Issue |
A&A
Volume 413, Number 1, January I 2004
|
|
---|---|---|
Page(s) | 381 - 393 | |
Section | Celestial mechanics and astrometry | |
DOI | https://doi.org/10.1051/0004-6361:20031446 | |
Published online | 17 December 2003 |
Theory of the Mercury's spin-orbit motion and analysis of its main librations
Observatoire Aquitain des Sciences de l'Univers, Université Bordeaux 1, UMR CNRS/INSU 5804, BP 89, 33270 Floirac, France
Corresponding author: N. Rambaux, rambaux@obs.u-bordeaux1.fr
Received:
16
June
2003
Accepted:
13
August
2003
The 3:2 spin-orbit resonance between the rotational and orbital motions of
Mercury (the periods are and
days respectively) results from a functional dependance of the tidal friction
adding to a non-zero eccentricity and a permanent asymmetry in the equatorial
plane of the planet. The upcoming space missions, MESSENGER and
BepiColombo with onboard instrumentation capable of measuring the rotational
parameters stimulate the objective to reach an accurate theory of the rotational
motion of Mercury. For obtaining the real motion of Mercury, we have
used our BJV model of solar system integration including the coupled spin-orbit
motion of the Moon. This model, expanded in a relativistic framework, had been
previously built in accordance with the requirements of the Lunar Laser Ranging
observational accuracy. We have extended the BJV model by generalizing the
spin-orbit couplings to the terrestrial planets (Mercury, Venus, Earth, and Mars).
The updated model is called SONYR (acronym of Spin-Orbit N-BodY Relativistic model).
As a consequence, the SONYR model gives an accurate simultaneous integration of the
spin-orbit motion of Mercury. It permits one to analyze the different families
of rotational librations and identify their causes such as planetary interactions or the
parameters involved in the dynamical figure of the planet. The spin-orbit motion of
Mercury is characterized by two proper frequencies (namely
yrs and
yrs) and its 3:2 resonance presents a second synchronism which can be understood as
a spin-orbit secular resonance (
yrs). A new determination
of the mean obliquity is proposed in the paper. By using the SONYR model, we
find a mean obliquity of 1.6 arcmin. This value is consistent with the Cassini
state of Mercury. Besides, we identify in the Hermean librations the impact of
the uncertainty of the greatest principal moment of inertia (
) on the obliquity and
on the libration in longitude (2.3 milliarcsec and 0.45 arcsec respectively for an increase of 1% on the
value). These determinations prove to be suitable for providing
constraints on the internal structure of Mercury.
Key words: methods: numerical / celestial mechanics / planets and satellites: individual: Mercury
© ESO, 2004
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