The **Doppler** Effect in

Astronomy and Cosmology

The **Doppler** Effect

A passing train

A passing ambulance

**Doppler** Effect in Cosmology 2

The **Doppler** Effect for Sound

The radio emits a series of “beeps,”

with period T. If the Flash is

stationary, he will hear the beeps

with a period T’ = T. There is no

**Doppler** shift.

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The **Doppler** Effect for Sound

Now the Flash starts running away from the radio.

The Flash is running away, and so the beeps take longer

to reach him, and so he hears a period T’, which is not

equal to T, but is bigger.

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The **Doppler** Effect for Sound

Now the Flash starts running away from the radio.

Suppose the Flash is running at a constant velocity, v, and

the sound is traveling at a speed v S. They start an initial

distance d apart. Flash hears the first beep at time

t 1 =

d

v s " v

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The **Doppler** Effect for Sound

Now the Flash starts running away from the radio.

The radio waits a time T to send out the next beep, while

the Flash is running the whole time. So, he hears the

next beep at time

t 2 = d + v s T

v s " v

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The **Doppler** Effect for Sound

Now the Flash starts running away from the radio.

So, the Flash hears a period T’=t 2 - t 1.

T " = vs vs # v

T =

T

1# v v S

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The **Doppler** Effect for Sound

Now the Flash starts running away from the radio.

Since the frequency is f =1/T’, then we can write

f " = 1# v $

&

%

v S

'

) f

(

**Doppler** Effect in Cosmology 8

The **Doppler** Effect for Sound

What if both are moving?

If the speed of the source is v 0, the speed of sound is v S,

and the speed of the receiver is v R, then

f " = v #

S m v &

R

% ( f

$ vS ± v0 '

**Doppler** Effect in Cosmology 9

!

The **Doppler** Effect for Light

Because light behaves

like a wave, it still has a

**Doppler** **effect**.

However, the equations

are different!

"

f =

c ± v

c m v f

The Special Theory of

Relativity.

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The **Doppler** Effect for Light

A source of light moving

at v = 0.7c.

Redshift.

Blueshift.

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Spectral Lines

When electrons in an atom

make a transition from a

bigger orbit to a lower one,

they emit light.

Every atom has a characteristic spectrum.

**Doppler** Effect in Cosmology 12

Spectrum of a Star

The Sun emits a continuous

spectrum like a blackbody with

a temperature of 5800 K.

The spectrum of the Sun

shows absorption lines.

By looking at

the spectrum,

we can

determine the

chemical

composition of

a star.

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Spectrum of Stars in a Distant Galaxy

The stars (of a certain type) have

the same spectrum, no matter

where they are.

The spectrum from stars

shows same absorption lines.

The lines are

shifted!

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Edwin Hubble

The Universe is

expanding!!!

v = H 0 d

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**Doppler** Effect in Cosmology 16

The Evolution of the Universe

**Doppler** Effect in Cosmology 17

The Cosmic Microwave Background

The Universe

started off

extremely hot and

dense, with LOTS of

high-energy photons

around.

As the Universe expands,

the UV photons can start

freestreaming from the

Surface of Last

Scattering at z ~ 1100.

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The Cosmic Microwave Background

The photon wavelength grows with the expansion!

The Universe has expanded by a factor of z ~ 1100

since the LSS, and so the photons are in the

microwave region.

If the Big Bang picture is correct, there should be a

Cosmic Microwave Background!

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Penzias and Wilson

The CMB was discovered

(accidentally) in 1964, and

has a perfect blackbody

spectrum with tiny

deviations!

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Tiny Deviations Lead to Structure in the Universe

COBE

WMAP

This is an area of active

research today, and is based

very much on the **Doppler**

**effect**!

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