A. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity of the spacecraft's orbit? B. What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get back? C. When (at 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?
You are planning a dream vacation to Mars. For the orbital dynamics part of the vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun and Mars is in a circular orbit 1.52 AU from the Sun. Assume the the orbits of Earth and Mars are coplanar and that they go around the Sun the same way. The orbit you plan to use for your trip is an ellipse with the Sun at 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 Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen is called a Hohmann Transfer Orbit.
A. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity of the spacecraft's orbit?
B. What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get back?
C. When (at 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?
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