section2_planetdensity_answers

section2_planetdensity_answers - Density of a Hot Jupiter...

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Density of a Hot Jupiter Last Thursday (February 1) in class, Professor Bailyn discussed a “Hot Jupiter” that is aligned in just the right way such that the planet periodically passes in front of the star (i.e. “transits”). We have observed another nearby sun-like star that also transits. In order to determine the composition of the star, you set out to measure the density. Since we know that density ( ρ ) = mass ( M ) / volume ( V ), we need to measure the mass and volume of the planet in order to get the density of the planet . v = 2 πa P a 3 = P 2 M 1 AU = 1 . 5 × 10 11 m v * M * = v p M p V = 4 3 πR 3 1 M ± = 2 × 10 30 kg ρ = M V A = πR 2 1 year = 3 × 10 7 s Step 1: Mass From Doppler measurements, it’s been found that the re±ex velocity of the star (due to the planet) is 85 m/s and that the period of the planet’s orbit is 3.5 days (= 10 - 2 yrs). What is the semi-major axis ( a ) of the planet’s orbit? a 3 = P 2 M = (10 - 2 ) 2 * 1 = 10 - 4 a = (100 × 10 - 6 ) 1 / 3 a = 5 × 10 - 2 A.U. = 7 . 5 × 10 9 m What is the velocity of the planet in its orbit?
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This note was uploaded on 02/06/2012 for the course BENG 100 taught by Professor Marksaltzman during the Spring '08 term at Yale.

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section2_planetdensity_answers - Density of a Hot Jupiter...

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