As it describes an elliptic orbit about the sun, a spacecraft reaches a maximum distance of 202 106 mi from the center of the

As it describes an elliptic orbit about the sun, a spacecraft reaches a maximum distance of 202 × 106 mi from the center of the sun at Point A (called the aphelion) and a minimum distance of 92 × 106 mi at Point B (called the perihelion). To place the spacecraft in a smaller elliptic orbit with aphelion at A' and perihelion at B', where A' and B' are located 164.5 × 106 mi and 85.5 × 106 mi, 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.

92 x 10% mi 202 x 10 mi B'B 164.5 106 mi--+- 85.5 106 ini