| Abstract: | In linearized general relativity the metric ofa body is described by a scalar potential and athree-vector potential. We here present a simpletransformation derivation of the linearized metric interms of these potentials, and calculate the exactscalar and vector potentials for a field with oblatespheroidal symmetry. The results for the externalpotentials do not depend on details of the densitydistribution inside the earth; both the scalar and vectorpotentials are fully determined by the total mass, thetotal angular momentum, and a radial parameter, all ofwhich are accurately known from observation. The scalar potential is accurate to roughly10-6 and the vector potential, which hasnever been accurately measured, should be accurate toabout 10-5. Applications include an accuratetreatmen t of the details of the motion of satellites, and theprecession of a gyroscope in earth orbit. |
