Geometric Structure of the Earth's Gravitational Field as Derived from Artificial Satellites

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Scientific paper

The structure of the earth's gravitational potential and its gradient is studied at sea level and in outer space (1000-km, 10,000-km, and 100,000-km elevation above sea level), with particular consideration given to the surfaces of constant potential and of constant gravitation. Their shape, curvature, etc., are computed and the results presented in tables and maps using the zonal part of the gravitational field as a reference frame. In a concluding section the geometry of the orthogonal trajectories of the equipotential surfaces (direction of the gradient field) is briefly touched. Among others, the curvature and torsion of the verticals are derived and the trajectories are integrated up to 10-km height for the gravity field and 100,000 km for the gravitational field.

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