Name……………..
Class…………..
Plymstock School Physics
Department
Module G485.5 Modelling the
Universe
student booklet
Lesson 52 – The Structure of the Universe
Objectives
(a) describe the principal contents of the universe, including stars, galaxies
and radiation;
(b) describe the solar system in terms of the Sun, planets, planetary satellites
and comets;
Outcomes
Be able to describe the principal contents of the universe, including stars,
galaxies and radiation.
Be able to describe the solar system in terms of the Sun, planets, planetary
satellites and comets.
Write your own definitions of these Keywords:
Universe
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Star
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Galaxy
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Sun
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Planet
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Moon
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Nebulae
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Comet
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Red giant
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White dwarf
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Main sequence star
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Super red giant
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Neutron star
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Black hole
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Supernova
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Binary star
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Quasar
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Radiation
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The Structure of the Universe Research Project
Create a presentation that describes the principal contents of the universe, including:
stars,
galaxies and
radiation
and describes the solar system in terms of the
Sun,
planets,
planetary satellites and
comets.
ALL (E-D) must define each term above
MOST (C-B) will give examples of each in and out of the Solar System as appropriate
SOME will explain the origin of the above elements and create a neat and logical
presentation using keywords correctly.
Lesson 53 notes – Stars
Objectives
(c) describe the formation of a star, such as our Sun, from interstellar dust
and gas;
(d) describe the Sun’s probable evolution into a red giant and white dwarf;
(e) describe how a star much more massive than our Sun will evolve into a
super red giant and then either a neutron star or black hole;
Outcomes
Be able to describe the formation of a star, such as our Sun, from interstellar
dust and gas.
Be able to describe the Sun’s probable evolution into a red giant and white
dwarf.
Be able to describe how a star much more massive than our Sun will evolve
into a super red giant and then either a neutron star or black hole.
The Hertzsprung-Russell diagram and the evolution of stars
The Hertzsprung-Russell diagram can be used to show the evolution of stars.
Two paths are shown:
(a) Figure 1 for stars of similar mass to the Sun (<3 solar masses)
(b) Figure 2 for stars of three or more times the mass of the Sun (> 3 solar
masses)
Spectral type: O
B
A
F
G
K
M
Red supergiants
Absolute magnitude
Luminosity
(Sun = 1)
10000
-5
1000
Red giants
100
0
10
Sun
1
+5
Main sequence
10-1
Figure 1
Mass < 3 solar
masses
+10
10-2
10-3
White dwarfs
10-4
+15
Surface temperature (K):
40000
Spectral type: O
20000
B
10000
A
6000
F
4000
G
3000
K
2000
M
Red supergiants
Absolute magnitude
Luminosity
(Sun = 1)
10000
-5
1000
Red giants
100
0
10
Sun
Figure 2
1
+5
Main sequence
10-1
10-2
+10
Mass > 3 solar
masses
10-3
10-4
White dwarfs
+15
Surface temperature (K):
40000
20000
10000
6000
4000
3000
2000
Lesson 54 questions – Stars
Name…………………………
/14)………%………
Class……………..
(
ALL
1.
Describe and explain the stages which take place in the birth of a Main
Sequence star.
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[Total 5 marks]
2.
When a star ceases to be Main Sequence, it may evolve in several
different ways.
Explain the circumstances which will lead to the formation of a neutron
star.
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[Total 4 marks]
3.
(i)
A star of mass 7 × 1030 kg becomes a neutron star of radius 10 km.
Calculate the average density of the neutron star, assuming that
50% of the original star’s mass has been lost.
density = ……………….. kg m–3
[3]
(ii)
State how the density of a neutron star compares to that of
materials commonly found on Earth.
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[2]
[Total 5 marks]
Lesson 55 notes – Astronomical distances
Objectives
(f) define distances measured in astronomical units (AU), parsecs (pc) and
light-years (ly);
(g) state the approximate magnitudes in metres, of the parsec and light-year;
(h) state Olbers’ paradox;
(i) interpret Olbers’ paradox to explain why it suggests that the model of an infinite,
static universe is incorrect (HSW 7);
Outcomes
Be able to define distances measured in astronomical units (AU), parsecs (pc)
and light-years (ly);
Be able to state the approximate magnitudes in metres, of the parsec and light-year;
Be able to state Olbers’ paradox.
Be able to interpret Olbers’ paradox to explain why it suggests that the model of an
infinite, static universe is incorrect.
Be able to convert distances from metres to parsecs to light-years.
