  In this paper the possibility of measuring some general relativistic effects
in the gravitational field of the Moon via selenodetic missions, with
particular emphasis to the future Japanese SELENE mission, is investigated. For
a typical selenodetic orbital configuration the post-Newtonian Lense-Thirring
gravitomagnetic and the Einstein's gravitoelectric effects on the satellites
orbits are calculated and compared to the present-day orbit accuracy of lunar
missions. It turns out that for SELENE's Main Orbiter, at present, the
gravitoelectric periselenium shift, which is the largest general relativistic
effect, is 1 or 2 orders of magnitude smaller than the experimental
sensitivity. The systematic error induced by the mismodelled classical
periselenium precession due to the first even zonal harmonic J2 of the Moon's
non-spherical gravitational potential is 3 orders of magnitude larger than the
general relativistic gravitoelectric precession. The estimates of this work
could be used for future lunar missions having as their goals relativistic
measurements as well.
