What is Hidden in the Gerber’s Gravitational Potential?

Paul Gerber proposed in 1898 a velocity-dependent gravitational potential intended to represent the rate of propagation of gravitation and to account for the anomalous perihelion advance of Mercury. The potential has the form of a Newtonian term multiplied by a retardation factor depending on the radial velocity divided by a propagation speed. Its historical importance is that, at leading order, it yields the same perihelion-advance formula later obtained in general relativity. This contribution analyzes the formula, decomposes its mathematical parts, identifies the physical information inserted into it. This paper tries to reveal what information is inserted into this formula: that gravity is not treated as an instantaneous action at a distance, the term dr/dt tells the potential whether the test body is moving inward or outward. This term contains information about motion, not only about static distance. The formula naturally introduces small corrections of order v/c (it eliminates the gravitation aberration), and v2/c2 with acceleration corrections. The cooperation of these corrections results in the correct value for the anomalous perihelion advance of Mercury. This inspiration was employed for the evaluation of the anomalous acceleration of Pioneer 10 and Pioneer 11 – the Pioneer anomaly. There were derived formulae for the outward and inward acceleration corrections of objects moving in the Solar system away from the Sun and towards to the Sun. Finally, we have proposed a general formula of the Gerber´s gravitational potential based on the probable behavior of blue- and redshifted gravitons leading to the correction known as the “dark matter” and “dark energy”. The lead angle of the graviton helix generates axial forces – attractive and repulsive forces.

Keywords: Blue- and Redshifted Gravitons, “Dark Energy”, “Dark Matter”, Gerber´s Gravitational Potential, Pioneer Anomaly, the Lead Angle of Helix Generates Axial Forces.