Radar
A radio pulse can be sent out and the time taken for the reflected pulse to be
received is recorded. If we know the speed of electromagnetic radiation in free
space and the time between transmission and reception the radar pulse
enables us to find the distance of the object.
Parallax
The difference in direction of a star viewed from the two ends of a line with a
length equal to the radius of the Earth’s orbit is called the PARALLAX of the
star.
Stars that are close to the earth have a larger parallax than ones far away. In other
words their position in the sky against far away stars when viewed from the Earth
changes significantly as the Earth orbits the Sun.
Earth
Distant stars
Parallax 
Centauri
2
Sun
Parallax 
Earth
Distant stars
Figure 1
By significantly we mean a fraction of a second of arc. In the example shown 
Centauri (distance 1.33 parsecs) has a parallax of 0.75 “ of arc.
Astronomical unit
One Astronomical unit (AU) is defined as the mean distance of the Earth from the
Sun (1.5x1011 m)
The light year
This is the distance that light travels in free space in one year = 9.5x1015 m
The Parsec
The radius of Earth’s orbit = 1.5x1011 m, and therefore the
distance is found from:
tan(1”) = 1.5x1011/d so
d = 3.06 x1016 m
1 parsec is the distance at which an object subtends an angle of
one second using the radius of the Earth’s orbit as the baseline.
Distances between galaxies are usually measured in light years
or Mega parsecs (Mpc).
One second of
arc
One parsec
1 Parsec = 3.06x1016 m = 2.04x105 AU = 3.26 light years
1 Mega parsec (Mpc) = 3.26x106 light years = 3.097x1022 m
Radius of Earth’s
orbit
Earth
Sun
Figure 2
The parallax of a number of stars is shown in the following table:
Star
Parallax Distance (l.y)
(" of arc)
A Centauri
4.3
0.750
Barnard's Star
0.545
6.0
Sirius
0.377
8.6
Procyon
0.285
11.4
Star
Parallax Distance (l.y)
(" of arc)
Vega
0.133
25
0.097
34
Arcturus
Aldebaran
0.054
60
Castor
0.001
570
At distances much greater than this the parallax method becomes
impossibly difficult to measure. Remember that 1" of arc is the angle
subtended by a human head almost ¾ of a kilometer away. Therefore the
parallax of Castor is the same as the angle subtended by a human head
at a distance of almost 750 km!
Another method for measuring larger distances had to be found.
Cepheid variables
The solution came early in the twentieth century as a result of studies of a variable
star (one whose brightness changes with time) in the constellation of Cepheus.
Period
Brightness
Radius
Figure 3
The brightness of the star varied in a particular way (see Figure 3) and in
1912 Miss Henrietta Leavitt of Harvard College observatory discovered an
important connection between the period and brightness. This is now known
as the period-luminosity relationship. Many other stars were found to vary in a
similar way and the group of stars was called Cepheid variables. (There are
actually two types of Cepheid variable but we will just consider one type here).
The period-luminosity relation means that if you can measure the period of a
Cepheid variable you can find its luminosity. Knowing how bright the star
really is and then measuring how bright it appears to be will then give the
distance of the star from the Earth. The discovery of Cepheid variables in the
Andromeda nebula (M31) enabled its distance from Earth (over two million
light years) to be found.
Two ways of presenting the period luminosity law are shown by the graphs in
Figure 4.
Luminosity (Sun = 1)
106
104
Population I Cepheid variables
102
1.0 -2.0
-1.0
0.0
1.0
2.0
3.0
log period (days)
Absolute magnitude
-5
-4
-3
-2
Population I Cepheid variables
-1
0
+1
0.1
1
10
100
Period (days)
Figure 4
Olber’s Paradox
Lesson 56 – Astronomical distances
Name…………………………
Class………..
(
/8)…….%….……
ALL
1.
The average orbital radius of Jupiter is approximately 5.2 AU.
Calculate the orbital radius of Jupiter in metres.
radius = ...................... m
[Total 1 mark]
MOST
2.
(a)
Suggest why many stars within our galaxy do not conform with
Hubble’s law.
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[2]
(b)
Estimate the age of the Universe, giving your answer in seconds.
Show your working and take the Hubble constant to be 75 km s–1
Mpc–1.
age = .............................. s
[3]
[Total 5 marks]
ALL
3.
Large distances in the Universe may be measured in parsecs. Explain
what is meant by a parsec.
