How to Measure Gravitational Aberration?

Abstract

AbstractIn 1905, Henri Poincaré predicted the existence of gravitational waves and assumed their speed equal to the speed of light. If additionally the gravitational aberration would have the same magnitude as the aberration of light, we would observe several paradoxical phenomena. For instance, the orbit of two bodies would be unstable, since two attractive forces arise that are not in line and hence form a couple. This will be modelled by a nonautonomous system of ordinary differential equations with delay. In fact, any positive value of the gravitational aberration increases the angular momentum of such a system and this may contribute to the expansion of the universe. We found a remarkable coincidence between the Hubble constant and the increasing distance of the Moon from the Earth.In 2000, Carlip showed that in general relativity gravitational aberration is almost cancelled out by velocity–dependent interactions. We show how the actual value of the gravitational aberration can be obtained by measurement of a single angle at a suitable time t* corresponding to the perihelion of an elliptic orbit. We also derive an a priori error estimate that expresses how accurately t* has to be determined to obtain the gravitational aberration to a prescribed tolerance.