AP Physics C Mechanics Motion of Orbiting Satellites FRQ

 Question

Two satellites, of masses m and 3m, respectively, are in the same circular orbit about the Earth’s center, as
shown in the diagram above. The Earth has mass M_e and radius R_e. In this orbit, which has a radius of 2R_e, the
satellites initially move with the same orbital speed v_o but in opposite directions.
a. Calculate the orbital speed v_o of the satellites in terms of G, M_e, and R_e
b. Assume that the satellites collide head-on and stick together. In terms of v_o find the speed v of the combination immediately after the collision.
c. Calculate the total mechanical energy of the system immediately after the collision in terms of G, m, M_e, and R_e. Assume that the gravitational potential energy of an object is defined to be zero at an infinite distance from the Earth.