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[Total 2 marks]
Lesson 57 - The Red Shift
Objectives
(j) select and use the equation
Δλ = v
λ c
(k) describe and interpret Hubble’s redshift observations;
(l) state and interpret Hubble’s law (HSW 1 & 2);
(m) convert the Hubble constant H0 from its conventional units (km s-1 Mpc-1) to SI
(s1);
Outcomes
Be able to select and use the equation
Δλ = v
λ c
Be able to describe Hubble’s redshift observations;
Be able to state Hubble’s law (HSW 1 & 2);
Be able to describe and interpret Hubble’s redshift observations;
Be able to state and interpret Hubble’s law (HSW 1 & 2);
Be able to convert the Hubble constant H0 from its conventional units (km s-1 Mpc-1)
to SI (s-1);
The Doppler Effect predicts that radiation from sources that are towards us will be
shifted towards shorter wavelengths (the blue end of the spectrum in the case of
visible light) and towards longer wavelengths (the red end of the spectrum) if they are
moving away from us.
Galaxy receding
Light waves ‘stretched’ – Red Shift
Galaxy approaching
Light waves ‘squashed’ – Blue Shift
Observations of the spectra of galaxies show that the light coming from many of these
is shifted significantly towards the red and this shows that they are moving away from
us at high speeds, many tens of thousands of kilometres per second. This shift towards
the red is called the Red Shift and is very good evidence for the expansion of the
Universe and for the origin of the Universe in the Big Bang.
Corona
Borealis
If the Doppler shift of lines within their
spectra can be measured their speed of
recession can be calculated. The speed (v)
relative to the observer on the Earth is
given by:
Boote
s
Velocity of galaxy (v) = c/ where  is
the wavelength of a line in the spectrum on
Earth,  is the shift in wavelength and c is
the speed of light.
Velocity 21 400 kms-1
Velocity 39 000
kms-1
Hydra
Velocity 61 000
kms-1
A diagrammatic version of the shift of two absorption lines for three galaxies
together with their speeds of recession is shown in the following diagram. The
comparison spectrum of an element on Earth, at rest compared with the
observer, is shown above and below each galactic spectrum.
For very high speeds the simple formula cannot be used and the effects of
special relativity have to be allowed for.
It is important to realise that the Doppler shift will depend on the original
wavelength and so lines in the red end of the spectrum will be shifted more
than those towards the violet end.
Hubble’s Law
Hubble measured red shift and distances and plotted these on a graph:We now have a linear
relationship which has
proved very useful while
posing some strange
conundrums (conundra?!)
How do we account for
the galaxies receding
faster the further away
they are?
Does this point to a time
aeons ago where all the
galaxies were in one
place?
Olbers’ paradox was solved by Hubble’s discovery because an expanding universe
means that the amount of light from a receding galaxy reaching the Earth per second
is reduced and also the fact that it is red shifted means that it has less energy when it
reaches us! Therefore, the more distant a galaxy, the less of a contribution it makes to
the total amount of light here on Earth and hence it is dark at night because the
Universe is expanding!
Converting Units
You can convert the value of H to SI units as follows:
Take the Hubble constant H to be 70 kms-1 Mpc-1
and one light year to be 9.46x1015 m
One Parsec = 3.26 light years = 3.0857x1016 m
therefore 1 Mpc = 3.0857x1022 m
So 70 kms-1Mpc-1
= 70x103/ 3.09x1016x106 = 2.27 x 10-18 ms-1m-1
Lesson 58 questions – Redshift
Name…………………….
Class………………
(
/31)……….%……..
ALL
1.
The mean density of the Universe, ρ0, is thought to be approximately 1 ×
10–26 kg m–3.
Calculate a value for the Hubble constant H0.
H0 =......................................................... s–1
[Total 2 marks]
2.
State Hubble’s law and define any symbols used.
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[Total 2 marks]
3.
Describe Olbers’ paradox and explain how the work of Edwin Hubble
provides an answer.
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[Total 5 marks]
4.
In 1929 Edwin Hubble showed that the Universe was expanding by
studying the light from stars and galaxies. Explain how.
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[Total 5 marks]
5.
(a)
Suggest why many stars within our galaxy do not conform with
Hubble’s law.
............................................................................................................
............................................................................................................
............................................................................................................
[2]
(b)
Estimate the age of the Universe, giving your answer in seconds.
Show your working and take the Hubble constant to be 75 km s–1
Mpc–1.
age = .............................. s
[3]
[Total 5 marks]
MOST
6.
