Keppler puzzled over it. So did Einstein. In fact, most of the greatest theorists had at least a thought or two about orbital motion, especially in the rise and growth of space science. Tan (physics, Alabama AandM U.) brings the concepts to the introductory and intermediate undergraduate levels, working primarily from first principles and beginning with Kepler's laws of planetary motion and Newton's law of gravitation. Thus armed, he explains the average and extremum values of variables, the central force problem, vector hodographs in planetary motion, planetary motion in Cartesian coordinates, the planetary problem in complex coordinates, Keplerian motion in the solar system, and planetary motion in three-dimensional space. He concludes with analyses of the motion of artificial earth satellites and the perturbations of satellite orbits, providing a fine treatment of the ellipse and its properties in an appendix.