Estimating Mercuryʹs 88-day libration amplitude from orbit

In this paper it is derived that the libration of Mercury can be described by γ=Φ0 sin M+Φ0/K sin 2M where Φ0 is the unknown libration amplitude, M is Mercuryʹs mean anomaly and K=−9.483. Φ0 can be determined by comparing pairs of images of the same landmarks taken by an orbiter at different positions of Mercury. If the angle between the orbit plane of a polar orbiter and Mercuryʹs line of periapsis is between −60° and 60° and if one landmark at the equator is imaged per day with a relative precision of 1.6 arcsec, then the libration amplitude can be determined in two Mercury years (176 days) with an accuracy of 1 arcsec or better, which is sufficient to answer the question whether Mercury has a solid or fluid core.