Caldervale High School
CfE Higher Physics
Our Dynamic Universe
Summary Notes
Section 6: The Expanding Universe
1. The Doppler Effect
Objects Moving Towards Us
We are all familiar with the “nee naw” sound from approaching emergency vehicles.
As the vehicle approaches, the sound we hear is ________________ in pitch than
when the vehicle is stationary .
This is because, as the sound source moves towards us, the sound wavelength it
emits gets “________________”. This shortening of wavelength is detected as a
sound with higher _________________ (or “pitch”).
The sound waves are distorted like this…
stationary source
moving source
stationary
observer
The change in the “observed” frequency is what we call “___________________
_______________________”.
The Doppler Effect is observed with _____________ ______ ____________, as
well as with other waves.
Blue Shift
We can observe the Doppler Effect in galaxies. Obviously we don’t hear light, but we
can detect a change in their _______________ ______________ (showing the e.m.
wavelengths emitted).
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If the galaxy is moving _________________ our
Milky Way, the spectra is shifted towards
________________ ___________________
and ________________ ___________________ .
We call this a “_____________ _____________”.
This is currently the case with our neighbouring galaxy, Andromeda (shown above).
No need to worry – it’s 2.5 million light years away!
Objects Moving Away From Us
As an emergency vehicle moves away from us, the sound we hear is ____________
in pitch than for the stationary vehicle.
This is because, as the sound source moves away from us, the sound wavelength it
emits gets “___________________”.
This lengthening of wavelength is detected as a sound with lower _______________
(or “pitch”).
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Red Shift
As stars and galaxies move away from us (that’s most of them!) we detect a change
in their _________________ ____________ towards _________________
_______________________ and ___________________ _________________.
We call it a “__________ _____________”.
Light from most galaxies and stars is “red shifted”, so scientists believe that the
Universe is _____________________. This is strong evidence for The Big Bang
Theory, coming up in this course very soon!
Note … localised gravity can explain the blue shift for Andromeda.
Red Shift and Blue Shift Images (see Powerpoint Slide for colours)
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Doppler Effect Calculations
Let
fs = source frequency in Hz
fo = observed frequency in Hz
v = velocity of the sound or light in ms-1
vs = velocity of the source in ms-1
Then for a sound or light source moving towards a stationary observer:
v
fo = fs
(v – v )
s
And for a sound or light source moving away from a stationary observer:
v
fo = fs
(v + v )
s
IMPORTANT NOTE
These Doppler Effect equations cannot be used for very fast moving sources
because relativistic effects would be substantial.
By “very fast” or “relativistic speeds” we generally mean speeds over 10% of the
speed of light or over 3 x 107 ms-1 or over 0.1c.
The Higher course doesn’t cover these calculations … BIG PHEW!!!
Worked Example 1
A police car siren emits sound with a frequency of 1000 Hz. The speed of sound in air is
340 ms-1.
a)
Determine the frequency observed by a stationary pedestrian when the police car is
moving towards the pedestrian at 20 ms-1.
b)
Determine the corresponding wavelength of sound detected by the observer.
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Worked Example 2
A 410 nm spectral line from Hydrogen is examined in a laboratory on Earth. A stellar
spectrum shows this line as red shifted to 440 nm
a)
Calculate the frequency of the spectral line from the Hydrogen source examined in
the laboratory.
b)
Calculate the frequency of the spectral line recorded in the stellar spectrum.
c)
Without relativistic considerations, determine the velocity of the star.
Redshift Quantified
Edwin Hubble noticed, way back in the 1920s, that light from the stars and galaxies
he observed was ________ shifted. So he presumed all stars and galaxies were
moving _______________.
He quantified the redshift (z) as “the ratio of the ________________ in wavelength
to the wavelength with the source at rest”.
In short …
z
=
 - 
o

rest
rest
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Of course later it was discovered that some stars and one galaxy are actually moving
towards us.
In this case the redshift value, z, is _____________________.
So a negative “redshift” is, in fact, a _____________ ________________.
For non-relativistic speeds (that’s less than about 10% of the speed of light, or
0.1c), the redshift of a star or galaxy can be simplified to
z
=
v
c
Where v is the recessional
velocity of the star or galaxy.
Worked Example 3
Consider again the Hydrogen line from Worked Example 2.
