The Post-Newtonian Treatment of the VLBI Experiment on September 8, 2002

TL;DR

This paper analyzes the VLBI experiment from 2002 within the first post-Newtonian approximation, deriving a correction to the Shapiro delay that depends on the measurable speed of gravity, providing a test of fundamental physics.

Contribution

It introduces an explicit parameterization of the speed of gravity into Einstein's equations and derives a 1.5 post-Newtonian correction to the Shapiro delay related to this speed.

Findings

Derived the 1.5 post-Newtonian correction to the Shapiro delay.

Confirmed the delay depends on the measurable speed of gravity.

Compared results with previous post-Minkowskian approximation.

Abstract

Gravitational physics of VLBI experiment conducted on September 8, 2002 and dedicated to measure the speed of gravity (a fundamental constant in the Einstein equations) is treated in the first post-Newtonian approximation. Explicit speed-of-gravity parameterization is introduced to the Einstein equations to single out the retardation effect caused by the finite speed of gravity in the relativistic time delay of light, passing through the variable gravitational field of the solar system. The speed-of-gravity 1.5 post-Newtonian correction to the Shapiro time delay is derived and compared with our previous result obtained by making use of the post-Minkowskian approximation. We confirm that the 1.5 post-Newtonian correction to the Shapiro delay depends on the speed of gravity $c_g$ that is a directly measurable parameter in the VLBI experiment.