Tides on the Moon: Theory and determination of dissipation

Solid body tides on the Moon vary by about 0.1m each month. In addition to changes in shape, the Moon's gravity field and orientation in space are affected by tides. The tidal expressions for an elastic sphere are compact, but dissipation introduces modifications that depend on the forcing period. Consequently, a Fourier representation of the tide-raising potential is needed. A mathematical model for the distortion-caused tidal potential may be used for the analysis of precise spacecraft tracking data. Since tides affect gravitational torques on the Moon from the Earth's attraction, the lunar orientation is also affected. Expressions for five periodic perturbations of orientation are presented. The rheological properties of lunar materials determine how the Moon responds to different tidal periods. New lunar laser ranging solutions for the tidal orientation terms are presented. The quality factor Q is 384 at 1month, 419 at 1year, 74 at 3years, and 58 at 6years. The ranging results can be matched with absorption band models that peak at similar to 120days and single relaxation time models that peak at similar to 100days. Combined models are possibilities. Dissipation can modify laser ranging solutions; previously reported core flattening is too uncertain to be useful. Strong lunar tidal dissipation, modeled to arise in the deep hot mantle, appears to be from a region with radius 535 km. Classical Maxwell-type dissipation is too weak to detect at 3 and 6year periods.