We describe the evolution of slowly spinning compact objects in the late inspiral with Newtonian corrections due to spin, tides, dissipation and post-Newtonian corrections to the point mass term in the action within the effective field theory framework. We evolve the system numerically using a simple algorithm for point particle simulations and extract the lowest-order Newtonian gravitational waveform to study its phase evolution due to the different effects. We show that the matching of coefficients of the effective field theory for compact objects from systems that the gravitational wave observatories LIGO-Virgo currently detects might be possible and it can place tight constraints on fundamental physics.
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