# A test of general relativity: Estimating PPN parameters gamma and beta from spacecraft radiometric tracking data

## Published in:

Nuclear Physics B-Proceedings Supplements 134,(2004) 181-183;

## Link to original published article:

http://dx.doi.org/10.1016/j.nuclphysbps.2004.08.028

## Abstract

The Theory of General Relativity (GR) can be tested by precisely measuring the shift of a spacecraft trajectory due to GR as it flies near the Sun. We apply the PPN metric to define the governing equations of motion for the spacecraft, and carry out a covariance analysis to estimate the Eddington-Robertson-Schiff parameters, gamma and 0, by simulating radiometric measurements of range, Very Long Baseline Interferometry, and Doppler. We show that the transient effect of GR over a short timespan is measurable to a significant level and that there is a potential for obtaining independent estimates of gamma and beta. Assuming the spacecraft state as the only additional uncertain parameters, our baseline study gives 1-sigma accuracies of sigma(gamma) = 8.90 x 10(-5) and sigma(beta) = 4.09 x 10(-4) with X-band tracking capability, and potentially an order of magnitude reduction if a K-band tracking system is used. These numbers serve as a lower bound on accuracy. When the additional uncertainties of station location errors, unmodeled non-gravitational accelerations, and solar quadrupole moment are included, sigma(gamma) and sigma(beta) can rise by one to two orders of magnitude. We show that these estimates are highly sensitive to the relative geometry between the spacecraft and Earth tracking stations, and discuss the bounds on error. sources needed to achieve significant accuracies.

## Date of this Version

January 2004