One trajectory that can be used to send spacecraft from Earth to Mars is an elli

Question

One trajectory that can be used to send spacecraft from Earth to Mars is an elliptical orbit that has Sun at one focus, its perihelion at Earth, and its aphelion at Mars. The spacecraft is launched from Earth and coasts along this ellipse until it reaches Mars, when a rocket is red to either put the spacecraft into orbit around Mars or cause it to land on Mars

a: Find the semimajor axis of the ellipse. (Hint: Draw a picture showing Sun and the orbits of Earth, Mars, and the spacecraft. Treat the orbits of Earth and Mars as circles.)

b: Calculate how long (in days) such a one-way trip to Mars would take

Explanation / Answer

The orbit you describe is known as a Hohmann ellipse for the German who first worked it out as a presumable minimum energy orbit, although taking a long time, and thus requiring large supplies for manned spacecraft. Basically you travel 180 degrees or exactly half the orbit. Orbits that take less time but more initial energy have their aphelion well beyond the orbit of Mars, and cross that orbit twice. The first crossing of course takes the least time. Such orbits are referred to in brief by the number of degrees the spacecraft traverses in the full elliptical orbit, with first crossing being less than 180 degrees and second crossings more than 180 but less than 270.
The semimajor axis will be {(Earth's distance from the Sun) + (Mars distance from the Sun)}/2
then use Kepler's third law for the period of the full orbit. Time from Earth-perihelion to Mars-aphelion will be half that

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.