The Gravitational Field of a Planet

Abstract

Deviations of the shape of a cosmic body from spherical symmetry show up in its gravitational field; conversely, corrections to the monopole gravitational field GM/r provide important information about the interior. The main deviation is due to rotation and corresponds to a correction in the gravitational potential proportional to 1/r³ (the quadrupole term). Smaller disturbances in the mass distribution produce on the surface smaller corrections which decrease with a higher power of the distance from the centre. The gravitational field of a generic, non-spherical body is appropriately described by a powerful mathematical tool, the set of spherical harmonic functions. This chapter introduces this tool and applies it to the earth. The physics of gravity anomalies of small size is also discussed.