  Direct imaging of exoplanets presents both significant challenges and
significant gains. The advantages primarily lie in receiving emitted and, with
future instruments, reflected photons at phase angles not accessible by other
techniques, enabling the potential for atmospheric studies and the detection of
rotation and surface features. The challenges are numerous and include
coronagraph development and achieving the necessary contrast ratio. Here, we
address the specific challenge of determining epochs of maximum angular
separation for the star and planet. We compute orbital ephemerides for known
transiting and radial velocity planets, taking Keplerian orbital elements into
account. We provide analytical expressions for angular star--planet separation
as a function of the true anomaly, including the locations of minimum and
maximum. These expressions are used to calculate uncertainties for maximum
angular separation as a function of time for the known exoplanets, and we
provide strategies for improving ephemerides with application to proposed and
planned imaging missions.
