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A planet of mass M moves around the Sun in an elliptical orbit and has angular momentum L. What is the magnitude of the areal velocity of the planet?
- 4L/M
- L/M
- 2L/M
- L/(2M)
Correct answer: L/(2M)
Solution
The areal velocity is defined as the area swept per unit time by the position vector. For a planet at distance r moving with velocity v: dA/dt = (1/2)|r x v| The angular momentum L = M|r x v|, so |r x v| = L/M. Therefore: dA/dt = (1/2)(L/M) = L/(2M). This is the statement of Kepler's second law (equal areas in equal times), and it holds for any central force orbit.
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