The breakdown of the orbit-averaging approximation in Eccentric Binaries

As gravitational waves are generated in a binary, energy and angular momentum are carried away, forcing the eccentricity of the system to decrease.~ In order to characterize this evolution in eccentricity two methods are generally used: one involves averaging the change in certain orbital elements over one orbital period, while the other does not employ this averaging and uses multiple-scale analysis instead.~In this talk, I will describe these methods and explain why they yield different answers for the evolution of the eccentricity of a binary in the late stages of inspiral.