This paper introduces a completely new relativistic theory of orbits based on the four force concept of the Goettingen mathematician Hermann Minkowski, who was a teacher of Einstein at ETH. From 1907 onwards Minkowski developed the contravariant covariant notation used today and the concept of relativistic four force in Minkowski spacetime which he developed after Einstein’s inference of relativistic momentum in 1905. So force and acceleration can be developed without Einstein’s version of general relativity, which looks more and more shaky the more I progress with my own thoughts, always with key help from AIAS colleagues in checking, graphics and animations. Nothing now stands between the theories of AIAS and its vast readership, everything we produce is read with great interest without any interference from censors. There have been some slight changes to the notes, and these have been incorporated in the final paper. The calculations have been checked as usual by computer algebra. There are as many applications of this theory as there are of special relativity itself. This particular paper constrains the applications to planar orbits in which an object of mass m moves relativistically. There are applications also to electrodynamics in which the Minkowski equation is used in the covariant form of the Lorentz force equation. There are unlimited numbers of applications to particle physics and so on, and relativistic quantum mechanics.

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