The Doppler Effect in Astronomy and Cosmologyfaculty.ucmerced.edu/dkiley/Redshift.pdf · Doppler...
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The Doppler Effect in Astronomy and Cosmology
Transcript of The Doppler Effect in Astronomy and Cosmologyfaculty.ucmerced.edu/dkiley/Redshift.pdf · Doppler...
The Doppler Effect inAstronomy and Cosmology
Doppler Effect in Cosmology 2
The Doppler EffectA passing ambulance
A passing train
Doppler Effect in Cosmology 3
The Doppler Effect for Sound
The radio emits a series of “beeps,”with period T. If the Flash isstationary, he will hear the beepswith a period T’ = T. There is noDoppler shift.
Doppler Effect in Cosmology 4
The Doppler Effect for SoundNow the Flash starts running away from the radio.
The Flash is running away, and so the beeps take longerto reach him, and so he hears a period T’, which is notequal to T, but is bigger.
Doppler Effect in Cosmology 5
The Doppler Effect for SoundNow the Flash starts running away from the radio.
Suppose the Flash is running at a constant velocity, v, andthe sound is traveling at a speed vS. They start an initialdistance d apart. Flash hears the first beep at time
!
t1
=d
vs" v
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The Doppler Effect for SoundNow the Flash starts running away from the radio.
The radio waits a time T to send out the next beep, whilethe Flash is running the whole time. So, he hears thenext beep at time
!
t2
=d + v
sT
vs" v
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The Doppler Effect for SoundNow the Flash starts running away from the radio.
So, the Flash hears a period T’=t2 - t1.
!
" T =v
s
vs# v
T =T
1# v vS
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The Doppler Effect for SoundNow the Flash starts running away from the radio.
Since the frequency is f =1/T’, then we can write
!
" f = 1#v
vS
$
% &
'
( ) f
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The Doppler Effect for SoundWhat if both are moving?
If the speed of the source is v0, the speed of sound is vS,and the speed of the receiver is vR, then
!
" f =vS m vR
vS ± v0
#
$ %
&
' ( f
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The Doppler Effect for Light
Because light behaveslike a wave, it still has aDoppler effect.
However, the equationsare different!
!
" f =c ± v
c m vf
The Special Theory ofRelativity.
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The Doppler Effect for Light
Redshift.
A source of light movingat v = 0.7c.
Blueshift.
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Spectral Lines
When electrons in an atommake a transition from abigger orbit to a lower one,they emit light.
Every atom has a characteristic spectrum.
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Spectrum of a StarThe Sun emits a continuousspectrum like a blackbody witha temperature of 5800 K.
By looking atthe spectrum,we candetermine thechemicalcomposition ofa star.
The spectrum of the Sunshows absorption lines.
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Spectrum of Stars in a Distant GalaxyThe stars (of a certain type) havethe same spectrum, no matterwhere they are.The spectrum from starsshows same absorption lines.
The lines areshifted!
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Edwin Hubble
The Universe isexpanding!!!
!
v = H0d
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Doppler Effect in Cosmology 17
The Evolution of the Universe
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The Cosmic Microwave Background
The Universestarted offextremely hot anddense, with LOTS ofhigh-energy photonsaround.
As the Universe expands,the UV photons can startfreestreaming from theSurface of LastScattering at z ~ 1100.
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The Cosmic Microwave BackgroundThe photon wavelength grows with the expansion!
The Universe has expanded by a factor of z ~ 1100since the LSS, and so the photons are in themicrowave region.
If the Big Bang picture is correct, there should be aCosmic Microwave Background!
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Penzias and WilsonThe CMB was discovered(accidentally) in 1964, andhas a perfect blackbodyspectrum with tinydeviations!
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Tiny Deviations Lead to Structure in the Universe
COBE
WMAPThis is an area of activeresearch today, and is basedvery much on the Dopplereffect!
