The vector treatment of Kepler's first law presented in most calculus textbooks is based on the existence of a constant vector that is associated with the exact inverse square force law. Such a treatment is not a general substitute for the methods based on the differential equations of motion. This worksheet demonstrates how to use Maple to solve the differential equations governing planetary motion, and how to visualize the Laplace-Runge-Lenz vector which is peculiar to the force law of the form k/r^2.