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solution_3 - ASTRONOMY 294Z The History of the Universe...

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ASTRONOMY 294Z: The History of the Universe Professor Barbara Ryden SOLUTIONS TO PROBLEM SET # 3 1) [20 points] You are given a ticket for running a red traffic light. For an ob- server halted at the light, the light emitted has a wavelength λ 0 = 700 nm . You tell the traffic cop that because you were approaching the light, the Doppler shift made it appear green ( λ = 500 nm ). How fast would you have been going if this were true? If the speed limit is 35 miles per hour, and the speeding fine is $ 1 for every mile per hour over the limit, how large a fine would you have to pay? From the formula for the Doppler shift (lecture for Thursday, January 17), your speed relative to the light would be v = λ - λ 0 λ 0 c = 500 nm - 700 nm 700 nm c = - 2 7 c . (1) (The negative sign means that you are moving toward the light.) A speed of 2/7 the speed of light is no trifle. In kilometers per second, it would be v = 2 7 (300 , 000 km / sec) = 85 , 714 km / sec . (2) In miles per hour, it would be v = 85 , 714 km / sec ˆ 0 . 621 miles 1 km ! 3600 sec 1 hour = 191 , 623 , 857 mph . (3) The resulting fine would be N $ = (191 , 623 , 857 mph - 35 mph) ˆ $1 1 mph ! = $191 , 623 , 822 . (4) Better to confess to running the red light!
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2) [20 points] Assume that a typical galaxy contains 100 billion stars, and that there is one galaxy per cubic megaparsec, on average.
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