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Unformatted text preview: Astronomy 210 Spring 2011 Homework Set #5: Solutions 1. A Newly Discovered Planet . (a) [5 points] Since the star is the same as the sun and thus has the Suns mass, we can use the simplified version of Kepler III: P 2 yr = a 3 AU . Using P = 0 . 837 days = 0.0023 yr, we have a AU = P 3 / 2 yr = 0 . 017 (1) and so a = 0 . 017 AU = 2 . 6 10 9 m = 0 . 045 a mercury = 3 . 7 R (2) We see that Kepler-10b has a much smaller orbit than Mercurys, and indeed is less than 4 stellar radii away from its host star. (b) [5 points] The average density of Kepler-10b is avg = M V = M 4 R 2 / 3 = 1 . 7 avg , = 9000 kg / m 3 (3) Kepler-10b has a density larger than Earths, and larger than rock and even most uncompressed metals. This indicates that the planet is rocky and certainly not a gas giant. (c) [5 points] Kepler-10b is the first confirmed rocky exoplanet! Objects with density of 3000 kg / m 3 can still be gas/ice giants. (d) [5 points] As usual, g = GM R 2 = 23 m / s 2 = 2 . 4 g (4) The surface gravity on Kepler-10b is a little over twice that of Earth, so your weight there would be about double what it is here....
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