Long-period forcing of Mercuryʹs libration in longitude

Planetary perturbations of Mercuryʹs orbit lead to forced librations in longitude in addition to the 88-day forced libration induced by Mercuryʹs orbital motion. The forced librations are a combination of many periods, but 5.93 and 5.66 years dominate. These two periods result from the perturbations by Jupiter and Venus respectively, and they lead to a 125-year modulation of the libration amplitude corresponding to the beat frequency. Other periods are also identified with Jupiter and Venus perturbations as well as with those of the Earth, and these and other periods in the perturbations cause several arc second fluctuations in the libration extremes. The maxima of these extremes are about 30″ above and the minima about 7″ above the superposed ∼ 60 ″ , 88-day libration during the 125-year modulation. Knowledge of the nature of the long-period forced librations is important for the interpretation of the details of Mercuryʹs rotation state to be obtained from radar and spacecraft observations. We show that the measurement of the 88-day libration amplitude for the purposes of determining Mercuryʹs core properties is not compromised by the additional librations, because of the latterʹs small amplitude and long period. If the free libration in longitude has an amplitude that is large compared with that of the forced libration, its ∼10-year period will dominate the libration spectrum with the 88-day forced libration and the long-period librations from the orbital perturbations superposed. If the free libration has an amplitude that is comparable to those of the long-period forced libration, it will be revealed by erratic amplitude, period and phase on the likely time span of a series of observations. However, a significant free libration component is not expected because of relatively rapid damping.