Inspiralling binary compacts generate gravitational waves detected by LIGO/VIRGO. Post Newtonian (PN) approximations of general relativity can give analytic solutions to the inspiral motion and gravitational radiation of systems. In this talk, we present the worldline EFT approach to calculate the 4.5PN radiation reactions, which is a next-to-next-to-leading order correction to the quadruple radiation. And we introduce a dynamical renormalization group method to obtain the analytical solutions to the equations of motion and spin precession equations up to the leading order in spin-orbit effects and radiation reaction.