Imagine another universe that is completely empty except for a large solid sphere at rest. Suddenly, an identical sphere pops into existence 1 trillion kilometers away. What
will happen?

Two identical stars with mass m orbit around their center of mass. each orbit is circular and has radius r, so that the two stars are always on opposite sides of the circle. (a) find the gravitational force of one star on the other. (b) find the orbital speed of each star and the period of the orbit. (c) how much energy would be required to separate the two stars to infinity?