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hw7_solutions

# hw7_solutions - Homework#7 Solutions Astro 10 spring 2010...

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Homework #7: Solutions Astro 10, spring 2010 General Notes to Graders: Please take a point off the total if there is no section number on the homework. If numerical answers are roughly correct, do not take marks off. Award part marks if the student has made some progress with the question. Be generous. 1. [10 points] Once again we use Kepler’s law to figure out the semi-major axis for these comets, comparing it to the Earth’s orbit. Because both these objects orbit the Sun, we don’t need to keep track of the Sun’s mass, as it will cancel out in the ratio. Thus, using P 2 a 3 , and letting P 1 = 1 year , a 1 = 1 AU be the Earth’s values, we have: ( P 2 P 1 ) 2 = ( a 2 a 1 ) 3 ( a 2 ) 3 = ( P 2 P 1 ) 2 ( a 1 ) 3 If we let P 2 = 200 years for the first comet, then a 2 = 34 . 2 AU . If we let P 2 = 100000 years for the second comet, then a 2 = 2154 . 4 AU . Given the above distances, the first comet most likely comes from the Kuiper Belt which exists roughly at Pluto’s orbit and a little beyond. The second comet, because it originates from much farther away, probably comes from the Oort Cloud . Notes to graders: 5 points for each comet (i.e. the correct distance and region it comes from). Students were not required to use a ratio to solve this problem, so it is fine if they plugged in values to the full version of Kepler’s 3rd law. It is also fine if they just used P 2 = a 3 where the units of P are years and the units of a are AU since this was discussed in class. Take 1 point off if correct but careless with units. 2. [10 points] a) The term ”albedo” refers to the reflectivity of a surface . Some materials such as ice reflect light very well (high albedo) whereas some materials such as carbon soot reflect almost no light (low albedo). The reason this is important to your geologist friend is because different mate- rials have different albedos (which can be measured on Earth), and so knowing an asteroid’s albedo gives you some sense as to its composition. It’s only a rough idea though, and when combined with other information (say the asteroid’s density, location in the solar system, etc...) you can get a more accurate estimate of the asteroid’s composition.

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