Consider a particle moving under an arbitrary central force F 1 (r) whose magnitude depends only on the distance r between the particle and a fixed center. Since the motion of a particle under a central force always lies in a plane, the position of the particle can be described by polar coordinates (r, θ 1), the radius and angle of the particle relative to the center of force (Figure 1). Both of these coordinates, r (t) and θ 1 (t), change with time t as the particle moves.