The proximity of Mercury’s spin to Cassini state 1

Astrophysics, abstract
astro-ph/0511419

From: Stan Peale [view email]

Date: Mon, 14 Nov 2005 22:21:56 GMT   (314kb)

In determining Mercury’s core structure from its rotational properties, the
value of the normalized moment of inertia, $C/MR^2$, from the location of
Cassini 1 is crucial. If Mercury’s spin axis occupies Cassini state 1, its
position defines the location of the state. The spin might be displaced from
the Cassini state if the spin is unable to follow the changes in the state
position induced by the variations in the orbital parameters and the geometry
of the solar system. The spin axis is expected to follow the Cassini state for
orbit variations with time scales long compared to the 1000 year precession
period of the spin about the Cassini state because the solid angle swept out by
the spin axis as it precesses is an adiabatic invariant. Short period
variations in the orbital elements of small amplitude should cause
displacements that are commensurate with the amplitudes of the short period
terms. By following simultaneously the spin position and the Cassini state
position during long time scale orbital variations over past 3 million years
(Quinn {\it et al.}, 1991) and short time scale variations from JPL Ephemeris
DE 408 (Standish, 2005) we show that the spin axis will remain within one
arcsec of the Cassini state after it is brought there by dissipative torques.
We thus expect Mercury’s spin to occupy Cassini state 1 well within the
uncertainties for both radar and spacecraft measurements, with correspondingly
tight constraints on $C/MR^2$.

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