ar X iv : a st ro - p h / 95 10 15 7 v 1 3 1 O ct 1 99 5 Testing the Strong Equivalence Principle with Mars Ranging Data

The year 1996 will mark the initiation of a number of new space missions to the planet Mars from which we expect to obtain a rich set of data, including spacecraft radio tracking data. Anticipating these events, we have analyzed the feasibility of testing a violation of the strong equivalence principle (SEP) with Earth-Mars ranging. Using analytic and numerical methods, we have demonstrated that ranging data can provide a useful estimate of the SEP parameter η. Two estimates of the predicted accuracy are quoted, one based on conventional covariance analysis, and the other based on “modified worst case” analysis, which assumes that systematic errors dominate the experiment. If future Mars missions provide ranging measurements with an accuracy of σ meters, after ten years of ranging the expected accuracy for the parameter η will be of order ση ≈ (1 − 12) × 10σ. In addition, these ranging measurements will provide a significantly improved determination of the mass of the Jupiter system, independent of the test of the SEP polarization effect. A possible inequality of passive gravitational and inertial masses of the same body leads to an SEP violation, which results in observable perturbations in the motion of celestial bodies. Thus according to the parametrized post-Newtonian (PPN) formalism the ratio of passive gravitational mass mg to inertial mass mi of a body with rest mass m, may be written (Nordtvedt, 1968) mg mi = 1 + η Ω mc = 1− η G 2mc ∫ ∫ V dzdz ρ(z)ρ(z) |z′ − z′′| , (1) where SEP violation is quantified by the parameter η. Note that general relativity, when analyzed in standard PPN gauge (Will, 1993), yields η = 0. Whereas for the Brans-Dicke theory, for example, η = (2 + ω), where ω is a free dimensionless parameter of the theory. The quantity Ω is the body’s gravitational binding energy. The solar binding energy produces the biggest contribution to the ratio (1) among all the celestial bodies in the solar system. For the standard solar model we obtain