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)
Physics (please help!!!!) - drwls, Friday, April 8, 2011 at 2:12am
a) When Earth has travelled one orbit, Mars will have completed 365.2/687 = 53.2% of an orbit. Mars will be 46.8% of an orbit behinbd Earth. Convert that to radians.
b) Extrapolate to find out how long it takes for Mars to fall 360 degrees behond Earth. That is when a new alignment will occur.
c) Figure out how far (in angle) Earth travels between alignments. It will be more than two complete revolutions. You only want the additional angle beyond two revolutions. (Use the time from part (b)). Convert that to radians.
For part A I got 2.94 rad, not sure if that's right... I still don't get part b... I just used the initial distance I got for Mars after 365.25 days and then multiplyed it by 3 and I got 363 days... I don't think that makes sense... I can't solve part c without part b.
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