Gravitons scattering from classical matter

The low energy scattering of gravitons from a composite extended system, which is made of classical massive bodies, is considered; by using the Feynman rules of effective quantum gravity, the corresponding cross-section is computed to lowest order in powers of the gravitational coupling constant. For the gravitons scattering from a rotating planet or a star, it is shown that the classical limit of the matter-gravitons coupling in the effective quantum gravity lagrangian leads to a low energy scattering amplitude which coincides with the expression obtained in classical general relativity.