A Hohmann transfer is a fuel efficient transfer orbit to an outer planet. The pr

Question

A Hohmann transfer is a fuel efficient transfer orbit to an outer planet. The process requires placing a spacecraft into an elliptical orbit about the Sun, such that the perihelion, the point closest to the Sun, is at the departure planet and the the aphelion, the point farthest from the Sun, is at the arrival planet. The entire trajectory is depicted below. (a) Use Kepler's third law to calculate how long it would take to go from the Earth to Mars on such an orbit. (b) Can such a transfer be undertaken at any time? Explain.

Explanation / Answer

a) time taken to go from Earth to Mars = (56 * 106 * 103)/16513.3

                                                              = 942 hours

                                                               = 39 days

b)   No, such a transfer can not be undertaken at any time . It can only be undertaken at a particular orbital position of Mars and Earth .

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