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The optimal way of transferring a space vehicle from an inner circular orbit to an outer coplanar circular 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 \( h_{1}=320 \mathrm{~km} \), which is to be transferred to a circular orbit at an altitude \( h_{2}=800 \mathrm{~km} \), determine:
(a) The required increases in speed at \( A \) and \( B \).
(b) The total energy per unit mass required to execute the
Figure \( 6.110 \)
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