Lunar studies at Kazan university: trends, results and prospects. I. Physical libration

The main results of the lunar physical libration investigations at Kazan University are presented in the article. The modern problems in the lunar spin-dynamics are considered. Much attention is paid to the finest effects of lunar libration, caused by its complicated interior structure. The parameters of the free libration of the Moon are discussed; a geometrical interpretation of the chandler-like wobble and the free core nutation is given. The targets and problems of the future Japanese project ILOM (In situ Lunar Orientation Measurement) are briefly described in the article. As part of the project it is planned to place a small optical telescope on the lunar surface with the purpose of detecting the lunar physical libration with millisecond accuracy. The computer simulation of the future observations is carried out for their optimization (efficient placement of the observation equipment on the lunar surface; testing of the sensitivity of the new observations to various features of the lunar interior structure). The results of the first stage of the simulation are presented in the paper. At this stage the software for the selection of stars and the reduction of their coordinates for the observation period is developed. The tracks for the selected stars are constructed and analyzed, and their sensitivity to the internal characteristics of the lunar body (in the first place, to the selenopotential coefficients) is tested.
The inverse problem of the physical libration is formulated. It is shown that observations of polar stars do not allow of determining libration in longitude $\tau(t)$. At the stage of solving the inverse problem, the manifestation of the viscoelastic properties of the Moon in the selenographic coordinates is investigated. In the spectrum of simulated residuals, those harmonics are identified which can serve as indicators to refine the viscoelastic parameters such as the Love number $k_2$ and the anelastic time delay.