  We present a novel method to study interacting orbits in a fixed mean
gravitational field associated with a solution of the Einstein field equations.
The idea is to consider the Newton gravity among the orbiting particles in a
geometry given by the main source. We apply the technique in the of study two
and three self-gravitating particles moving around a black hole, i.e., in a
Schwarzschild geometry. We also compare with the equivalent Newtonian problem
and noted differences in the structural stability, e.g., binary systems were
found only in the general relativistic approach.
