A spacecraft and a satellite are at diametrically opposite positions in the same circular orbit of altitude

Question:

A spacecraft and a satellite are at diametrically opposite positions in the same circular orbit of altitude 500 km 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.