Prospects for Measuring the Post-Newtonian \(\boldsymbol{\gamma}\) Parameter Using Two Satellites Equipped with Highly Stable Atomic Clocks and a Doppler Compensation System

Abstract

We investigate the possibility of experimentally determining the PPN \(\gamma\) parameter by measuring the gravitational frequency shift of signals exchanged by two satellites in heliocentric orbits. The satellites are supposed to be equipped with highly stable atomic clocks and the Gravity Probe A non-relativistic Doppler compensation system. We demonstrate that the Doppler compensation system significantly lowers the requirements to the satellite velocity determination accuracy but, at the same time, cancels out the leading contribution, of \(O(c^{-3})\), to the frequency shift due to \(\gamma\). We derive an equation for the Doppler-compensated frequency shift due to \(\gamma\) in the next-to-leading order, \(O(c^{-4})\), and show that it is greatly enhanced by numerical factors that rapidly grow in magnitude for signals that propagate close to the gravitational field source. Due to these ‘‘enhanced’’ factors, the accuracy of the proposed experiment with the best of the currently available clocks, such as the JILA SrI, can reach \(1.7\times 10^{-7}\) after 5 yr of data accumulation, if performed in the optimal orbital configuration. This is an order of magnitude worse than our earlier estimate for the accuracy of a similar experiment that does not rely on the Doppler compensation system but 2 orders of magnitude better than the current best result obtained with the Cassini interplanetary probe. Finally, we discuss aspects of the practical realization of the proposed experiment, including prospects for realizing it as part of a multi-science mission that also targets other kinds of gravitational experiments.