  The Earth, Mars, Sun, Jupiter system allows for a sensitive test of the
strong equivalence principle (SEP) which is qualitatively different from that
provided by Lunar Laser Ranging. Using analytic and numerical methods we
demonstrate that Earth-Mars ranging can provide a useful estimate of the SEP
parameter $\eta$. Two estimates of the predicted accuracy are derived and
quoted, one based on conventional covariance analysis, and another (called
``modified worst case'' analysis) which assumes that systematic errors dominate
the experiment. If future Mars missions provide ranging measurements with an
accuracy of $\sigma$ meters, after ten years of ranging the expected accuracy
for the SEP parameter $\eta$ will be of order $(1-12)\times 10^{-4}\sigma$.
These ranging measurements will also provide the most accurate determination of
the mass of Jupiter, independent of the SEP effect test.
