I think that the main aim of this four author paper (Horst Eckardt, Ray Delaforce, Gareth Evans and myself) will be a vivid demonstration of the complete failure of Einstein’s general relativity (EGR) to describe the basics of observed orbits, I emphasize the adjective “observed”. It is not just an approximate failure, but what is known in science as a qualitative failure, in every day terms a total failure. In addition EGR cannot describe the newly discovered fractal properties of the conical sections, again a total failure. I discovered the way to show this total failure almost by accident. I wrote down the equation
r = alpha / ( 1 + epsilon cos (x theta))
and this equation describes the precessing elliptical orbits, a large class of orbits. Using lagrangian dynamics the new universal force law was discovered. It turns out that the above equation can describe ALL orbits using only x. It would be very difficult to find an orbit that it does not describe. In addition it gives the fractal conical sections, hitherto unknown in pure mathematics, the multi leaved petal orbits and so on. If one places oneself back in 1788, when Lagrange inferred his method, the reasonable enlightenment of his contemporaries such as Voltaire or Mozart would have smiled the smile of reason. EGR cannot produce this equation, it produces a scowl of dark matter and the junk rap of false authority in science.