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 / = 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 / = v R /c . What happens when v R approaches + c or- c ? Does this result make sense? = 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: = 1 + V R c 1 / 2 1- V R c- 1 / 2- 1 = 1 + V R 2 c 1 + V R 2 c- 1 = 1 + V R c + V R 2 c 2- 1 since V R 2 c 2 is negligible: = V R c As V R c = 1 + c c 1- c c ! 1 / 2- 1 = 2 1 / 2- 1 = = - = = As V R - c = 1 +- c c 1-- c c ! 1 / 2- 1 = 2 1 / 2- 1 =- 1 = - =- 1 - =- = 0 As V R c , observed and as V R - c , observed 0. This makes sense because the observed wavelength will range from 0 to as...
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problem_set_4_sol - Astronomy 160: Frontiers and...

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