Spin dynamics of the LAGEOS satellite in support of a measurement of the Earth's gravitomagnetism.

LAGEOS is an accurately tracked, dense spherical satellite covered with 426 retroreflectors. Ciufolini has suggested the launch of an additional satellite (LAGEOS-3) into an orbit supplementary to that of the 1976-launched LAGEOS-1. In addition to providing a more accurate real-time measurement of the Earth's length of day and polar wobble, this paired-satellite experiment would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite, and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. Consequently, we undertake here a theoretical effort to model the spin dynamics of LAGEOS. In this paper we derive, and solve numerically, a set of Euler equations that evolve the angular momentum vector for a slightly oblate spheroid of brass orbiting an Earth-like mass, idealized as being a perfect sphere and having a perfect polar-oriented dipole magnetic field. We have identified three phases of the rotational dynamics---a fast spin phase, a spin-orbit resonance phase, and an asymptotic (tidally locked) phase. From our numerical runs we give analytic expressions for this tidally locked phase.