The Physical Librations of the Moon Caused by its Tidal Deformation

The Moon, like Earth, is not completely solid, and experiences deformation changes, for example due to the tides, caused by the gravitational pull of the Earth's orbit in a complex and resonant nature of the motion of the Moon. It is shown that these deformations lead to temporary variations of Moon inertia tensor components and consequently to the variations in the movement of the poles of the Moon, as well as to the variations of axial rotation. The indicated variations module is in the order of 10--12 mas (millisecond of arc). There variations are important for the development of the high-precision theory of lunar physical libration, suitable for modern projects for the reclamation of the Moon, in particular the Japanese project ILOM, which contemplates installing the telescope on the lunar surface and determining its orientation accuracy of the order of 1--0.1 msd, as well as the Russian lunar program, providing the launch of five automatic stations to the Moon in 2019--2024

The research was carried out with the financial support of the Russian Science Foundation (RSF grant no. 17-71-10254)

References

[1] Barkin Yu.V. Perturbated rotational motion of weakly deformable celestial bodies. A&AT, 2000, vol. 19, iss. 1, p. 19--65. DOI: 10.1080/10556790008241350

[2] Barkin M.Yu. The perturbed rotational motion equations of a celestial body with variable mass geometry in Andoyers variables. Mathematics and Mathematical Modeling, 2016, no. 5, pp. 1--18. DOI: 10.7463/mathm.0516.0847523

[3] Barkin Yu.V., Ferrandiz J.M., Navarro J.F. Terrestrial tidal variations in the selenopotential coefficients. A&AT, 2005, vol. 24, iss. 3, pp. 215--236. DOI: 10.1080/10556790500496487

[4] Williams J.G., Boggs D.H., Ratcliff J.T. Lunar moment of inertia and Love number. 42nd Lunar and Planetary Science Conf. Available at: https://www.lpi.usra.edu/meetings/lpsc2011/pdf/2610.pdf (accessed: 25.12.2018).

[5] Kudryavtsev S.M. Long-term harmonic development of lunar ephemeris. A&A, 2007, vol. 471, no. 3, pp. 1069--1075. DOI: 10.1051/0004-6361:20077568

[6] Rambaux N., Williams J.G. The Moons physical librations and determination of their free modes. Celest. Mech. Dyn. Astr., 2011, vol. 109, iss. 1, pp. 85--100. DOI: 10.1007/s10569-010-9314-2

[7] Barkin Yu.V., Hanada H., Matsumoto K., et al. Effects of a physical libration of the Moon caused by a liquid core, and determination of the fourth mode of a free libration. Sol. Syst. Res., 2014, vol. 48, iss. 6, pp. 403--419. DOI: 10.1134/S003809461406001X

[8] Barkin Yu.V. Theory of physical libration of the Moon caused by a liquid core: Cassinis motion. Cosmic Res., vol. 54, iss. 4, pp. 325--333. DOI: 10.1134/S0010952516030023

[9] Barkin Yu.V., Barkin M.Yu. Theory of physical libration of the Moon with the liquid core: forced librations. Cosmic Res., 2016, vol. 54, iss. 6, pp. 458--474. DOI: 10.1134/S0010952516060010

[10] Hanada H., Heki K., Araki H., et al. Application of PZT telescope to In situ Lunar Orientation Measurement (ILOM). In: Sansò F. (eds). A Window on the Future of Geodesy. International Association of Geodesy Symposia, vol. 128. Berlin, Heidelberg, Springer, 2005, pp. 163--168. DOI: https://doi.org/10.1007/3-540-27432-4_29