ch44_p43 - 43. (a) During the time interval t, the light...

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43. (a) During the time interval t , the light emitted from galaxy A has traveled a distance c t . Meanwhile, the distance between Earth and the galaxy has expanded from r to r' = r + r α t . Let c t rr r a t ∆∆ = =+ , which leads to t r cr = . (b) The detected wavelength λ ' is longer than λ by λ t due to the expansion of the universe: λ ' = λ + λ t . Thus, ∆λ λ λλ λ = ′ − == t r . (c) We use the binomial expansion formula (see Appendix E): () 2 2 1 11 1 1! 2! n nn x nx xx ±= ± + + < " to obtain 12 23 1 2! . r r r r crc c c c c r cc c αα ª º −− ∆λ § · §· = + + + « » ¨ ¸ ¨¸ λ− © ¹ ©¹ « » ¬ ¼ ≈+ + " (d) When only the first term in the expansion for ∆λ λ is retained we have ∆λ λ r c . (e) We set ∆λ λ v c Hr c and compare with the result of part (d) to obtain = H . (f) We use the formula ∆λ λ = rc r b g to solve for r :
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() ( ) 8 88 2.998 10 m s 0.050 6.548 10 ly 6.5 10 ly. 1 0.0218 m s ly 1 0.050 c r α × ∆λ λ == = × × +∆λ λ + (g) From the result of part (a), 81 5 16 6.5 10 ly 9.46 10 m ly 2.17 10 s, 2.998 10 m s 0.0218 m s ly 6.5 10 ly r t cr ×× ∆= = = × ×− × which is equivalent to 6.9 × 10 8 y. (h) Letting
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This note was uploaded on 01/23/2011 for the course PHYSICS 17029 taught by Professor Rebello,nobels during the Fall '10 term at Kansas State University.

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ch44_p43 - 43. (a) During the time interval t, the light...

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