We first briefly recall method used for qualitative discussion of motion in one dimension. Many of these ideas will be used here for radial motion in three dimensions. Simplest physical systems of interest, for example, Sun and Earth system, are two body systems interacting via a potential-dependent only the distance between the two bodies only. This problem can be reduced to an equivalent one-body problem in a spherically symmetric potential. #### 2.1 Recall and Discuss — One dimension **Equilibrium Points** If a particle, moving in one dimension, is released from rest at some point, it will in general move towards lower potential energy. If it is released at a minimum or maximum of the potential, it will remain at rest It therefore follows that at these points \( \dot x = \ddot x = 0 \) Let \( x_0 \) be a point where the particle in equilibrium. If the point \( x_0 \) is a