problem_set_2_solutions

problem_set_2_solutions - Astronomy 160: Frontiers and...

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Astronomy 160: Frontiers and Controversies in Astrophysics Homework Set # 2 Solutions 1) How big a shift in the wavelength of green light will this instrument be able to detect? We know (from class) that the wavelength of green light is 5000 ˚ A (= 5 × 10 - 7 m). So, if the Doppler precision of the Rocky Planet Finder is 1 m/s, that means we need to ±nd what wavelength shift a 1 m/s motion will induce in 5000 ˚ A light. Δ λ λ 0 = v c Δ λ 5 × 10 - 7 [m] = 1 [m/s] 3 × 108 [m/s] Δ λ = 5 × 10 - 7 3 × 108 [m] Δ λ = 2 × 10 - 15 m So, a 1 m/s velocity produces a 2 × 10 - 15 m change in the wavelength of green light. 2) Show that, for a nearly circular orbit, a = GM/V 2 , where V is the total velocity of the system ( V = V planet + V star ) . We know that: a 3 = GMP 2 4 π 2 For a circular orbit, we know that the circumference of the circular orbit is just 2 πa and that the planet covers that distance in one period ( P ). So, the velocity of the planet in its orbit is: v P = 2 πa P If we re-arrange the equation, we get: P = 2 πa v P Now, if we plug in this way of expressing the period into the ±rst equation, we get: 1
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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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problem_set_2_solutions - Astronomy 160: Frontiers and...

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