Estimating the Libration of Mercury by Remote Sensing of Gravity and Altimetry

One of the most intriguing scientific questions about Mercury is whether the planet possesses a liquid core. One way that this can be ascertained is through the measurement of the longitudinal libration of Mercury about its rotation axis. The MESSENGER (Mercury Surface, Space, Environment, Geochemistry, and Ranging) mission to Mercury will attempt this measurement by deriving the rotation of the planet from remotely sensed observations of the Mercury gravity field and the planet's shape. For a fully fluid core the libration is expected to be an approximately 350-m-amplitude oscillation (at the equator) about the mean rotation of the planet. Thus, the shape of the planet undergoes a librational oscillation in the same way that features on the surface participate in the motion. In this sense altimetric topography can be considered analogous to imaging, with the important exception that for altimetry, the long wavelengths corresponding to low degrees and orders in a spherical harmonic expansion, can be precisely determined from orbital measurements. The rotation of the planet thus introduces a time dependence of the topographic image in an inertial (i.e. fixed) reference frame and the libration is a variation in the planetary rotation rate, manifest as an oscillation of the topographic image. Similarly, gravity measures the distribution of mass within a planet and as such can be viewed as providing a vertically integrated 'image' of the internal density structure. For a librating planet the gravitational field will also reveal a variation in the rotation rate, manifest as an oscillation of the field with respect to an inertial reference frame. While the long-wavelength gravity field contains contributions from the radial distribution of mass with depth, the long wavelength terms are most sensitive to the mass distribution of the deep interior. Thus, both the topography and the gravity independently can be used to determine the (irregular) rotation of a planet, although the topographical method measures the rotation of the crust while the gravity measures the rotation of the distributed mass, and these are not necessarily identical. For example, for a planet that contains a fluid outer core that is effectively decoupled from the mantle the gravity field will not librate in the manner of a solid body. The libration obtained from the variable rotation of the gravity field will represent a combination of contributions due to a librating mantle and a differentially rotating fluid core. Differential rotation of the Earth's inner core had been theoretically predicted from three dimensional geodynamical models and subsequently reported from seismic observations. A difference between the libration of the lithosphere as determined from altimetry and the deep interior as determined from gravity, if it could be detected, might provide further insight into the nature of core-mantle coupling. Additional information is contained in the original extended abstract.