  The orbits of stars close to a massive black hole are nearly Keplerian
ellipses. Such orbits exert long term torques on each other, which lead to an
enhanced angular momentum relaxation known as resonant relaxation. Under
certain conditions, this process can modify the angular momentum distribution
and affect the interaction rates of the stars with the massive black hole more
efficiently than non-resonant relaxation. The torque on an orbit exerted by the
cluster depends on the eccentricity of the orbit. In this paper, we calculate
this dependence and determine the resonant relaxation timescale as a function
of eccentricity. In particular, we show that the component of the torque that
changes the magnitude of the angular momentum is linearly proportional to
eccentricity, so resonant relaxation is much more efficient on eccentric orbits
than on circular orbits.
