  One of the outstanding problems of classical celestial mechanics was the
restricted 3-body prob- lem, in which a planetoid of small mass is subject to
the 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 last
decades, a systematic investigation of quantum corrections to the Newtonian
potential has been carried out in the literature on quantum gravity. The
present paper studies the effect of these tiny quantum corrections on the
evaluation of equilibrium points. It is shown that, despite the extreme
smallness of the corrections, there exists no choice of sign of these
corrections for which all qualitative features of the restricted 3-body problem
in Newtonian theory remain unaffected. Moreover, first-order stability of
equilibrium points is characterized by solving a pair of algebraic equations of
fifth degree, where some coefficients depend on the Planck length. The
coordinates of stable equilibrium points are slightly changed with respect to
Newtonian theory, because the planetoid is no longer at equal distance from the
two bodies of large mass. The effect is conceptually interesting but too small
to be observed, at least for the restricted 3-body problems available in the
solar system.
