The Determination of the External Gravity Field of the Earth from Observations of Artificial Satellites

Abstract

Summary The principles and results of the determination of the external gravity field of the Earth from the motions of artificial satellites are reviewed. Since the general ideas and results are by now widely understood, most attention will be given to problems that still remain in the theory and its application. These will include : the functional form in which the external potential is expressed; exact solutions in the theory of orbits; the statistical difficulties of deriving coefficients of spherical harmonic components of the field from observations of a restricted number of satellites; current estimates of the harmonic coefficients of the external field; the theory of the near field and comparisons between satellite results and surface measurements of gravity; and the bearing of the results on the physical state of the Earth’s interior. It is now more than eight years since the observations of the first artificial satellites gave accurate indications of the ellipticity of the Earth, and in the intervening time it has become widely known that observations of artificial satellites give accurate and detailed information about the external gravity field of the Earth, so that most of this review can be devoted to a discussion of problems which are still outstanding. These are: the best way of describing the external field of the Earth, the numerical problems which arise in determining the field from the observed motions of artificial satellites, and the problem of making detailed comparisons between the field as derived from the motions of artificial satellites and that observed on the surface of the Earth. These problems do not, perhaps, affect the major results that have been obtained from observations of artificial satellites, for example the knowledge that we have of the flattening of the Earth, but the accuracy now obtainable in the observations of artificial satellites shows that the finer details of theory and of numerical determinations have to be considered. This is of especial importance perhaps in the study of the physics of the Earth’s interior, for the knowledge that we can derive about that subject from the observed external potential comes mainly from the values of the harmonics of high order in the potential and it is the values of these harmonics which are particularly affected by the considerations just mentioned.