How To Measure Gravitational Aberration?

In 1905, Henri Poincaré predicted the existence of gravitational waves and assumed that their speed c[g] would be that of the speed of light c. If the gravitational aberration would also have the same magnitude as the aberration of light, we would observe several paradoxical phenomena. For instance, the orbit of two bodies of equal mass would be unstable, since two attractive forces arise that are not in line and hence form a couple. This tends to increase the angular momentum, period, and total energy of the system. This can be modelled by a system of ordinary differential equations with delay. A big advantage of computer simulation is that we can easily perform many test for various possible values of the speed of gravity [1]. In [2], Carlip showed that gravitational aberration in general relativity is almost cancelled out by velocity-dependent interactions. This means that rays of sunlight are not parallel to the attractive gravitational force of the Sun, i.e., we do not see the Sun in the direction of its attractive force, but slightly shifted about an angle less than 20``. We show how the actual value of the gravitational aberration can be obtained by measurement of a single angle at a suitable time instant T corresponding to the perihelion of an elliptic orbit. We also derive an a priori error estimate that expresses how acurately T has to be determined to attain the gravitational aberration to a prescribed tolerance. [1] M. Křížek: Numerical experience with the finite speed of gravitational interaction, Math. Comput. Simulation 50 (1999), 237-245. [2] S. Carlip: Aberration and the speed of gravity, Phys. Lett. A 267 (2000), 81-87.