Weber-like interactions and energy conservation

Velocity dependent forces varying as $k(\hat{r}/r)(1 - μ\dot{r}^2 + γr \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only if $γ=2μ$. 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.

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