The influence of orbital dynamics, shape and tides on the obliquity of Mercury

Earth-based radar observations of the rotational dynamics of Mercury (Margot et al. 2012) combined with the determination of its gravity field by MESSENGER (Smith et al. 2012) give clues on the internal structure of Mercury, in particular its polar moment of inertia C, deduced from the obliquity (2.04 +/- 0.08) arcmin. The dynamics of the obliquity of Mercury is a very-long term motion (a few hundreds of kyrs), based on the regressional motion of Mercury's orbital ascending node. This paper, following the study of Noyelles & D'Hoedt (2012), aims at first giving initial conditions at any time and for any values of the internal structure parameters for numerical simulations, and at using them to estimate the influence of usually neglected parameters on the obliquity, like J3, the Love number k2 and the secular variations of the orbital elements. We use for that averaged representations of the orbital and rotational motions of Mercury, suitable for long-term studies. We find that J3 should alter the obliquity by 250 milli-arcsec, the tides by 100 milli-arcsec, and the secular variations of the orbital elements by 10 milli-arcsec over 20 years. The resulting value of C could be at the most changed from 0.346mR^2 to 0.345mR^2.Comment: Accepted for publication in Advances in Space Researc

The rotation of Io predicted by the Poincar\'e-Hough model

This note tackles the problem of the rotation of Io with the 4-degrees of freedom Poincar\'e-Hough model. Io is modeled as a 2-layer body, i.e. a triaxial fluid core and a rigid outer layer. We show that the longitudinal librations should have an amplitude of about 30 arcseconds, independent of the composition of the core. We also estimate the tidal instability of the core, and show that should be slowly unstable.Comment: arXiv admin note: text overlap with arXiv:1111.301

A numerical exploration of Miranda's dynamical history

The Uranian satellite Miranda presents a high inclination (4.338{\deg}) and evidences of resurfacing. It is accepted since 20 years (e.g. Tittemore and Wisdom 1989, Malhotra and Dermott 1990) that this inclination is due to the past trapping into the 3:1 resonance with Umbriel. These last years there is a renewal of interest for the Uranian system since the Hubble Space Telescope permitted the detection of an inner system of rings and small embedded satellites, their dynamics being of course ruled by the main satellites. For this reason, we here propose to revisit the long-term dynamics of Miranda, using modern tools like intensive computing facilities and new chaos indicators (MEGNO and frequency map analysis). As in the previous studies, we find the resonance responsible for the inclination of Miranda and the secondary resonances associated, likely to have stopped the rise of Miranda's inclination at 4.5{\deg}. Moreover, we get other trajectories in which this inclination reaches 7{\deg}. We also propose an analytical study of the secondary resonances associated, based on the study by Moons and Henrard (1993).Comment: 14 pages, 8 figure

Spin-orbit evolution of Mercury revisited

While it is accepted that the eccentricity of Mercury (0.206) favours entrapment into the 3:2 spin-orbit resonance, open is the question how and when the capture took place. A recent work by Makarov (2012) has demonstrated that trapping into this resonance is certain if the eccentricity is larger than 0.2, provided that we use a realistic tidal model, the one which is based on the Darwin-Kaula expansion of the tidal torque. The physics-based tidal model changes dramatically the statistics of the possible final spin states. First, we discover that after only one encounter with the spin-orbit 3:2 resonance this resonance becomes the most probable end-state. Second, if a capture into this (or any other) resonance takes place, the capture becomes final, several crossings of the same state being forbidden by our model. Third, within our model the trapping of Mercury happens much faster than previously believed: for most histories, 10 - 20 Myr are sufficient. Fourth, even a weak laminar friction between the solid mantle and a molten core would most likely result in a capture in the 2:1 or even higher resonance. So the principal novelty of our paper is that the 3:2 end-state is more ancient than the same end-state obtained when the constant time lag model is employed. The swift capture justifies our treatment of Mercury as a homogeneous, unstratified body whose liquid core had not yet formed by the time of trapping. We also provide a critical analysis of the hypothesis by Wieczorek et al. (2012) that the early Mercury might had been retrograde, whereafter it synchronised its spin and then accelerated it to the 3:2 resonance. Accurate processing of the available data on cratering does not support that hypothesis, while the employment of a realistic rheology invalidates a key element of the hypothesis, an intermediate pseudosynchronous state needed to spin-up to the 3:2 resonance.Comment: Extended version of the submitted paper, accepted for publication in Icaru

Theory of the rotation of Janus and Epimetheus

The Saturnian coorbital satellites Janus and Epimetheus present a unique dynamical configuration in the Solar System, because of high-amplitude horseshoe orbits, due to a mass ratio of order unity. As a consequence, they swap their orbits every 4 years, while their orbital periods is about 0.695 days. Recently, Tiscareno et al.(2009) got observational informations on the shapes and the rotational states of these satellites. In particular, they detected an offset in the expected equilibrium position of Janus, and a large libration of Epimetheus. We here propose to give a 3-dimensional theory of the rotation of these satellites in using these observed data, and to compare it to the observed rotations. We consider the two satellites as triaxial rigid bodies, and we perform numerical integrations of the system in assuming the free librations as damped. The periods of the three free librations we get, associated with the 3 dimensions, are respectively 1.267, 2.179 and 2.098 days for Janus, and 0.747, 1.804 and 5.542 days for Epimetheus. The proximity of 0.747 days to the orbital period causes a high sensitivity of the librations of Epimetheus to the moments of inertia. Our theory explains the amplitude of the librations of Janus and the error bars of the librations of Epimetheus, but not an observed offset in the orientation of Janus.Comment: Accepted for publication in Icaru