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A planet moves in an elliptical orbit around the Sun. Its minimum distance from the Sun (perihelion) is r_min and its maximum distance (aphelion) is r_max. If the planet's angular velocity at perihelion is w, what is its angular velocity at aphelion?

1. (sqrt(r_min/r_max)) * w
2. (sqrt(r_max/r_min)) * w
3. (r_max/r_min)² * w
4. (r_min/r_max)² * w

Correct answer: (r_min/r_max)² * w

Solution

By conservation of angular momentum, m*r_min²*w = m*r_max²*w', giving w' = (r_min/r_max)² * w.

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