Changing Mass Corrects Newtonian Gravity

Abstract

Newton's inverse-square law of universal gravitation assumes constant mass. But mass increases with speed and perhaps with gravity. By SR, mass is increased over the rest mass by gamma. Rest mass is here postulated to increase under gravity, by 1/alpha =1+GM/rc^2. We examine the consequences of introducing this changing mass into Newton's law in flat spacetime. This variable mass affects the metric, relative to an observer away from the influence of gravity, contracting both lengths and times (as measured) by alpha/gamma. The gravitational force, as in orbital calculations, differs from Newton's law by the factor (gamma/alpha)^3, and is not quite inverse square. Without adjustable parameters, this accounts fully for the classical tests of GR. The postulated "fifth force" appears at the 10^-9 g level. Gravitationally-influenced space remains Euclidean, but the mass-metric changes make it seem curved when measured.