Abstract
We derive the equations of motion for an N-body system in the Einstein-Cartan gravity theory at the first post-Newtonian order by exploiting the Weyssenhoff fluid as the spin model. Our approach consists in performing the point-particle limit of the continuous description of the gravitational source. The final equations provide a hint for the validity of the effacing principle at 1PN level in Einstein-Cartan model. The analogies with the general relativistic dynamics involving the macroscopic angular momentum are also discussed.