problem_set_4_sol

# problem_set_4_sol - Astronomy 160 Frontiers and...

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Unformatted text preview: Astronomy 160: Frontiers and Controversies in Astrophysics Homework Set # 4 Solutions 1) The formula for the relativistic Doppler shift is Δ λ/λ = 1 + v R /c 1- v R /c ! 1 / 2- 1 . Show that the post-Newtonian approximation reproduces the result we used before, namely that Δ λ/λ = v R /c . What happens when v R approaches + c or- c ? Does this result make sense? Δ λ λ = 1 + V R c 1- V R c ! 1 / 2- 1 if V R c << 1, then we can use the approximation (1 + ) n ≈ 1 + n as follows: Δ λ λ = 1 + V R c 1 / 2 1- V R c- 1 / 2- 1 = 1 + V R 2 c 1 + V R 2 c- 1 Δ λ λ = 1 + V R c + V R 2 c 2- 1 since V R 2 c 2 is negligible: Δ λ λ = V R c As V R → c Δ λ λ = 1 + c c 1- c c ! 1 / 2- 1 = 2 1 / 2- 1 = ∞ Δ λ λ = λ- λ λ = ∞ λ = ∞ As V R → - c Δ λ λ = 1 +- c c 1-- c c ! 1 / 2- 1 = 2 1 / 2- 1 =- 1 Δ λ λ = λ- λ λ =- 1 λ- λ =- λ λ = 0 As V R → c , λ observed → ∞ and as V R → - c , λ observed → 0. This makes sense because the observed wavelength will range from 0 to ∞ as...
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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_4_sol - Astronomy 160 Frontiers and...

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