Gravitational Effects of Rotating Bodies ∗

We study two type effects of gravitational field on mechanical gyroscopes (i.e. rotating extended bodies). The first depends on special relativity and equivalence principle. The second is related to the coupling (i.e. a new force) between the spins of mechanical gyroscopes, which would violate the equivalent principle. In order to give a theoretical prediction to the second we suggest a spin-spin coupling model for two mechanical gyroscopes. An upper limit on the coupling strength is then determined by using the observed perihelion precession of the planet’s orbits in solar system. We also give predictions violating the equivalence principle for free-fall gyroscopes . It is known that the gravitational couplings of intrinsic spins of elementary particles have been investigated for long time in both theory and experiment (see, e.g., Ref. [1] and the literature quoted there). On the other hand, some experiments have been performed by use of mechanical gyroscopes and give contradictory results [2-6]. However, in theory the spin of a mechanical gyroscope (i.e. the rotation of an extended body) is essentially different from the intrinsic spin of an elementary particle. A reasonable deduction is then that the gravitational couplings of intrinsic spin could not be used to describe those of the spin of mechanical gyroscope. Thus it is necessary to study theoretically such effects of possible spin-gravitational couplings on the motion of the center-of-mass for a mechanical gyroscope in an external gravitational field. This is just the aim of the present paper. The project supported partially by the Ministry of Science and Technology of China under Grant Nos. 95-Yu-34 and NKBRSF G 19990754 and the National Natural Science Foundation of China under Grant Nos. 10047004 and 19835040 † Email: [email protected]