Two Gravitationally Interacting Masses · USAPhO 2012 #A4
Physics · mechanics
Problem
Two masses m separated by a distance l are given initial velocities v₀ as shown in the diagram. The masses interact only through universal gravitation.
[Figure: Two masses m separated by distance l, each with initial velocity v₀ pointing in the same direction perpendicular to the line connecting them]
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?