  The classical equations of the Newtonian 3-body problem do not only define
the familiar 3-dimensional motions. The dimension of the motion may also be 4,
and cannot be higher. We prove that in dimension 4, for three arbitrary
positive masses, and for an arbitrary value (of rank 4) of the angular
momentum, the energy possesses a minimum, which corresponds to a motion of
relative equilibrium which is Lyapunov stable when considered as an equilibrium
of the reduced problem. The nearby motions are nonsingular and bounded for all
time. We also describe the full family of relative equilibria, and show that
its image by the energy-momentum map presents cusps and other interesting
features.
