Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-22T09:53:13.329Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of the Dynamical Figure of the Moon on Its Rotational-Translational Motion

Published online by Cambridge University Press:  14 August 2015

G. I. Eroshkin
G. I. Eroshkin*
Affiliation:
Institute of Theoretical Astronomy, Leningrad, U.S.S.R.

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The influence of the dynamical figure of the Moon on its rotation with respect to its mass centre (the physical libration) is determined by means of the theorem on the angular moment of a rigid body. In the expansion of the Moon's force function in spherical harmonics all the second and the third order harmonics are taken into consideration. For the determination of the Moon's physical libration components a linear system of differential equations of the second order with constant coefficients is constructed.

The integration displays the essential influence of the new terms in the force function expansion. For evaluation of the disturbed elements of the lunar orbit due to the nonsphericity of the Moon's dynamical figure the Lagrange's equations are solved. The disturbing function is taken in an expansion form in powers of the eccentricity of the lunar orbit and of the inclinations of the Moon's equator and its orbit with respect to the ecliptic. The commensurability of the Moon's mean motion and its angular velocity of rotation produces in the major semi-axis of the lunar orbit secular perturbations of the first order.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 62: The Stability of the Solar System , 1974 , pp. 201 - 207
Copyright
Copyright © Reidel 1974 

References

Akim, E. L.: 1966, Dokl. Akad. Sci. 170, 4, 799 (in Russian).Google Scholar
Brumberg, V. A.: 1967, Bull. Inst. Theor. Astron. 11, 73 (in Russian).Google Scholar
Brumberg, V. A., Evdokimova, L. S., and Kochina, N. G.: 1971, Celes. Mech. 3, 197.CrossRefGoogle Scholar
Eckert, W. J.: 1965, Astron. J. 70, 787.CrossRefGoogle Scholar
Goudas, C. L.: 1964, Icarus 3, 375.CrossRefGoogle Scholar
Habibullin, Sh. T.: 1966, Trudy KGO 34, 3 (in Russian).Google Scholar
Hayn, F.: 1923, Encykl. math. Wiss. 6, 2a, 1020.Google Scholar
Koziel, K.: 1948, Acta Astron. , Ser. a, 4, 61.Google Scholar
Lidov, M. L. and Neishtadt, A. I.: 1973, Preprint IPM N9.Google Scholar
Lorell, J.: 1970, The Moon 1, 190.CrossRefGoogle Scholar
Michael, W. N. Jr. and Blackshear, W. Th.: 1972, The Moon 3, 388.CrossRefGoogle Scholar
Michael, W. N. Jr., Blackshear, W. Th., and Gapcynski, J. P.: 1970, in Morando, B. (ed.), Dynamics of Satellites , Springer Verlag, Berlin, p. 42.CrossRefGoogle Scholar
Weimer, Th.: 1966, in La Lune à l'ère spatiale , Paris.Google Scholar