Abstract
The dynamical behaviour of N interacting bodies of arbitrary shape and composition, rotating and vibrating under their mutual influence of their gravitational attractions is central for the field of celestial mechanics. Principally, this gravitational N-body problem can be divided into three parts: (1) the local problem, (2) the global problem and (3) the way how the local and the global problems are related. The local problem deals with the physics of the various bodies involved, i.e., their individual gravitational fields and how the various local physical interactions between the dynamics of the local sub-systems (atmosphere, ocean, solid sphere, fluid cores etc.) influence their time behaviour. This local problem should be treated in a local coordinate system that is moving with the body under consideration. The global problem deals with the overall translational and rotational motions of the bodies in some ‘global’ coordinate system that encompasses all N bodies of the system. Finally, one needs a framework that matches the various local systems with the global system: an adequate theory of (astronomical) reference systems. Such a theory of reference systems is unproblematic in the Newtonian space-time due to its absolute properties. However, already in Special Relativity (and especially in GR) the construction of such an important theory of local and global reference systems is highly problematic. In this chapter a theory of astronomical reference systems is formulated at the first post-Newtonian approximation to Einstein’s theory of gravity.
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Soffel, M.H., Han, WB. (2019). Astronomical Reference Systems. In: Applied General Relativity. Astronomy and Astrophysics Library. Springer, Cham. https://doi.org/10.1007/978-3-030-19673-8_9
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