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.
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Adler, R.J. Metric for an Oblate Earth. General Relativity and Gravitation 31, 1837–1854 (1999). https://doi.org/10.1023/A:1026734805268
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DOI: https://doi.org/10.1023/A:1026734805268