A space vehicle is in circular orbit about the earth. The mass of the vehicle is

Question

A space vehicle is in circular orbit about the earth. The mass of the vehicle is 3820 kg. The radius of the orbit is 2RE. It is desired to transfer the vehicle to a circular orbit of radius 4RE.
(A) What is the minimum energy expenditure required for the transfer?

(B) An efficient way to accomplish the transfer is to use a semielliptical orbit (known as a Hohmann transfer orbit), as shown. What velocity changes are required at the points of intersection, A and B? Express the change in speed as the percentage of the speed just before the change.

(C) For the Hohmann transfer orbit, calculate the kinetic energy just before point A, just after point A, just before point B and just after point B. Express the results as a ratio to the kinetic energy of a circular orbit of radius 2RE.

Explanation / Answer

A) PEi = -GMm / 2RE PEf = -GMm / 4RE So, energy required for the transfer = PEf - PEi = GMm / 4RE = 6.673 x 10^(-11) x 5.97 x 10^(27) x 3820 / (4 x 6378100) where, RE = radius of earth = 6378100 m = 5.97 x 10^(13) J. B) Hohmann transfer orbit is not shown. C) Same as above, Hohmann transfer orbit is not shown with A and B marked.

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