410nm recorded in the lab and 440nm observed from a star.
a)
Calculate the redshift value, z.
b)
Assuming the star is moving with a non- relativistic velocity, determine its
recessional velocity.
c)
How does your answer compare with Worked Example 2c)?
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Section 6: The Expanding Universe
2. Hubble’s Law
After numerous studies of the redshifts of stellar objects in the 1920s, Edwin Hubble
made a profound discovery!
Hubble discovered that …
1.
The velocity at which stars are moving away from us is _________________
______________________ to their distance from us.
2.
Further away stars are moving away _________________
than those
nearby.
3.
Some stars are grouped at distances well beyond our Milky Way!!! Let’s call
them “_______________________”. This answered the main question of
the time, “Does the Universe only consist of The Milky Way?”
4.
Our Universe is ________________________ !!!
In 1920s, this was astonishing news as most people assumed that the
Universe was stable and infinite. This news clashed with many religious
beliefs too. It was the first piece of evidence for the ________ ___________
_____________________.
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Hubble’s Law
From Hubble’s graph, and the addition of more accurate data points in later years,
we have the relationship:
v  d
v = Ho d
v = the recessional velocity of star (in ms-1)
d = the distance to the star (in m)
Ho = Hubble’s Constant (in s-1) … found from the gradient of the best line fit.
Ho = 2.34 x 10-18 s-1
NOTE:
The accuracy of the measurement of Hubble’s Constant, based on the line of best fit,
has improved greatly over the years with the detection of very distant stars and
galaxies.
For simplicity, we will use the unit “s-1”. Astronomers, however, use a different unit
for Hubble’s Constant which is based on the astronomical units of velocity (kms-1)
and distance (Mparsec). This gives a different numerical value too.
Worked Example
A spectral line from Helium has a wavelength of 492 nm in the lab. During a spectral
analysis of a star, the line shows up as 500 nm.
a)
Determine the redshift value, z, and use it to calculate the recessional velocity
of the star.
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Worked Example (cont.)
b)
Use Hubble’s Law to estimate how far away the star is from Earth.
The Age of the Universe
A further conclusion that can be made from Hubble’s discovery is an estimation of
the age of the Universe!
If we assume the rate of expansion of the Universe is ________________ (although
gravitational effects would make this unlikely and recent studies suggest the outer
parts might be accelerating!) then we can simply rearrange Hubble’s Law to
determine how long the star has been moving.
This would be when the Universe ________________ .
So …
We know that
Then …
We can rearrange Hubble’s Law to d / v = 1 / Ho
So …
d / v = t for objects moving at a constant rate.
t =
1 / Ho
.
This would give an estimation of the Age of the Universe as …
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In Summary
So here’s what we can find out by analysing light from the stars just with a telescope:





The different wavelengths of light emitted.
The elements that make up the star.
How fast the star is moving relative to us.
How far away the star is.
Approx AGE OF THE UNIVERSE!!
You can use the rest of this page to record your response to this amazing
information 
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Section 6: The Expanding Universe
3. The Evidence is Mounting
Evidence for the Expansion of the Universe
In 1920’s Hubble’s work led to the idea that the Universe is expanding. In the years
that followed, other pieces of evidence strengthened this theory. Even nowadays,
further evidence continues to be revealed.
3 important pieces of evidence for an expanding Universe (and the Big Bang
Theory) are listed below.
1.
Hubble’s observations of ________________ tells us that most galaxies
and stars are moving apart.
2.
Temperature Measurements of Cosmic Microwave Background (CMB)
Radiation are as predicted by the _______
3.
___________
____________.
The darkness of the night sky tells us there must be galaxies whose light
has still to reach us. So they cannot be _____________________ old.
Expansion of the Evidence ()
1.
“Hubble’s observations of redshift tells us that most galaxies and stars
are moving apart.”
As explained earlier in your notes, the redshift from stellar objects,
particularly distant galaxies, allows measurements of their _______________
and ____________________ from us to be made.
So, going __________ in time, it is suggested that all galaxies were once
together at some fixed point: all matter and energy in the Universe was once
concentrated into an infinitesimally small, infinitely hot, infinitely dense,
something – we call this hypothetical thing a ________________________!