Astronomers are searching for planets which orbit distant stars. The
planets are not visible from the Earth. Their existence is revealed by the
star’s motion which causes a shift in the wavelength of the light it emits.
A large planet P is shown orbiting a star S in the Fig. 1. Both the star and
the planet rotate about their common centre of mass C.
P
C
S
light to Earth
Fig. 1
When measured from a stationary source in the laboratory, a spectral line
has a wavelength  of 656.3 nm.
The light from star S is examined over a period of 74 hours. The change
in wavelength ∆ for the same spectral line is recorded. The velocity has
been calculated and the data shown in Fig. 2.
∆λ /10–15 m
velocity / m s–1
1
6.7
3.1
6
38.1
17.5
12
66.0
30.3
19
76.0
34.9
23
69.1
31.7
29
43.8
20.1
35
6.8
3.1
41
–32.2
–14.8
48
–66.0
–30.3
55
–76.0
–34.9
61
–62.5
–28.7
67
–32.2
–14.8
time / h
74
6.1
Fig. 2
(i)
Use the Doppler equation relating ∆ with velocity v to calculate the
change in wavelength for the final velocity of 6.1 m s–1.
change in wavelength = ………….........m
[3]
(ii)
Plot a graph of the star’s velocity against time using the grid in Fig.
3. The first seven points are already completed. The data required
from Fig. 2 are repeated beneath the grid.
velocity / m s –1
40
30
20
10
time
80 / h
0
10
20
30
40
50
60
70
–10
–20
–30
–40
Fig. 3
[2]
time / h
velocity / m s
41
–14.8
48
–30.3
55
–34.9
61
–28.7
67
–14.8
74
6.1
–1
(iii)
Draw a curve through all the points on the graph.
[1]
(iv)
On Fig. 1, mark a point on the star’s orbit that would correspond to
a velocity of zero on the graph. Label this point X.
[1]
(v)
Use your graph to estimate the time T for the planet to make one
complete revolution around the star.
time .........................h
[1]
(vi)
The mass M of the star is estimated to be 4 × 1030 kg. Calculate the
radius of the planet’s orbit using the relationship below.
r=
3
GMT 2
4π 2
radius = .....................m
[2]
[Total 10 marks]
7.
The mean density of the Universe, 0, is thought to be approximately 1 ×
10–26 kg m–3.
Calculate a value for the Hubble constant H0.
H0 = ...........................s–1
[Total 2 marks]
Lesson 59 notes – The Expanding Universe
Objectives
(n) state the cosmological principle;
(o) describe and explain the significance of the 3K microwave background radiation
(HSW 1).
(a) explain that the standard (hot big bang) model of the universe implies a finite age
for the universe (HSW 1, 2, 7);
(b) select and use the expression age of universe ≈ 1/H0;
Outcomes
Be able to state the cosmological principle;
Be able to describe the significance of the 3K microwave background radiation (HSW
1).
Be able to select and use the expression age of universe ≈ 1/H0;
Be able to explain the significance of the 3K microwave background radiation (HSW
1).
Be able to explain that the standard (hot big bang) model of the universe implies a
finite age for the universe (HSW 1, 2, 7);
The cosmological principle
The cosmological principle says that if you looked at the universe in any direction it
would look the same over very large distances. Our view of the Universe is the same
as anybody (anything!) else’s as the density over large distances is constant. i.e. the
Universe is isotropic (the same in all directions) and homogeneous (uniform density).
Cosmic microwave background - the Echo of the Big Bang
The Universe is thought to have begun some 13.7 thousand million years ago
with an enormous explosion that we call the Big Bang. The temperatures at
that time were unimaginably huge but as time passed since the Big Bang the
Universe cooled. The temperature in deep space dropped and dropped. The
background radiation moved into the infrared and the cooling continued.
The photons produced in the Big Bang have
continued ‘cooling’ ever since. The temperature
of deep space has now reached 2.725 K and the
temperature will carry on falling as long as the
universe continues expanding.
In 1948 George Gamow, Ralph Alpher, and
Robert Herman predicted that the ‘remains’ of
this radiation should still be observable even
after such an enormous time.
In 1965 two American astronomers, Arno
Penzias and Robert Wilson were using the antenna at the Bell laboratories in
New Jersey (see photo credit Bell Laboratories) for scanning the sky when
they found that there was a background "noise" (like static in a radio). This
uniform signal was in the microwave range with a wavelength of about 7 cm
and seemed to come from all parts of the sky. Penzias and Wilson tried to get
rid of this annoying background interference. They ejected the pigeons living
in the horn of the antenna and even cleaned out their droppings but still the
signal persisted. (Modern estimates for the peak intensity of this radiation
give a wavelength around 2mm).
