Lunar rotational dissipation in solid body and molten core

Analyses of Lunar Laser ranges Shaw a displacement in direction of the Moon 's pole of rotation which indicates that strong dissipation is acting on th e rotation. Two possible sources of dissipation are monthly solid-body tide s raised by the Earth (and Sun) and a fluid core with a rotation distinct f rom the solid body. Both effects have been introduced into a numerical inte gration of the lunar rotation. Theoretical consequences of tides and core o n rotation and orbit are also calculated analytically. These computations i ndicate that the tide and core dissipation signatures are separable. They a lso allow unrestricted laws for tidal specific dissipation Q versus frequen cy to be applied. Fits of Lunar Laser ranges detect three small dissipation terms in addition to the dominant pole-displacement term. Tidal dissipatio n alone does not give a good match to all four amplitudes. Dissipation from tides plus fluid core accounts for them. The best match indicates a tidal Q which increases slowly with period plus a small fluid core. The core size depends on imperfectly known properties of the fluid and core-mantle inter face. The radius of a core could be as much as 352 km if iron and 374 km fo r the Fe-FeS eutectic composition. If tidal Q versus frequency is assumed t o be represented by a power law, then. the exponent is -0.19 +/- 0.13. The monthly tidal Q is 37 (-4,+6), and the annual Q is 60 (-15,+30). The power presently dissipated by solid body and core is small, but it may have been dramatic for the early Moon. The outwardly evolving Moon passed through a c hange of spin state which caused a burst of dissipated power in the mantle and at the core-mantle boundary. The energy deposited at the boundary plaus ibly drove convection in the core and temporarily powered a dynamo. The rem anent magnetism in lunar rocks may result from these events, and the peak f ield may mark the passage of the Moon through the spin transition.