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One of the outstanding problems of classical celestial mechanics was therestricted 3-body prob- lem, in which a planetoid of small mass is subject tothe Newtonian attraction of two celestial bodies of large mass, as it occurs,for example, in the sun-earth-moon system. On the other hand, over the lastdecades, a systematic investigation of quantum corrections to the Newtonianpotential has been carried out in the literature on quantum gravity. Thepresent paper studies the effect of these tiny quantum corrections on theevaluation of equilibrium points. It is shown that, despite the extremesmallness of the corrections, there exists no choice of sign of thesecorrections for which all qualitative features of the restricted 3-body problemin Newtonian theory remain unaffected. Moreover, first-order stability ofequilibrium points is characterized by solving a pair of algebraic equations offifth degree, where some coefficients depend on the Planck length. Thecoordinates of stable equilibrium points are slightly changed with respect toNewtonian theory, because the planetoid is no longer at equal distance from thetwo bodies of large mass. The effect is conceptually interesting but too smallto be observed, at least for the restricted 3-body problems available in thesolar system.

Restricted three-body problem in effective-field-theory models of gravity