For a given orbital period and eccentricity, we determine the maximum time lapse between the winter solstice and the spring equinox on a planet. In addition, given an axial precession path, we determine the effects on the seasons. This material can be used at various levels to illustrate ideas such as periodicity, eccentricity, polar coordinates, and vectors, in courses as diverse as precalculus, calculus, linear algebra, differential equations, and geometry. (Contains 6 figures.)