Improving gravity theory tests with solar system "grand fits"

Because the general relativistic perihelion precession of Mercury's orbit is a secular perturbation, it has the potential to be measured with ever-increasing precision as the duration of the observations grows. This can be realized, however. only if Mercury's sidereal orbital frequency is determined to a correspondingly improved precision, and that is not achievable by means of ranging to Mercury, alone. "Grand fits" of the observed ranges to Mercury with either those to Mars or to the Moon are shown to more fully realize the inherent sensitivities of the measurements to post-Newtonian perturbations; in such combined fits Mercury's perihelion precession is inferred from four well-measured frequencies of the pertinent body dynamics. Doing a grand fit of existing solar system ranging data cannot only yield a substantially improved test of general relativity, it can push the search for a very weakly coupled, Yukawa-like interaction between the solar system bodies, supplementing general relativity's metric tensor force, to higher levels of precision.