The spin-orbit resonant rotation of Mercury: a two degree of freedom Hamiltonian model
It is well known that the resonant motion of Mercury is blocked in a spin-orbit resonance of the 3/2 type. There are many publications on the subject (the review of 22 references is given in the article). Here, the two degree-of-freedom Hamiltonian system, averaged over the short periods, is used to describe the libration about the resonant spin-orbit 3/2 motion by two pairs of action-angle variables. The following basic hypotheses were used in the simplified analytic model: Mercury is a rigid non spherical body, the gravity field is truncated after the second degree terms, the orbital motion of Mercury is Keplerian, the spin axes is parallel to the third axes of inertia. The authors are planning to include and to investigate later on the following perturbations: the higher coefficients of the gravity field, the angle between the spin axes and the principal axes of inertia, the non-Keplerian orbital motion (indirect planetary perturbations) and the direct planetary perturbations. It should be noted that according to the many investigations of V. V. Vidyakin, N. Ye. Saburova (since 1990--1992) on the rotation-translation motion of rigid bodies (the latest paper is: Arkhangelsk State Technical University, Sci. Works of Appl. Math. Dept., No. 3 , (2004)) for an three-axial body moving in the field of the homogeneous sphere (point mass) some special conditions relative to its moments of inertia, say \(A,B,C\), must be fulfilled (for example, \(A=B=C\) !) or the body should be specially oriented. Otherwise the center of mass of such body will not be moving along the Keplerian ellipse (as it was supposed in the article reviewed). The numerical values obtained by their simplified model are in perfect agreement with those obtained by \textit{N. Rambaux} and \textit{E. Bois} [Astron. Astrophys. 413, No. 1, 381--393 (2004), doi:10.1051/0004-6361:20031446]
scientific article; zbMATH DE number 2140055