Modeling the obliquity of Mercury

Measuring the obliquity of Mercury is crucial to determine its internal structure, in particular its polar inertial momentum C. The well-known Peale's experiment tells us that this quantity, combined to the measurements of the longitudinal librations, gives the size of Mercury's molten core. The inversion of the obliquity is classically made thanks to Peale's formula. This formula considers the gravity coefficients J2 and C22, and assumes the inclination of Mercury and its node velocity to be constant with respect to a Laplace Plane that must be carefully determined. We here propose an alternative formula, that is Laplace-Place free, and considers additional coefficients like J4, and secular variations of Mercury's dynamics. We are in good agreement with Peale's formula. This allows us to estimate the accuracy of the theoretical modelization of Mercury's obliquity, and to quantify the influence of usually neglected effects.