Kepler’s second law, the statement that a planet sweeps out equal areas in equal times,...

Kepler’s second law, the statement that a planet sweeps out equal areas in equal times, can be derived by a geometrical argument. To see how one might construct such a geometrical proof, consider the simpler case of a planet moving with constant velocity as shown in Figure Q5.6. The points A, B, C, . . . are spaced at equal time intervals. Show that this planet obeys Kepler’s second law; that is, show that it sweeps out equal areas in equal times. Hint: Calculate the areas of triangles OAB, OBC, and so on.