By pointing the ‘telescope’ in a variety of directions they concluded that the
interference wasn't radiation from our galaxy or extraterrestrial radio sources
and because it remained constant throughout the year it couldn't have come
from the solar system or even from a 1962 above-ground nuclear test,
because in a year that fallout would have shown a decrease.
Finally they realised that it was not random noise causing the signal but
something that pervaded the whole Universe. This was the cosmic
background radiation with a ‘temperature’ of around 2.7K and was given an
evocative name the ‘echo of the Big Bang’. It is the residual radiation
predicted by Gamov and others and is the result of the Universe cooling from
the unimaginably hot state over the intervening 13000 million years. The
detection of the CMB supports the Big Bang idea of the Universe because the
cooling of the Universe after the Big Bang would suggest an expansion over
many millions of years.
We can detect the radiation produced by this temperature in our homes. It has
been estimated that about 1% of the background hiss on your television set is
due to the after effects of this enormous fireball.
Penzias and Wilson received the 1978 Nobel Prize in Physics for their discovery.
The age of the universe
Since v = H0d
v/d = H0
v=d/t
d/td = H0d
1/t = H0
t = 1/H0
This t is the time it has taken for the galaxies to expand into the space they occupy
now. And since all galaxies seem to be accelerating away from every other galaxy it
follows that if we rewind back to the beginning they would have all started at the
same point.
The best value for the age of the universe is 13+/- 1 billion years. The error comes
from our ability to measure the velocity and position of distant galaxies from their
luminosity and Redshift.
Lesson 59 questions - The Expanding Universe
Name……………………
(
/24)………..%……….
Class……………….
ALL
1.
State the Cosmological Principle.
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
[Total 2 marks]
2.
Describe the important properties of the cosmic microwave background
radiation and how the standard model of the Universe explains these
properties. Explain their significance as evidence for the past evolution of
the Universe.
In your answer, you should make clear how your explanation links with
the evidence.
.....................................................................................................................
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[Total 5 marks]
3.
State Hubble’s law and define any symbols used.
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
[Total 2 marks]
4.
In 1929 Edwin Hubble showed that the Universe was expanding by
studying the light from stars and galaxies. Explain how.
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
[Total 5 marks]
5.
(a)
Suggest why many stars within our galaxy do not conform with
Hubble’s law.
............................................................................................................
............................................................................................................
............................................................................................................
[2]
(b)
Estimate the age of the Universe, giving your answer in seconds.
Show your working and take the Hubble constant to be 75 km s–1
Mpc–1.
age = .............................. s
[3]
[Total 5 marks]
6.
Describe the important properties of the cosmic microwave background
radiation and how the standard model of the Universe explains these
properties. Explain their significance as evidence for the past evolution of
the Universe.
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
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[Total 5 marks]
Lesson 60 notes - BIG BANG – BIG CRUNCH?
Objectives
(c) describe qualitatively the evolution of universe 10-43 s after the big bang to the
present;
(d) explain that the universe may be ‘open’, ‘flat’ or ‘closed’, depending on its density
(HSW 7);
(e) explain that the ultimate fate of the universe depends on its density;
(f) define the term critical density;
(g) select and use the expression for critical density of the universe
ρ = 3 Ho2
8πG
(h) explain that it is currently believed that the density of the universe is close to, and
possibly exactly equal to, the critical density needed for a ‘flat’ cosmology (HSW 7).
Outcomes
Be able to describe qualitatively the evolution of universe 10-43 s after the big bang
to the present;
Be able to explain that the universe may be ‘open’, ‘flat’ or ‘closed’, depending on its
density (HSW 7);
Be able to explain that the ultimate fate of the universe depends on its density;
Be able to define the term critical density;
Be able to select and use the expression for critical density of the universe
ρ = 3 Ho2
8πG
Be able to explain that it is currently believed that the density of the universe is close
to, and possibly exactly equal to, the critical density needed for a ‘flat’ cosmology
(HSW 7).
In the beginning…
It is now generally accepted by most astronomers that the Universe as we know it
began with an unimaginably huge explosion some 14 000 000 000 years (1.4x1010
years). We call this the Big Bang. The age of the universe is therefore 1.4x1010 years.
