The possible use of loosely bound Rydberg atoms for remote gravimetric measurements is explored. The first-order corrections to the nonrelativistic nS and nP states for ng2 are obtained for the first time. A procedure to evaluate corrections of any order is outlined and applied to the 1S state in a spherical symmetry. It is shown that observations of the effects described in this Letter near objects of neutron-star-like densities are possible in principle only in the absence of significant magnetic fields.