The Precession of Mercury's Perihelion
There is a famous discovery in Science where the Precession of Mercury Perihelion played a fundamental role…J
Of course, I am referring to the "Prediction" (in fact, Postdiction) of the Precession of Mercury's Perihelion by Einstein's General Relativity.
A little research on the subject showed me that the precession was already known by the time of the prediction and was in agreement with many models where the proposers guessed left and right the actual formula for the Gravitational Potential. Some of those models had velocity dependence, although not in the manner I proposed.
In addition, the precession of Mercury was the result of many interactions with the planets of the Solar System. The unexplained precession component was of the order of 42.3 arc seconds per century.
Let's see if one can solve that problem in a different paradigm, say, in the Hypergeometrical Universe paradigm.
First let's write the equation for the Hypergeometrical Gravitational Force.
Remember that this equation is not guessed (Ansatz) but derived from first principles!!!!!!!!!!!!!!!!!!!! Not only the equation but also the Gravitational Constant G!!!!!!
If we consider that the Sun is not rotating, thus V1=0 the final force sensed by Mercury is given by:
Adiabatic integration upon R yields the potential
Which is also equation (1) on the Gerber Model reproduced from Gerber's original work in Jaume Gine paper.
A German school teacher named Paul Gerber proposed in 1898 a velocity–dependent potential that predicts exactly the observed value for the anomalous precession of Mercury’s perihelion...
The proposed Gerber’s velocity–dependent potential is equal to my limiting potential when the other body is not rotating. I wrote that Berger, Faraday, etc. guessed their potentials (Ansatz) to emphasize that the potential presented in the above Equation (1) was derived from first principles in my Hypergeometrical Universe Theory.
Jaume Gine provides in his paper a "derivation" of the Gerber's Model using retarded potentials. This approach leads to extra higher order derivatives in the potential description (due to higher order derivatives of the bodies positions with respect to time). Those items are not acceptable and are not present in my model.
This means that the Hypergeometrical Universe Theory also "predicts" the Precession of Mercury's Perihelion and thus equates and surpasses General Relativity in its achievement:
PS- Next I will present the derivation of the Gravitational Lensing within the Hypergeometrical Universe Paradigm.