The Gravitational Field of an Isolated Body

Abstract

Deviations of the shape of a cosmic body from spherical symmetry manifest themselves in its gravitational field; conversely, corrections to the monopole term GM/r provide important, though incomplete, information about the interior. The main, axially symmetric deviation is due to rotation and corresponds to a correction in the gravitational potential proportional to 1/r ³ (the quadrupole term). The potential induced by the tides raised by a nearby body, also ∝ 1/r ³, is symmetric around the axis joining the centres. Smaller disturbances in the mass distribution produce smaller corrections; they decrease faster with the distance from the centre. The gravitational field of a generic, non-spherical body is appropriately described by a powerful mathematical tool, the multipole series of the spherical harmonic functions. This chapter introduces this method and applies it to the Earth. Gravity anomalies due to small scale inhomogeneities are also discussed. The last section briefly deals with the gravity fields of planetary bodies.