A satellite is placed into an elliptic orbit about the earth. Knowing that the ratio vA/vP of the velocity at the apogee A to the velocity at the perigee P is equal to the ratio rP/rA of the distance to the center of the earth at P to that at A, and that the distance between A and P is 50,000 mi, determine the energy per unit weight required to place the satellite in its orbit by launching it from the surface of the earth. Exclude the additional energy needed to overcome the weight of the booster rocket, air resistance, and maneuvering.

50.000 mi