The optimal way of transferring a space vehicle from an inner circular orbit to an outer coplanar orbit is to fire its engines as it passes through A to increase its speed and place it in an elliptic transfer orbit. Another increase in speed as it passes through B will place it in the desired circular orbit. For a vehicle in a circular orbit about the earth at an altitude h1 = 320 km, which is to be transferred to a circular orbit at an altitude h2 = 800 km, determine

(a) The required increase in speed at A and B,

(b) The total energy per unit mass required to execute thetransfer.