Theory of the Mercury’s spin-orbit motion and analysis of its main librations

Astrophysics, abstract
astro-ph/0306387

From: Nicolas Rambaux  <rambaux@obs.u-bordeaux1.fr>

Date: Thu, 19 Jun 2003 18:43:41 GMT   (498kb)

Authors:
Nicolas Rambaux,
Eric Bois (Observatoire Aquitain des Sciences de l’Univers, Bordeaux, France)

Comments: 15 pages, 14 figures, 3 tables, submitted to A & A

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 relativistic BJV model
of solar system integration including the coupled spin-orbit motion of the
Moon. We have extended this model by generalizing the spin-orbit couplings to
the terrestrial planets, notably Mercury. The updated model is called SONYR
(acronym of Spin-Orbit N-BodY Relativistic model). The SONYR model giving an
accurate solution of the spin-orbit motion of Mercury permits to analyze the
different families of the Hermean rotational librations. The spin-orbit motion
of Mercury is characterized by two proper frequencies (namely 15.847 and 1066
years) and its 3:2 resonance presents a second synchronism which can be
understood as a spin-orbit secular resonance (278 898 years). By using the
SONYR model, we find a new determination of the mean obliquity, namely 1.6
arcminutes. Besides, we identify in the Hermean librations the impact of the
uncertainty of the greatest principal moment of inertia (cmr2) on the
obliquity and on the libration in longitude (2.3 mas and 0.45 as respectively
for an increase of 1% on the cmr2 value). These determinations prove to be
suitable for providing constraints on the internal structure of Mercury.

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