What makes astronomers believe that the energy source in quasars is only a few light months across (the distance light travels in a few months)

When a 5.0kg cart undergoes a 2.2m/s increase in speed, what is the impulse of the cart

It is really hard for me right know

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?