Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics; i.e., at the Lagrangian libration points of stable equilibrium, the planetoid is not exactly at an equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. Therefore, the present paper investigates, eventually, a restricted three-body problem involving Earth, the Moon, and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist.