MOTION IN A SCHWARZSCHILD FIELD .I. PRECESSION OF A MOVING GYROSCOPE

A simple hypothesis is used to obtain, in lowest order, the precessional angular velocity of a slowly moving gyroscope in a Schwarzschild gravitational field. The hypothesis is that, at least to first approximation, the motion of the spin vector in a small displacement is the sum of two effects: (1) the motion the spin would have if it moved by parallel transfer in the curved 3-space, and (2) the motion of the spin as calculated directly from the principle of equivalence, treating the gravitational field in the vicinity of the gyroscope as though it were uniform. The precessional angular velocity obtained is in agreement with the general relativistic result. In another paper it will be shown that the same hypothesis also leads to the general relativistic result for the lowest order deflection of light by the central mass. These derivations are useful because they help to show how the motion of the spin vector can be understood from a [formula omitted] dimensional viewpoint. © 1969, American Association of Physics Teachers. All rights reserved.