  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 Levy 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 Tholen et al (2007) 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.
