Consider a system of N particles that interact via an attractive gravitational force that is proportional to the distance between particles: Fij = -kmimj(rj - ri) where k is a positive constant and i, j = 1 .... N. Determine the trajectories of the particles. (Hint: Choose a reference frame in which the CM is at rest at the origin).

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.