to first order, they are in
complete agreement with those obtained from the classical
Liouville equations.
Then we adapt our calculations to the real data obtained from the
polar motion of the Earth (polhody). For that purpose, we
characterize precisely the differences in radius and in
angle
between the polar coordinates
and
representing respectively the motion of the axis of rotation of the Earth and the motion of its angular momentum axis,
with respect to an Earth-fixed reference frame, after showing the
influence of the choice of the origin on these coordinates, and on
the determination of the Chandler period as well. Then we show
that the phase lag δ responsible for the damping for the
selected time interval, between Feb. 1982 and Apr. 1990, might be
of the order of
, according to a
numerical integration starting from our analytical equations.
Moreover, we emphasize the presence in our calculations for both
χ and θ, of an oscillation with a period
, due to the triaxial shape of our planet, and generally not taken into account.
In a last step, we apply our analytical formulation to the polar
motion of Mars, thus showing the high dependence of its damping on
the poorly known value of its Love number k. Moreover we
emphasize the large oscillations of Mars' polar motion due to the
triaxiality of this planet.
Key words: methods: analytical / solar system: general
© ESO, 2005
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