Weber-like interactions and energy conservation

Abstract

Velocity-dependent forces varying as$k(\hat r/r)(1 - \mu \dot r^2 + \gamma r\ddot r)$ (such as Weber force), here calledWeber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only ifγ=2µ. As a consequence, it is shown that gravitational theories employing Weber-like forces cannot be conservative and also yield both the precession of the perihelion of Mercury as well as the gravitational deflection of light.