General-relativistic celestial mechanics. I. Method and definition of reference systems

Abstract

er, the great increase in precision of current, and foreseeable, observational techniques in the solar system makes it now necessary to reconsider this traditional (post-Newtonian) way of tackling the gravitational dynamics of N-body systems.Indeed, modern technology is giving us access to highprecision data on both the global celestial mechanics of the solar system, and the local relativistic gravitational environment of the Earth, and on the way they fit together. We have in mind high-precision techniques such as 43 3273 1991 The American Physical Society 3274 THIBAULT DAMOUR, MICHAEL SOFFEL, AND CHONGMING XU 43 the following. Concerning the global mechanics of the solar system: radar ranging to the planets (with, e.g. , a few meters accuracy for the Viking landers on Mars), laser ranging to the Moon (few centimeters level), and the timing of millisecond pulsars (sub-microsecond level).Concerning the local environment of the Earth: the comparison, at the 100 nanosecond level, of stable atomic clocks (via, for instance, the Global Positioning System) and laser ranging to artificial satellites (such as LAGEOS, at the 1-cm level). Concerning the fitting of the local Earth environment to the global structure of the solar system, and/or of the external universe at large, we have in mind, in particular, the very long baseline interferometry technique, which determines baselines on the surface of the Earth, and the position of the rotation pole, with centimeter accuracy, the length of the day at the few millisecond level, and relative angles between distant objects, as seen on the Earth, with a precision better than a milliarcsecond. For an introduction to these techniques, and a review of their impact on general relativity see Soffel.In order to match the high precision of this wealth of (present and forseeable) data, one needs a correspondingly accurate relativistic theory of celestial mechanics able to describe both the global gravitational dynamics of a system of N extended bodies, the local gravitational structure of each, arbitrarily composed and shaped, rotating deformable body, and the way each of these X local structures meshes into the global one. The traditional post-Newtonian approach to relativistic celestial mechanics fails, for both conceptual and technical reasons, to bring a satisfactory answer to this problem. This traditional post-Newtonian approach uses only one global coordinate system x"=(ct, x,y, z), to describe an N bodysystem, and models itself on the Newtonian approach to celestial mechanics consisting of decomposing the problem into two subproblems [Tisserand' (Vol. I, pp. 51 -52);Pock j: (i) the external problem, to determine the motion of the centers of mass of the N bodies; (ii) the internal problem, to determine the motion of each body around its center of mass. However, the treatments of both subproblems in the traditional post-Newtonian approach are unsatisfactory. The external problem is attacked by introducing some collective variable, say z'(t), i=1,2,3, generalizing the Newtonian c...

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