The Metric for the Gravitational Field of the Oblate Earth and the Equatorial Orbits of a Satellite

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Abstract
A coordinate transformation has been found which transforms the Schwarzschild metric for the field of a spherical body into a special case of the general axially symmetric metric first derived by Levi-Civita and by Weyl, referred to as the LCW form. The transformed Schwarzschild metric is perturbed in such a way as to retain the LCW form and the field equations are solved approximately for the perturbing terms. With values of the arbitrary constants appearing in the solution found by a reduction to Newtonian theory, the metric obtained is taken to be that of the Earth's field. The equatorial orbits of a free particle are discussed and the advance of perigee is calculated.

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