Using a model of circular coplanar orbits and an analysis accurate to first order in the sun's gravitational radius, Ross and Schiff discussed the recent proposal to test general relativity by measuring round-trip travel times of radar pulses transmitted from the earth towards an inner planet. Their main conclusion, that such measurements would be sensitive to a nonlinear term in Einstein's theory, we find to be invalid. Since first-order differences between Newtonian and Einsteinian orbits are well known to depend on a nonlinear term in the metric, one might expect the round-trip travel times also to depend in first order on such a term. Curiously, this expectation is not realized for circular orbits. When expressed as a function solely of clock readings, the first-order formula for travel time in the circular-orbit model is strictly independent of the nonlinear term. Even were the combined use of radar-pulse travel times and the results of "exact" optical measurements envisioned, their sensitivity to this nonlinear term would be masked almost completely by unavoidable uncertainties in the estimates of other unknown parameters such as the mass of the sun. For noncircular orbits, however, the travel-time measurements will be noticeably sensitive to this nonlinear term through its effect on the advance of the perihelion. In addition to re-examining the circular-orbit model, we describe the operational procedures that we have developed for testing general relativity with data obtained from actual planetary observations. These data cannot be expected in the near future to provide a significant test of more than the first-order influence of solar gravity on radar-pulse travel times and the non-Newtonian advance of Mercury's perihelion, as we previously pointed out.

• Received 16 December 1965

DOI:https://doi.org/10.1103/PhysRev.145.1005