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.

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16-12-2022
Physics

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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.

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-12-21T08:00:33+01:00

A chemical rocket may launch a satellite into a Hohmann transfer orbit and maintain it there until it reaches the farthest point in the orbit by performing two very powerful burns.

These chemical rockets aren't very effective, though. They would have perished because it would have taken four weeks to return to Earth orbit.

One (very powerful) engine burn is all that the Hohmann transfer orbit requires. But the interval between the two engine burns is nearly half an orbit, or 2 weeks in the event of an Earth to Moon transfer, as opposed to 3 days for the Apollo approach.

That translates into four times as much food, oxygen, and cramping in the muscles, which results in increased mass and fuel. Apollo 13 remained on its orbit around the Moon after their oxygen tank exploded, depriving them of electrical power and heating, and returned to Earth after nearly 5 days.

They would have perished if they had been in a Hohmann transfer orbit, which would have taken around 4 weeks to return to.

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