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Viscoelastic Relaxation within the Moon and the Phase Lead of its Cassini State
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- Author / Creator
- Organowski, Olivier
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In the year 1693, the Franco-Italian astronomer Giovanni Domenico Cassini publishedthree empirical laws describing the orbital and rotational motions of the Moon. Cassini’sThird Law describes the orientations of the lunar equatorial plane and the lunar orbital planevis-a-vis the ecliptic. Specifically, it states that the lunar orbit normal and the lunar figureaxis remain co-planar with the ecliptic normal. However, measurements from lunar laserranging observations conducted in the decades following the Apollo missions unequivocallydemonstrate the existence of a small 0.265 arc-second phase lead between the theoreticalstate, as described by Cassini, and the observed state of the Moon. This fact is suggestive ofthe existence of dissipation mechanisms within the Moon. Examples of previously proposeddissipation mechanisms include viscous dissipation in the Moon’s fluid core and solid-bodytides induced by the gravitational pull of the Earth and Sun. The objective of this studyis to propose an additional dissipation mechanism, namely the viscoelastic relaxation of asolid inner core. This hypothesis is analyzed from the perspective of the angular momentumdynamics of the Moon and its constituent layers; a numerical model of the Moon is constructed,consisting of 5 homogeneous regions (a solid inner core, a fluid outer core, a lowseismic velocity zone, a mantle and a crust). The model is constrained by the observed lunarmass, the moment of inertia of the solid Moon and other selenodetic and seismic observations.Viscoelastic deformations are incorporated into the angular momentum dynamics ofthe Moon. This is done by evaluating the elastic-gravitational equations and computing theappropriate deformation parameters. The objective is to demonstrate that a Maxwelliansolid inner core can influence the observed misalignment of the mantle rotation vector. Therotational dynamic model developed here demonstrates that the orientation of the inner corerelative to the mantle is dependent upon its viscoelastic properties. Through the exchangeof torques with the mantle, the relative misalignment of the inner core will manifest itselfas a shift in the position of the mantle’s rotation axis. It has been demonstrated here thatfor specific inner core parameters, such as radius, viscosity, etc., it is possible to reproducethe observed 0.265 arcsecond misalignment in the mantle rotation vector.
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- Graduation date
- Spring 2019
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.