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Gravitation

Assume the Earth has a circular orbit around the sun of radius and that Mars has a circular orbit around the sun of radius . To send a satellite to Mars that requires the least amount of energy the satellite is given an elliptical orbit whose perihelion corresponds to Earth's orbital distance and whose aphelion corresponds to Mars orbital distance as shown in the fig. (see the attachment).

For the following questions, ignore the gravitational pulls on the satellite due to Earth and Mars and consider the gravitational effects on the satellite to be due only to the sun.

a. With what speed must the satellite be launched at the position of the Earth in order to reach Mars?
b. What is the relative speed of the satellite to Earth at the time of launch?
c. How long will it take for the satellite to reach Mars?
d. In relation to Earth when the satellite is launched, where must Mars be located so that when the satellite arrives,
Mars will be at the correct location (conjunction)?
e. What is the relative speed of the satellite to Mar's when it arrives on Mars?

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