As it describes an elliptic orbit about the sun, a spacecraft caches a maximum distance of...

As it describes an elliptic orbit about the sun, a spacecraft caches a maximum distance of 325 × 106 km from the center of the sun at point A (called the aphelion) and a minimum distance of 143 × 106 km at point B (called the perihelion) . To place the spacecraft in a smaller elliptic orbit with aphelion A' and perihelion B', where A' and B' are located 264.7 × 106 km and 137.6 × 106 km, respectively, from the center of the sun, the speed of the spacecraft is first reduced as it passes through A and then is further reduced as it passes through B'. Knowing that the mass of the sun is 332.8 × 103 times the mass of the earth, determine (a) the speed of the spacecraft at A (b) the amounts by which the speed of the spacecraft should be reduced at A and B' to insert it into the desired elliptic orbit.