LAUSR

Abstract The shell theorem, proved by Newton in his Principia (1687), states that the net force exerted by a uniform spherical shell on a body located anywhere inside it is zero, as long as the force is proportional to the inverse square of the distance between the interacting bodies. This null result remains valid whenever the interaction depends only on the distance between the bodies, but not on their relative motion. In this work, I develop a direct closed-form evaluation of the integral of the elements of force to show that Weber-like interactions, which take into account the relative motion between the body and the shell, yield a nonzero force opposite to the acceleration of the body with respect to the shell, whatever be its position and velocity. For gravitational interactions, this nonzero force is relevant in cosmology since it can be identified with the force of inertia, as caused by the celestial sphere (i.e., the set of distant stars), which allows for a full mathematical implementation of Mach’s principle.