Draw a free body diagram for a satellite in an elliptical orbit showing why its speed increases as it approaches its parent body and decreases as it moves away.

Solution 21CQ

We are required to show that the speed of a satellite revolving around its parent body in an elliptic orbit increases or decreases according as it approaches the body or moves away from the same. This can be demonstrated from the phenomenon of angular momentum conservation as stated in Kepler’s second law of planetary motion. This law states that as a planet revolves around the sun, it sweeps out equal areas at equal time intervals. During this motion, the total angular momentum of the planet remains constant.

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We can show the free body diagram of a satellite as follows.

Consider three positions A, B and C of the satellite along its elliptical orbit around the parent body which is located at the point O. The directions of centripetal force and the velocities along the elliptical path at each point are shown. Let the distances of the satellite’s position at A, B and C from the parent body are , and . Let be the mass of the satellite and is its velocity.