Aberration and the Speed of Gravity in the Jovian Deflection Experiment

We describe our explicit Lorentz-invariant solution of the Einstein equations for the deflection experiment of 2002 September 8 when a moving body, Jupiter, passed within 3.7 ’ of a distant quasar. We show that measurement of the retardation of gravity is equivalent to measurement of the time derivatives of the metric tensor in the post-Newtonian expansion of the light geodesics equation, and we use the gravito-magnetic field to illustrate the concepts. In particular, the v/c term of the deflection, which we measured to 20 % accuracy, is associated with the aberration of Jupiter’s gravity field caused by its finite speed of propagation. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will and Samuel, and show that their interpretations are not entirely consistent with a retarded Liénard-Wiechert solution to the Einstein equations, and do not properly incorporate how the phase of the radio waves from the quasar is perturbed by the retarded gravitational field of Jupiter. Although all of the formulations predict the same deflection to the order of v/c, our formulation shows that the underlying cause of this deflection term is associated in general relativity with the propagation speed of gravity and not of light, and that the interpretations predict different deflections at higher orders of v/c. PACS numbers: 04.20.-q, 04.80.Cc I.