  We provide an elegant way of solving analytically the third post-Newtonian
(3PN) accurate Kepler equation, associated with the 3PN-accurate generalized
quasi-Keplerian parametrization for compact binaries in eccentric orbits. An
additional analytic solution is presented to check the correctness of our
compact solution and we perform comparisons between our PN-accurate analytic
solution and a very accurate numerical solution of the PN-accurate Kepler
equation. We adapt our approach to compute crucial 3PN-accurate inputs that
will be required to compute analytically both the time and frequency domain
ready-to-use amplitude-corrected PN-accurate search templates for compact
binaries in inspiralling eccentric orbits.
