  We utilize the dynamical renormalization group formalism to calculate the
real space trajectory of a compact binary inspiral for long times via a
systematic resummation of secularly growing terms. This method generates closed
form solutions without orbit averaging, and the accuracy can be systematically
improved. The expansion parameter is $v^5 \nu \Omega(t-t_0)$ where $t_0$ is the
initial time, $t$ is the time elapsed, and $\Omega$ and $v$ are the angular
orbital frequency and initial speed, respectively, and $\nu$ is the binary's
symmetric mass ratio. We demonstrate how to apply the renormalization group
method to resum solutions beyond leading order in two ways. First, we calculate
the second order corrections of the leading radiation reaction force, which
involves highly non-trivial checks of the formalism (i.e. its
renormalizability). Second, we show how to systematically include
post-Newtonian corrections to the radiation reaction force. By avoiding orbit
averaging we gain predictive power and eliminate ambiguities in the initial
conditions. Finally, we discuss how this methodology can be used to find
analytic solutions to the spin equations of motion that are valid over long
times.
