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hw6_solutions

# hw6_solutions - Homework#6 Solutions Astro 10 spring 2010...

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Homework #6: 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. [5 points] Remember that the Copernicus model was the only one to explain the phases on Venus properly, because it proposed that Venus orbited the Sun. To get a crescent phase, Venus would need to be on the near side of the Sun (from Earth’s perspective), whereas a gibbous phase would required Venus to be on the far side of the Sun (again, from Earth’s perspective) - with the 1st quarter Venus somewhere in between. Therefore, since the crescent Venus is physically closer to Earth than a gibbous or quarter Venus, we expect the crescent Venus to be largest in the sky . (of course, remember that Venus orbits inside Earth’s orbit) Notes to graders: Students should have a discussion equivalent to this in content to receive full credit. 2. [10 points] a) You need a slightly modified version of Kepler’s law here. In class, we learned that P 2 a 3 for the Solar system. If you look at Newton’s full version of this law, however, you’ll see that it is in reality more like P 2 a 3 /M , where M is the central mass. Kepler’s version works with planets in the Solar system, because they orbit the Sun, and so M is the Sun’s mass in all cases and cancels out in ratios. I should note here that Newton’s full version of Kepler’s law has a term like M 1 + M 2 . It’s important to realize, however, that a planet’s mass versus a star’s mass is insignificant. We can therefore drop the planet’s mass and worry only about the star’s mass. Since we’re talking about a planet orbiting another star, we must use P 2 a 3 /M . We’re told that this other star has a mass equal to 3 times the Sun’s mass. Let us now use Kepler’s modified law in ratio form, comparing this mystery planet with the Earth. Let ”1” denote the Earth values, and ”2” denote the mystery planet values, such that P 1 = 1 year , M 1 = M Sun , a 1 = 1 AU , P 2 = 3

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