“Mercury’s Rotation and Interior”

Professor S. J. Peale
University of California Santa Barbara
Two spacecraft, MESSENGER (on its way), and BepiColombo (to be launched), will determine many of the properties of the planet Mercury in the near future, and radar observations have already constrained the rotation state with high precision. As part of the increasing study of Mercury motivated by the flood of information we are about to receive, we shall describe Mercury’s rotation state, how it came about, and inferences that follow about the internal structure of the planet. Dissipative processes bring Mercury to a rotation state where its rotational angular velocity is 1.5 times the orbital mean motion, and where the spin axis orientation corresponds to Cassini state 1. In this Cassini state, the spin axis and orbit normal precess around the Laplace plane normal on the orbital precession time scale, while the three vectors remain coplanar. Cassini’s laws for the rotation of the Moon describe a similar configuration. The most probable generation of Mercury’s intrinsic magnetic field detected by the spacecraft, Mariner 10, is by dynamo action from motions of an interior conducting fluid comprising a molten core. Keeping the core molten over the age of the solar system is problematic. But if Mercury occupies Cassini state 1, the values of the amplitude of physical libration in longitude about the resonant rotation state φ0 (88 day period), the obliquity ι, and the second degree coefficients in the expansion of Mercury’s gravitational field, J2 and C22, determine the principal moment of inertia about the spin axis C and the ratio Cm/C, where Cm is the moment of inertia of the mantle alone. The verification and extent of a molten core are thereby effected. Idealized models with fixed parameters, from which core properties are derived, must be checked, since planetary perturbations of Mercury’s orbit vary the orbital parameters and the Laplace plane relative to which Mercury’s orbit precesses. These variations have the potential of frustrating the determination of the interior properties. But we shall see that the 88 day forced libration is simply superposed onto longer period forced librations induced by the orbital variations, and onto any unexpected free libration, allowing its amplitude to still be measured. The spin axis will remain within 1” of the instantaneous position of the Cassini state after being brought there by dissipation. So the obliquity ι should therefore be at least this close to the Cassini state obliquity ιc. The MESSENGER and BepiColombo spacecraft measurements of φ0, ι = ιc, J2 and C22 and radar determinations of ι0, and ι should therefore constrain the interior structure of Mercury quite well. In fact, radar measurements that I will describe have already determined the 88 day forced libration amplitude (~ 60”) and have confined the spin axis to within 6” of Cassini state 1. The unexpectedly large amplitude of the forced libration already implies that Mercury has a molten core.