DPS 34th Meeting, October 2002
Session 30. Extrasolar Planets and Systems
Poster, Chair(s): , Thursday, October 10, 2002, 4:00-6:30pm, Exhibit Hall

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[30.06] Numerical Evaluation of Love's Solution for Tidal Amplitude: Extreme tides possible

T.A. Hurford, R. Greenberg, S. Frey (Univ. of Arizona)

Numerical evaluation of Love's 1911 solution [1] for the tidal amplitude of a uniform, compressible, self-gravitating body reveals portions of parameter space where extremely large (or even large negative) tides are possible. Love's solution depends only on (a) the ratio of gravity to the rigidity, \rho g R / \mu , and (b) the ratio of rigidity to Lamé constant, \mu / \lambda . The solution is not continuous; it includes singularities, around which values approach plus-or-minus infinity, even for parameters in a range plausible for planetary bodies. The effect involves runaway self-gravity.

For rocky bodies up to Earth-sized, the solution is well behaved and the tidal amplitude is within ~20 % of that given by the standard Love number for an incompressible body.

For a moderately larger or less rigid planet, the Love number could be enhancedgreatly, possibly to the point of disruption. A thermally evolving planet could hit such singularities as it evolves through elastic-parameter space. Similarly, a growing planet could hit these conditions as \rho g R increases, possibly placing constraints on planet formation. For example, a large rocky planet not much larger than the Earth or Venus could hit conditions of extreme tides and be susceptible to possible disruption, conceivably placing an upper limit on growth. The growing core of a giant planet might also be affected. Depending on elastic parameters, planetary satellites may also experience more extreme tides than usually assumed, with potentially important effects on their thermal, geophysical, and orbital evolution. \\ \\ [1] Love, A.E.H., Some Problems of Geodynamics, New York Dover Publications, 1967

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Bulletin of the American Astronomical Society, 34, #3< br> © 2002. The American Astronomical Soceity.