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2.
“Temperature Measurements of Cosmic Microwave Background (CMB)
Radiation are very cold, as predicted by the Big Bang Theory.”
If there was really a Big Bang, then photons of light emitted during it would
have increased in _____________________ into the ___________________
region, by now, as the Universe expanded.
This radiation should be uniformly distributed across the Universe and have a
“peak wavelength” (more on this later) indicating a very _______ temperature
due to ____________________ of the Universe during its expansion.
In 1965, the idea of CMBR became a reality! It was detected in ___________
_____________ (where hotter radiation from stars and galaxies was not
hiding it). These Cosmic Microwaves are believed to have been emitted
_____________ the birth of our known Universe – during the “______
__________”.
It was accidentally detected by 2 scientists, Penzias and Wilson, while they
were investigating the use of __________________ for Telecommunications.
They even received the Nobel Prize for their accidental discovery.
This evidence is arguably the _________ ____________________ evidence
for The Big Bang Theory and Expanding Universe.
3.
“The darkness of the night sky tells us there must be galaxies whose
light has still to reach us. So they can’t be infinitely old.”
More of an observation than a measurement, the question “Why is the Night
Sky Dark” has been raised for centuries. (In 1576 by Digges; in 1610 by
Kepler and formally in 1823 by Heinrich Olbers).
The question stemmed from the assumption at the time that the Universe was
infinite and static.
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If this was true then surely there would be an
infinite wall of ______________ at night time,
in all ___________________.
And yet there was so much darkness at night,
between the stars.
BUT if the Universe is NOT infinitely old, and
big, then either there might be no galaxies yet
formed in some directions, or some that are so
distant, their light has not yet reached us.
This would account for large areas of darkness between the ______________
stars and galaxies whose light has reached us.
And, if the Universe is NOT infinitely old, then it was created at some time in
the past, which is consistent with Big Bang Theory.
Dark Matter
By measuring the orbital ______________ of stars in a galaxy, the ____________ of
the galaxy can be estimated.
However, the rotational speeds at the outer parts of observed galaxies are only
possible if the mass of the galaxy is much _________________ than what we can
detect. There seems to be mass that’s “_________________”!
This “missing mass” is now called “________
__________________”.
Dark Energy
It is expected that gravitational effects should slow down the expansion of the
Universe. HOWEVER, measurements indicate that the rate of __________________
is in fact _____________________!
So, there must be some energy we cannot detect that overcomes ______________.
We call it ___________
______________.
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In Fact …
So ______ % !!! of what’s out there,
we know virtually nothing about!
We can only assume it’s there
because of how it ____________ the
stuff we
can observe.
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Section 6: The Expanding Universe
4. Temperature Considerations
Temperature and Colour
The radiation emitted by stellar objects can give us information about the
temperature of the objects.
When heated, at first objects emit invisible ___________________.
On further heating they glow … _________________
Hotter again we get … ________________
And even hotter gives … ________________
Then … _________________
then ________________ .
In fact, hundreds of years ago, potters recognised that the colour their materials
glowed in the kiln gave them an actual measurement of the _________________ of
the kiln:
Dark Red
Cherry Red
Orange
Yellow
White
… 550oC … 823 K
… 750oC … 1023 K
… 900oC … 1173 K
… 1000oC … 1273 K
… 1200oC … 1373 K
Black-body Radiation
Very hot ___________ and ________________ usually emit _________________
spectra of radiation as opposed to the ______________ spectra we detect from
gases.
A surface that can emit and absorb all wavelengths of the em spectrum is called a
____________________. Its continuous spectrum is called ________________
____________________.
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A black-body spectrum can be identified by the following shape characteristics:
1.
A bell shape that __________ steeply, at shorter wavelengths, to a ________
______________, then _______ _______ gently at longer temperatures.
2.
As the object temperature increases, the overall ___________ remains the
____________, but the _________ _________________ shifts to a
_____________ value.
3.
As the object temperature increases, the _________________ for all emitted
wavelengths, _______________.
intensity
Typical Black-body Spectra
a)
Determine the peak
wavelength for each of the temperatures in the
diagram.
b) Stars behave quite like “black bodies”.
Describe what happens to the peak wavelength emitted by a star, as its
temperature increases.
__________________________________________________________
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