USAPhO 2012 Semi-Final Problem A4

Two masses m separated by a distance l are given initial velocities v_{0} as shown in the diagram. The masses interact only through universal gravitation.

a. Under what conditions will the masses eventually collide?
b. Under what conditions will the masses follow circular orbits of diameter l ?
c. Under what conditions will the masses follow closed orbits?
d. What is the minimum distance achieved between the masses along their path?

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