The Observatory works on the librations of Mercury. According to the Peale experiment, we know that the C20, C22, the obliquity and the amplitude of libration allow us to determine the moments of inertia of Mercury and its internal structure. We know the libration amplitude, which was calculated by Jean-Luc Margot to be at the level of 35 seconds of arc. Marie Yseboodt, researcher at the Observatory, attempted to calculate the obliquity from the Cassini laws. There are four Cassini states for Mercury, the most probable one is the one in which Mercury has an obliquity of 1.6 minutes of arc. This value is not certain as the laws of Cassini have only been developed in an empirical way. In order to determine the probable cases and the value of the obliquity, Marie Yseboodt has precisely calculated the position of the Laplace plane. The values of C20 and C22 were measured by Mariner 10 with an uncertainty of 50%.
The BepiColombo and Messenger probes will take more comprehensive and more accurate datas than those taken by Mariner 10 or from the Earth. They greatly refine the accuracy of the results of our calculations.
Scientists at the ROB calculated the libration of Mercury. They worked on the spin-orbit coupling on the basis of different models of the interior of Mercury. They have calculated the effects of core-mantle coupling on the rotation of Mercury in the case of zero obliquity of Mercury and a keplerian orbit. They used a numerical approach by working with the software SONYR acronym for "Spin-Orbit Relativistic N-body model" and generated a set of libration for the different models of the interior of Mercury with different dimensions for the seed, the kernel (liquid or solid) and the mantle. They showed that the influence of inertial coupling is of the order of a millisecond of arc, the amplitude of libration to 88 days depends primarily on the radius of the core or equivalent to the concentration of sulfur in the ring, and the potential values for the libration amplitude varies in an interval of about 20 seconds of arc, indicating the possibility of discriminations between several models of internal structure in using specific measures future BepiColombo and Messenger. For more information: see Rambaux, Van Hoolst, Dehant, and Bois (2007).