Estimating parameterized post-Newtonian parameters from spacecraft radiometric tracking data

The theory of general relativity can be tested by precisely measuring small changes in the trajectory of a spacecraft traveling near the sun. An important aspect of such a measurement is the potential of estimating the parameterized post-Newtonian parameters gamma and beta independently. We present a detailed covariance analysis of such a trajectory, analyzing uncertainties in the spacecraft state and gamma and beta. The radiometric data types simulated in our analysis are range, very long baseline interferometry, and Doppler measurements. Also included are the effects of Earth and spacecraft relative geometries, station-location errors, stochastic accelerations, and uncertainties in the solar quadrupole moment J(2). For an X-band tracking system, we show that if the steady-state stochastic accelerations, station-location, and solar quadrupole moment errors are known better than 10(-14) km/s(2), 0.1 m, and 10(-8), respectively, the experiment can achieve unbiased estimates sigma(gamma) = 8.90 X 10(-5) and sigma(beta) = 4.09 X 10(-4). To achieve this level of precision on accelerations requires a drag-free spacecraft or accurate accelerometers