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A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance r2. If v1 and v2 are the linear velocities at these points respectively, then the ratio v1 / v2 is

1. (r2 / r1)^2
2. (r2 / r1)
3. (r1 / r2)^2
4. (r1 / r2)

Correct answer: (r1 / r2)

Solution

According to the law of conservation of angular momentum, m * v1 * r1 = m * v2 * r2. Simplifying, we get v1 / v2 = r2 / r1. Hence, the correct ratio is (r1 / r2).

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