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.

Certain systems do not completely return to themselves when a subsystem moves through a closed circuit in physical or parameter space. A geometric phase, known classically as Hannay's angle and quantum mechanically as Berry's phase, quantifies such anholonomy. We study the classical example of a bead sliding frictionlessly on a slowly rotating hoop. We elucidate how forces in the inertial frame and pseudo-forces in the rotating frame shift the bead. We then computationally generalize the effect to arbitrary-not necessarily adiabatic-motions. We thereby extend the study of this classical geometric phase from theory to experiment via computation, as we realize the dynamics with a simple apparatus of wet ice cylinders sliding on a polished metal plate in 3D printed plastic channels.