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January 30, 2015

January 30, 2015

Posted by **sara** on Thursday, February 16, 2012 at 9:21pm.

Mars orbits the Sun at a mean distance of 228 million km, in a period of 687 days. The Earth orbits at a mean distance of 149.6 million km in a period of 365.26 days. All answers should be in the range (0, 2pi)

a) Suppose Earth and Mars are positioned such that Earth lies on a straight line between Mars and the Sun. Exactly 365.26 days later, when the Earth has completed one orbit, what is the angle between the Earth-Sun line and the Mars-Sun line? (in rad)

b) The initial situation in part a) is a closest approach of Mars to the Earth. What is the time between 2 closest approaches? Assume constant orbital speeds and circular orbits for both Mars and Earth. (Hint: when angles are equal) (in days)

c) Another way of expressing the answer to part (b) is in terms of the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations. What is that angle? (in rad)

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