We examine the evolution of an almost circular Keplerian orbit interacting with unbound perturbers .
We calculate the change in eccentricity and angular momentum that results from a single encounter , assuming the timescale for the interaction is shorter than the orbital period .
The orbital perturbations are incorporated into a Boltzmann equation that allows for eccentricity dissipation .
We present an analytic solution to the Boltzmann equation that describes the distribution of orbital eccentricity and relative inclination as a function of time .
The eccentricity and inclination of the binary do not evolve according to a normal random walk but perform a Lévy flight .
The slope of the mass spectrum of perturbers dictates whether close gravitational scatterings are more important than distant tidal ones .
When close scatterings are important , the mass spectrum sets the slope of the eccentricity and inclination distribution functions .
We use this general framework to understand the eccentricities of several Kuiper belt systems : Pluto , 2003 ~ { } { EL _ { 61 } } , and Eris .
We use the model of to separate the non-Keplerian components of the orbits of Pluto ’ s outer moons Nix and Hydra from the motion excited by interactions with other Kuiper belt objects .
Our distribution is consistent with the observations of Nix , Hydra , and the satellites of 2003 ~ { } { EL _ { 61 } } and Eris .
We address applications of this work to objects outside of the solar system , such as extrasolar planets around their stars and millisecond pulsars .