You are plannirg a dream vacation to Mars. For the orbital dynamics part of the vacation alerting assume that Earth is in a circuLsr orbit 1.00 AU from the Sun and Mars is in a circular orbit 1.52 AU from the Sun. Assume the the orbitsof Earth and Mars are coplanar and that they go around the Sin the same way. The orbit you plan to use for your trip is an ellipse with the Sun al one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mara' orbit at 1.52 AU. Your spacecraft wi go around the Sun In the same sense as Earth and Mars. The orbit you have chosen is called a Hohmann Transfer Orbit. For this problem assume that the orbital period of Earth is 365 days and the orbital period of Mars is 684 days. 1. Check that Kepler's Third Law holds for Earth and Mars. 2. Whal is the semi-major axis a of the spacecraft's orbit? What is the eccentricity e of the spacecraft's orbit? 3. What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take lo get back? 4. When fat what Earth Mars configuration) do you launch to go? In other words. where does Mars need to be relative to Earth in order for you to get to Mars successfully?
- Where is Earth when you arrive at Mars? 6. Where does Earth need to be relative to Mars for you to return safely to Earth? 7. How long to you have to wan on Mars before you can launch for home? 8. What is your total trip time? Care to go?
- If you miss your launch configuration In question 4 or 617. how long do you have to wait for the next one?
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