As it describes an elliptic orbit about the sun, a spacecraft reaches a maximum distance of 325 × 106 km from the center of the sun at point A (called the aphelion) and a minimum distance of 148 × 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.