A space vehicle is in a circular orbit of 1400-mi radius around the moon. To transfer to a...

A space vehicle is in a circular orbit of 1400-mi radius around the moon. To transfer to a smaller orbit of 1300-mi radius, the vehicle is first placed in an elliptic path AB by reducing its speed by 86 ft/s as it passes through A. Knowing that the mass of the moon is 5.03 × 1021 lb · s2/'ft, determine(a) the speed of the vehicle as it approaches B on the elliptic path, (b) the amount by which its speed should be reduced as it approaches B to insert it into the smaller circular orbit.