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Y. V. Barkin (Sternberg Astronomical Institute, Moscow), J.M. Ferrandiz (Alicante University, Spain)
Present significance of the study of rotation of the Moon and Mercury (M&M)considered as a core-mantle system arises from planned missions to these bodies. An investigation of the resonant rotation of Mercury, begun by Colombo G. (1966), will play main part for Messenger and BepiColombo missions to Mercury. New accurate data about the Moon dynamics will be obtained from a series of future missions to the Moon. In this connection the new approach to the study of M&M resonant dynamics are suggested. Within these approaches M&M are considered as a system of two non-spherical interacting bodies: a liquid core and a mantle. The porpoise of study is to construct the analytical theories of resonant rotational motion of two-layer body (M&M). In first we give an explanation and illustration of the main regularities of M&M rotation and formulate generalized Cassiniís laws. Main resonant properties of Mercury motion were described first as generalized Cassiniís laws (Colombo, 1966). But Colombo and some anotherís scientists (Peale, 1969; Beletskii, 1972; Ward, 1975, Barkin, 1978) considered Mercury (and the Moon) as rigid non-spherical body sometimes taking into account a tidal deformation. Here we have been formulated these laws and their eneralization for a two-layer model of Mercury and the Moon. The mantle of M&M is considered as non-spherical, rigid (or elastic) layer. Inner shell is a liquid core, which occupies a ellipsoidal cavity of M&M (Poincare model). The Mercury system moves in the gravitational field of the Sun in a traslatory-rotary regime of the resonance 3:2 and the Moon system Ė in synchronous regime. We take into account gravitational attraction of the Sun (for Mercury) and gravitational attraction of the Moon and Sun (for the Moon). For the study of M&M rotation we have been used specially designed canonical equations of motion in Andoyer and Poincare variables (Barkin, Ferrandiz, 2001) and special analytical methods of construction of the conditionally-periodic solutions and investigation of their neighborhood earlier used in the theory of rigid Moon rotation (Barkin, 1978, 1986). For numerical evaluations of discussed dynamical effects in M&M motions we have used known dynamical and structural parameters of the Moon and Mercury (Peale, 1996; Williams et al., 2003). In particular the frequencies of free oscillations of M&M core-mantle systems were evaluated: 148 years and 27.2068 days for the Moon and 713 years and 58.6150 days for Mercury. A new phenomenon of a small splitting of the angular momentum vectors of the mantle and liquid core (for the Moon angular splitting is 0.0327 arcsec) was discovered and described analytically. Analytical formulae for perturbations of the first order in rotation of two-layer M&M were obtained for Andoyer and Poincare variables and their amplitudes were tabulated. The general scheme of construction of second and higher order perturbations is described.
Barkin's work was accepted by grant SAB2000-0235 of Ministry of Education of Spain and partially by grants AYA2001-0787 and ESP2001-4533.
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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.