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A planet orbits the sun in an ellipse with orbital period 40 months and total ellipse area A. The planet takes 12 months to travel from point D to point E, and 1 month to travel from point B to point C. Find the angular momentum of the planet per unit mass per unit area.
- 0.05 /month
- 0.025 /month
- 0.01 /month
- None of these
Correct answer: 0.025 /month
Solution
By Kepler's second law, the planet sweeps equal areas in equal times, so dA/dt = A/T = A/40 per month. Angular momentum per unit mass per unit area = (dA/dt)/A = 1/40 = 0.025 /month.
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