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The one-loop long distance quantum corrections to the Newtonian potentialimply tiny but observable effects in the restricted three-body problem ofcelestial mechanics, i.e., both at the Lagrangian points of stable equilibriumand at those of unstable equilibrium the Newtonian values of planetoid'scoordinates are changed by a few millimetres in the Earth-Moon system. First,we find that the equations governing the position of both noncollinear andcollinear quantum libration points are algebraic fifth degree and ninth degreeequations, respectively. Second, we discuss the prospects to measure, with thehelp of laser ranging, the above departure from the equilateral trianglepicture, which is a challenging task. On the other hand, a modern version ofthe planetoid is the solar sail, and much progress has been made, in recentyears, on the displaced periodic orbits of solar sails at all libration points.By taking into account the quantum corrections to the Newtonian potential,displaced periodic orbits of the solar sail at libration points are again foundto exist.

Quantum Effects on all Lagrangian Points and Prospects to Measure Them in the Earth-Moon System