Comparative rotational dynamics of the Moon, Mercury and Titan

Abstract

Constant and periodic variations in the gravitational coefficients of second harmonics of gravitational potential of the Moon, Mercury and Titan caused by the attraction of their external bodies are described analytically. On the base of a plane model of translatory–rotary motion of the above-mentioned elastic bodies on elliptical orbits the main variations in the coefficients C 20, C 22 and S 22 with periods that are a multiple of the orbit period have been obtained and evaluated. Dynamic effects in resonant rotation of the Moon, Mercury and Titan considered as an unchangeable non-spherical bodies are studied on the basis of two simple models: firstly, the plane motion on the unperturbed elliptic orbit; secondly, the rotation of Titan on the precessing circular orbit. Peale's hydrostatic values of Titan's gravitational field parameters C 20 and C 22 (Peale, 1973 Peale, SJ. (1973). Rev. Geophys. Space Phys., 11: 767[Crossref], [Web of Science ®] , [Google Scholar]) and two sets of their model values are used in paper to evaluate the unperturbed, forced and resonant effects in the rotation of Titan. For Mercury we also use an average equilibrium model of elastic body rotating in resonance 3:2 with an orbital motion. Another model of Mercury is based on the modern radio-location data (Peale et al., 2004). For the Moon, well-known dynamical characteristics are used. Obtained Cassini's positional parameters, amplitudes of periodic librations in longitude, periods of resonant librations and other characteristics of studied celestial bodies are given in mutual comparison.