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section2_planetdensity - • What is the mass of the planet...

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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 reflex 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? What is the velocity of the planet in its orbit?
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Unformatted text preview: • What is the mass of the planet? Step 2: Volume In addition to the radial velocity measurements made above, you also observe the planet making transits across the star. These transits last for 2.5 hours and, at the point of greatest eclipse, block out 1% of the light from the star. Time From Center of Transit (minutes) 60 120-60-120 Relative Flux 0.995 0.990 1.000 • Assuming that the radius of the star is the same as that of the Sun (7 × 10 8 m), what is the radius of the planet ? • What is the volume of the planet? Step 3: Density • What is the density of the planet? • How does that density compare to that of water (1000 kg/m 3 )? • What does this density tell you about the composition of the planet? BONUS: How could you have Fgured out the star’s radius if that information were omitted from the problem?...
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