Estimate the escape velocity of the galaxy from the solar circle, assuming that the galaxy’s matter is spherically distributed, and that the galaxy has a flat rotation curve at a speed of 240 km/s out to a distance of 20 kpc.

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?