**By Thomas Foster** (University of Oxford).

At two different points in its orbit, a comet has velocities \vec v_1 and \vec v_2. If:

(i) \vec v_1 and \vec v_2 are orthogonal and

(ii) |\vec v_1|=2|\vec v_2|,what is the smallest possible eccentricity of the orbit?

Hint 1, Hint 2, Hint 3, Best solutions and final results

Chinese translation of problem 2 (中文)

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