Alien suns reversing in exoplanet skies

Earth's rapid spin, modest tilt, and nearly circular orbit ensure that the sun always appears to move forward, rising in the east and setting in the west. However, for some exoplanets, solar motion can reverse causing alien suns to apparently move backward. Indeed, this dramatic motion marginally occurs for Mercury in our own solar system. For exoplanetary observers, we study the scope of solar motion as a function of eccentricity, spin-orbit ratio, obliquity, and nodal longitude, and we visualize the motion in spatial and spacetime plots. For zero obliquity, reversals occur when a planet's spin angular speed is between its maximum and minimum orbital angular speeds, and we derive exact nonlinear equations for eccentricity and spin-orbit to bound reversing and non-reversing motion. We generalize the notion of solar day to gracefully handle the most common reversals.