The effect of tides and an inner core on the forced longitudinal libration of Mercury

Mercuryʹs longitudinal libration at a period of 88 days depends on the moment of inertia of the planetʹs silicate outer part and as such contains information on the interior structure and composition of Mercury. Secondary effects on the libration may affect the interpretation of libration observations in terms of interior structure properties and may also provide further information on Mercuryʹs interior. Here we assess the importance of the effects of tides and the existence of a solid inner core on the librations of Mercury with particular focus on the 88 days libration amplitude. Tides affect the librations of Mercury by changing the gravitational torque exerted by the Sun on Mercury and by changing the polar moment of inertia. We show that they slightly decrease the 88 days libration amplitude by about 1–2 m, which is below the current and future expected observational precision. We further demonstrate that the effect of an inner core on Mercuryʹs 88 days libration amplitude is also below the observational precision for small inner cores, but could be observed if Mercuryʹs inner core is larger than at least 1000 km. An inner core also changes considerably the free libration period by up to 25% if the inner core is very large. Besides giving information on the moment of inertia of the silicate shell, observations of Mercuryʹs libration can therefore also yield information on the inner core.