Passing through resonance: The excitation and dissipation of the lunar free libration in longitude

Details Passing through resonance: The excitation and dissipation of the lunar free libration in longitude Passing through resonance: The excitation and dissipation of the lunar free libration in longitude

Oct 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..57..307e&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 57, no. 1-2, p. 307-324

Astronomy and Astrophysics

Astronomy

5

Deformation, Libration, Longitude, Moon, Orbit Calculation, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Viscoelasticity, Earth-Moon System, Fourier Series, Lunar Rangefinding, Series Expansion

Scientific paper

The acceleration of the mean lunar longitude has a small effect on the periods of most terms in a Fourier expansion of the longitude. There are several planetary perturbation terms that have small amplitudes, but whose periods are close to the resonant period of the lunar libration in longitude. Some of these terms are moving toward resonance, some are moving away from resonance, and the periods of those terms that do not include the Delaunay variables in their arguments are not moving. Because of its acceleration of longitude, the Moon is receding from the Earth, so the magnitude of the restoring torque that the Earth exerts on the rotating Moon is gradually attenuating; thus resonance itself is moving, but at a much slower rate than the periods of the accelerating planetary perturbations. There are five planetary perturbation terms from the ELP-2000 Ephemeris (with amplitudes of 0.00001 sec or greater) that have passed through resonance in the past two million years. One of them is of special interest because it appears to be the excitation source of a supposed free libration in longitude that has been detected by the lunar laser ranging experiment. The amplitude of the term is only 0.00021 sec but it could be the source of the approximately 1 sec amplitude free libration term if the viscoelastic properties of the Moon are similar to those of the Earth.

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