Tidal dissipation in the moon

Astronomy and Astrophysics – Astronomy

Scientific paper

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Euler Equations Of Motion, Gravitational Effects, Lunar Rangefinding, Lunar Rotation, Lunar Tides, Selenology, Astronomical Models, Energy Dissipation, Least Squares Method, Mechanical Properties, Stress Distribution, Stress Tensors, Moon, Tidal Effects, Dissipation, Motion, Rotation, Elasticity, Q Value, Frequency, Mathematical Models, Observations, Analysis, Data, Parameters

Scientific paper

Euler's equations of motion, modified to include elasticity and solid friction, were used to study the rotation of the moon. Two heuristic models for the anelasticity were considered: Q independent of frequency and Q inversely proportional to the frequency and Q inversely proportional to the frequency of the strain oscillation. Parameters in each model were estimated by weighted least squares from 9 years of lunar laser range observations. The root mean square of the postfit range residuals was 19 cm in each case. For a strain period of 1 month, the estimates of Q obtained with the two models were similar and surprisingly low: 23 + or - 6. The range of uncertaintly, + or - 6, represents our estimate of the true standard deviation of the estimate of Q, as affected by systematic errors; it is 3 times larger than the formal, statistical, standard error.

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