A spacecraft and a satellite are at diametrically opposite positions in the same circular...

A spacecraft and a satellite are at diametrically opposite positions in the same circular orbit of altitude 310 mi above the earth. As it passes through point A, the spacecraft fires its engine for a short interval of time to increase its speed and enter an elliptic orbit. Knowing that the spacecraft returns to A at the same time the satellite reaches A after completing one and a half orbits, determine (a) the increase in speed required, (b) the periodic time for the elliptic orbit.