Net Force <i>F</i> = <i>γ</i>³<i>ma</i> at High Velocity

Abstract

Newton’s theory of gravitation has been outdated by relativity theory explaining specific phenomena like perihelion precession of Mercury, light deflection and very recently the detection of gravitational waves. But the disappearance of the obvious gravitational force and the variation of time are arguable concepts difficult to directly prove. Present methodology is based on hypotheses as expressed in a previous article: a universal time and an inertial mass variable according to the Lorentz factor (which could not be envisioned at Newton’s age). Because this methodology is mainly stood on Newtonian mechanics, it will be called neo-Newtonian mechanics. This theory is in coherence with the time of the Quantum Mechanics. In Newtonian mechanics, all forces, including gravitational force, are deducted from the linear momentum. Introducing the variable inertial mass, the result of the demonstration is an updated expression of the net force at high velocity: F = γ 3 m g a . If such a factor in γ 3 can look a bit strange at first sight for a force, let us remind that the lost energy in a synchrotron is already measured in γ 4 . Next article will be on the perihelion precession of Mercury within neo-Newtonian mechanics.