ch44-p051 - 51. (a) During the time interval t, the light...

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51. (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 ct r r ra 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 λ λ 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! . rr r r r r crc c c c c r cc c αα −− ∆λ ⎛⎞ = + + + ⎜⎟ λ− ⎝⎠ ≈+ + " (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 : ( ) ( ) 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 × ∆λ λ = × × +∆λ λ +
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(g) From the result of part (a), () ( ) 81 5 16 88 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 α ×× ∆= = = × ×− × which is equivalent to 6.9 × 10
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This note was uploaded on 05/19/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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ch44-p051 - 51. (a) During the time interval t, the light...

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