By Jaan Kalda (TalTech).
A satellite orbits a planet. At point A, its speed is v_1. At point B, its speed is v_2 and its velocity vector forms a right angle with the velocity vector at point A. At point C, the velocity is exactly opposite to the velocity at point A, with a magnitude of v_3. Find the eccentricity of the orbit. Also determine the exact numerical value of the eccentricity when v_1 = 1km/s, v_2 = 2km/s, and v_3 = 3km/s.
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