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A planet travels in an elliptical orbit with the Sun at one focus. It takes time T1 to travel the arc from point A to point B, and time T2 to travel the arc from point C to point D. The area swept by the planet (with respect to the Sun) during CD is twice the area swept during AB. What is the relationship between T1 and T2?
- T1 = T2
- T1 = 2T2
- T1 = 0.5T2
- Data insufficient
Correct answer: T1 = 0.5T2
Solution
By Kepler's second law, the planet sweeps area at a constant rate; since the area swept during CD is twice that swept during AB, the time T2 must be twice T1, giving T1 = 0.5 * T2.
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