Astronomy - Hohmann Transfer Orbit

[GPalm]

The most efficient way to reach Mars from Earth is following the Hohmann Transfer Orbit
(Wolfgang Hohmann, 1925). A spaceship must first get free of Earth (it still orbits the Sun
together with Earth, at 30 km/s, at a distance of 1 AU), then it adds speed so that its aphelion
(in its orbit around the Sun) just grazes the orbit of Mars, A = 1.524 AU (ignoring ellipticity).



(a) Draw the orbits of Earth and Mars, together with the Hohmann Transfer Orbit.


(b) What are the minimum and maximum separation from the Sun? What is the semi-major
axis of this orbit?


(c) Using the Newtonian derivation of Kepler's 3rd law once again, determine the orbital
period, and hence the time taken to reach Mars from Earth. Express your answer in
months.

 

[gneill]

The most efficient way to reach Mars from Earth is following the Hohmann Transfer Orbit
(Wolfgang Hohmann, 1925). A spaceship must first get free of Earth (it still orbits the Sun
together with Earth, at 30 km/s, at a distance of 1 AU), then it adds speed so that its aphelion
(in its orbit around the Sun) just grazes the orbit of Mars, A = 1.524 AU (ignoring ellipticity).



(a) Draw the orbits of Earth and Mars, together with the Hohmann Transfer Orbit.


(b) What are the minimum and maximum separation from the Sun? What is the semi-major
axis of this orbit?


(c) Using the Newtonian derivation of Kepler's 3rd law once again, determine the orbital
period, and hence the time taken to reach Mars from Earth. Express your answer in
months.

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