Is it possible to test directly general relativity in the gravitational field of the Moon?

In this paper the possibility of directly measuring some general relativistic effects in the gravitational field of the Moon via selenodetic missions, with particular emphasis on the future Japanese SELENE mission, is investigated. For a typical selenodetic orbital configuration the post-Newtonian Lense–Thirring gravitomagnetic and Einstein's gravitoelectric effects on the satellite orbits are calculated and compared with 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 one or two orders of magnitude smaller than the experimental sensitivity.