At what point in an elliptical orbit is the acceleration maximum? At what point is it minimum? Justify your answers.

Solution 17DQ GM The expression for acceleration is given by g = r2 …..(1), where G is the gravitational constant, M is the mass of the body around which revolution is done and r is the separation between the two bodies. In an elliptic orbit, the closest point between the two bodies is when the revolving body is at the perihelion and the farthest point is when the revolving body is at the aphelion. It can be understood from the figure shown below. Since the acceleration is inversely related to the separation (from equation (1)), therefore acceleration will be maximum at the perihelion and will be minimum at the aphelion.