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ABSTRACT. The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different 'Schwarzschild radii'. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.1. In both non-relativistic and special relativistic mechanics, classical and quantum, the twobody problem for (spinless) point particles is reduced to the conceptually simpler problem of a single effective particle moving in an external field. The only exception to this picture so far seems to be the general theory of relativity, where the two-body problem has been treated in a considerably more complicated way: as a field-theoretic problem with singularities [1, 2] (or as a problem of finite size bodies interacting with a gravitational field [31). Here we propose to treat gravitational two-particle interaction in much the same way as electromagnetic interactions have been tackled previously [4,5] in the quasipotential approach [6] which found its natural place in the constraint Hamiltonian framework of References [7] and [8] . 1 Unlike other first-order (in 1/c 2 ) semi-relativistic treatments (based on a quantum field theoretic derivation of the two-particle potential) [12] , our approach is fully relativistic. Here we shall consider the two-body problem in the leading order of perturbation 1 Revised version of Trieste preprint IC/80/124 (August 1980)

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