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The most efficient way to send a spacecraft from the earth to another planet is by...

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Physics

The most efficient way to send a spacecraft from the earth toanother planet is by using a Hohmann transfer orbit (thefigure (Figure 1)). If the orbits of the departure and destinationplanets are circular, the Hohmann transfer orbit is an ellipticalorbit whose perihelion and aphelion are tangent to the orbits ofthe two planets. The rockets are fired briefly at the departureplanet to put the spacecraft into the transfer orbit; thespacecraft then coasts until it reaches the destination planet. Therockets are then fired again to put the spacecraft into the sameorbit about the sun as the destination planet.

a) For a flight from earth to Mars, in what direction must therockets be fired at the earth and at Mars: in the direction ofmotion, or opposite the direction of motion? What about from aflight from Mars to the earth?Explain.

b) How long does a one-way trip from the the earth to Mars take,between the firings of the rockets?

c) To reach Mars from the earth, the launch must be timed sothat Mars will be at the right spot when the spacecraft reachesMars's orbit around the sun. At launch, what must the angle betweena sun-Mars line and a sun-earth line be?.

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