B. M. Barker

Nongeodesic motion in general relativity

The equations of motion of a spinning body in the gravitational field of a much larger mass are found using both the Corinaldesi-Papapetrou spin supplementary condition (SSC) and the Pirani SSC. These equations of motion are compared with our previous result derived from Guptas quantum theory of Gravitation. It is found that the spin-dependent terms differ in each of the above three results due to a different location of the center of mass of the spinning body. As expected, these terms are not affected by the choice of either Schwarzschild or isotropic coordinates. Finally, for the presently planned Stanford gyroscope experiment, we find the maximum secular displacement of the orbit of the gyro with respect to the orbit of its non-rotating housing to be of the order of (10−7 cm/year)t, a result much smaller than Schiffs result which is proportional to time squared.

Spin nutation in binary systems due to general relativistic and quadrupole effects

We consider two spinning compact objects in a binary system where the orbital angular momentum is much greater than the spin angular momenta. The amplitude and frequency of the spin nutation of body 2 ( and body 1 by interchanging indices) due to general relativistic and quadrupole effects are given. The spin nutation frequency of either body is found to be equal to the difference in the two spin precession frequencies.