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Unformatted text preview: 32. First, we ﬁnd the speed of the receding galaxy from Eq. 3830:
β =
= 1 − (f /f0 )2
1 − (λ0 /λ)2
=
1 + (f /f0 )2
1 + (λ0 /λ)2
1 − (590.0 nm/602.0 nm)2
= 0.02013
1 + (590.0 nm/602.0 nm)2 where we use f = c/λ and f0 = c/λ0 . Then from Eq. 4519,
r= v
βc
(0.02013)(2.998 × 108 m/s)
=
=
= 3.13 × 108 ly .
H
H
19.3 mm/s · ly (Note: if one uses the classical Doppler shift formula instead of the relativistic version in Eq. 3830,
one obtains r = 31.7 × 108 ly, which is reasonably close to the value we obtained above. This is to be
expected since β ≈ 0.02
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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