A satellite is going along an elliptical path around the earth. We need to find the relation between rate of area swept by it in terms of its radius and the problem is as shown in the diagram below.

A satellite is going along an elliptical path around the earth. We need to find the relation between rate of area swept by it in terms of its radius and the problem is as shown in the diagram below.

Solution

According to second law of Kepler, the velocity vector of a planet sweeps equal area in equal intervals of time. Taking that into consideration, we can solve the problem as shown in the diagram below.