The contribution of observations of satellites to the determination of the Earth's gravitational potential

The history of the determination of the external gravitational potential of the Earth is sketched briefly. A discussion of the principles by which the potential may be derived from the observations of changes in the orbits of artificial satellites is followed by outlines of the principal theories and by detailed consideration of the formal differences between them that arise from differences in the ways that the orbits are described and it is shown that those formulae on which most of the numerical results depend are equivalent in the principal theories. The usual methods of treatment break down in certain special conditions and the analysis of these cases is also considered although they are not of great practical importance in the derivation of the potential; similarly a short account is given of the behaviour of a satellite having an orbital angular velocity commensurable with the spin angular velocity of the Earth. Methods by which satellites are observed are mentioned and the main numerical results on the external potential of the Earth are discussed critically. Finally the results are compared with those derived from observations of gravity on the surface of the Earth and the application of the results to problems of geodesy, of the physical state of the Earth and of the motion of the Moon are described.