**Authors:** Akindele O. Adekugbe Joseph

The two-theory approach to gravitation at the second stage of evolutions of spacetime/intrinsic spacetime and parameters/intrinsic parameters in a gravitational field of arbitrary strength, comprising of the theory of gravitational relativity/intrinsic theory of gravitational relativity (TGR/øTGR) on flat spacetime/flat intrinsic spacetime and the metric theory of absolute intrinsic gravity (øMAG) on curved absolute intrinsic spacetime, isolated at the neighborhood of one gravitational field source in the earlier articles, is advanced to the situations where two, three and several gravitational field sources are scattered in the Euclidean 3-space about a location where the theories are formulated. Gravitational time dilation, gravitational length contraction and assemblage of parameter transformations in the context of TGR, are extended to the neighborhood of several gravitational field sources. Extension of TGR to the situation where a number N of gravitational field sources are interacting (the N-body problem), is accomplished for N=2 and N=3 and shown to admit of straight forward extension to larger values of N, except that it becomes increasingly cumbersome as N increases beyond 4. On the other hand, øMAG admits of easy and straight forward extension to the N-body problem for any value of N. Einstein's principle of equivalence is validated in the context of TGR at the neighborhood of any number of gravitational field sources, from which its universal validity follows.

**Comments:** 42 Pages. An article in volume one of THE FUNDAMENTAL THEORY...monograph series on an evolving fundamental theory of physics with a complete theory of relativity and gravitation in four-world as its foundation.

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[v1] 2012-08-28 07:10:24

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