1.2 The Modified Kepler Problem.................... 16

We give a new formulation of the N-Body Problem that is free from the drawbacks of the classical one, yet preserves the properties of planetary motion, in particular Kepler’s three famous laws. A re-markable feature of the reformulated problem is that the gravita-tional action can now be repulsive (this is always the case with mass-less particles), as well as attractive. Applications are made to non-standard problems which involve massless particles (e.g. The Comp-ton Effect, The Twin Paradox, The Doppler Effect), and a novel theory is given for The Formation Of The Solar System Through Capture. Finally, we investigate the properties of Confined Sub-Systems, i.e. sub-systems of the N bodies that remain permanently in very close proximity, which can be invoked as an explanation for The Missing Mass In Galaxies, and as a model for both The Struc-ture Of Electrons And Of Atomic Nuclei. Our reformulation thu