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Unformatted text preview: Astronomy 1F03 Problem Set 2 - Solutions Tuesday Oct 12th, 2010 1. a) Using Kepler’s Laws of Planetary Motion, calculate the orbital period of an Oort Cloud comet if the semi-major axis of the comet’s orbit is 40,000 AU. a = 40 , 000 AU, use Kepler’s Third Law: P 2 = a 3 , P = 8 × 10 6 yr. Note that P must be in years and a in AU. b) What is the maximum possible aphelion distance (maximum distance from the Sun) for a short period comet with an orbital period of 130 years. (Hint: You will need to consider what the maximum distance from the Sun is for an extreme elliptical orbit.) If the orbital period is 130 years then according to Kepler’s Third Law, P 2 = a 3 , a = 130 (2 / 3) = 25 . 66 AU. The most eccentric orbit possible has e = 1 . Equivalently, the Sun is at one end of the very long, narrow ellipse. In this case r max = (1 + e ) a = 2 a = 51 . 32 AU 2. a) Assume that the current rate of meteor impacts on the Moon that create 10 km diameter craters is one every 10 Million years. Determine how long it would take to cover the whole surface of the Moon with cratersevery 10 Million years....
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