  In this article, we study the tidal effects in the gravitationally bound
two-body system at next-to-next-to leading post-Newtonian order for spin-less
sources in massless scalar-tensor theories. We compute the conservative
dynamics, using both a Fokker Lagrangian approach and effective field theory
with the PN-EFT formalism. We also compute the ten conserved quantities at the
same NNLO order. Finally, we extend our results from simple ST theories to
Einstein-scalar-Gauss-Bonnet gravity. Such results are important in preparation
of the science case of the next generation of gravitational wave detectors.