Time and space both originated at the same time with the Big Bang. Before that there
was no space and no time – the Big Bang ‘created’ space and time. We cannot ask
what happened before the Big Bang because before that moment nothing existed – no
space and no time!
It is interesting to compare time with distance and think of a scale where a distance of
one metre represents a thousand million years. The age of the Universe is then
represented by a distance of around 14m, a million years by 1 mm and one human
lifespan by 0.1m!
The fascination of Cosmology is the ability to ‘look back’ to the beginning of
the Universe and predict what may have happened then.
Moments after the big bang
Time after the Big Bang
10-43 s
10-34 - 1010 s
10-10 s
1s
3m
300 000 years
500 000 years
1 million years
1 billion (109) years
15 billion years
Nature of the Universe
Grand unification epoch
Electroweak epoch
Quark epoch
Particle soup dominates
Neutrons and protons formed
Helium nuclei formed
Microwave background fills the universe
Temperature falls further. Infra red.
Atoms form. Stars and galaxies exist
The universe becomes transparent
The first stars. Heavy elements form.
The present day
Temperature
1015 K
1010 K
109 K
6000 K
750 K
18 K (-255 C)
2.7 K (-270.3
C)
The Big Bang - the beginning of the Universe
As thousands of years passed the Universe cooled from the initial enormous
temperatures of the Big Bang (some 1015 K).
At some time in the past, roughly 500 000 years after the Big Bang the
Universe became dark. The radiation emitted had passed over the barrier
between visible and the infra red. From then there was no light until the
primeval matter had condensed into atoms and these had slowly grouped
together under gravitational attraction to make the embryo of a star.
Eventually the temperature in the centre of these stars had become high
enough for nuclear fusion to take place - the first star was born and blazed out
into the darkness of space - there was light!
The fate of the Universe – closed, flat or open
Radius of
the
Universe
Open Universe – continued expansion
Flat Universe – expansion but slowing
Closed Universe – the Big Crunch
Time since the Big Bang
The fate of the Universe depends on how much matter there is.
Using the Hubble constant H = 70 kms-1 Mpc-1 we have found that the critical
density for the Universe is 9.2x10-27 kgm-3. Now actual measurements
suggest a density if some 4x10-28 kg m-3. This is too low to prevent a run-aw
ay expansion but astronomers believe that a large amount of the mass of the
Universe exists as "dark matter", much of which has so far been undetected.
We define a quantity called  where:
The quantity = Actual average density of matter in the Universe/Critical density of
the Universe The critical density will decide whether the Universe is:
(a) open – a run-away expansion (<1)
(b) flat – an expansion but slowing  = 1)
(c) closed – a final contraction, the Big Crunch (>1)
Critical density of the Universe
The Hubble constant (H) is also important
in predicting the ultimate fate of our
universe, related to the concept of its
critical density.
One galaxy
escaping from all
the rest
The velocity of recession of a galaxy can
be considered as its escape velocity from
the rest of the Universe
By Hubble’s formula:
Velocity of recession (v) = HR where R is the
distance of the galaxy.
But the escape velocity is given by the formula:
Mass of the “rest” of the
Universe (M)
Escape velocity (v) = [2GM/R] so v2 =
2GM/R
where G is the gravitational constant (see Gravitation section)
Therefore:
v2 = 2GM/R = [2G
But from the first equation v2= H2R2 and so:
Critical density = 3H2/8G
[We have assumed both constant v and a constant value of the Hubble constant (H) in
this simplified calculation.]
If the density of the Universe is greater than this the universe will contract, if it is less
it will expand for ever!
Lesson 60 questions
Name…………………………
Class………………..
MOST
1.
(
/38)…………%…………..
Explain why our understanding of the very earliest moments of the
Universe is unreliable.
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[Total 2 marks]
2.
The future of the Universe may be open, closed or flat. Explain the
meaning of the terms in italics, using a graph to illustrate your answer.
‘size measure’
of Universe
age of Universe
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[Total 4 marks]
3.
Some Cosmologists have estimated that as much as 90% of the total
mass of a galaxy is made up of gas, referred to as dark matter.
(i)
Suggest the nature and origin of this gas.
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[2]
(ii)
The precise amount of dark matter in the Universe is unknown.
Explain how the presence of dark matter affects the average
density of the Universe and thus has a role in determining the
ultimate fate of the Universe itself.
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[4]
[Total 6 marks]
4.
Describe and explain two pieces of evidence which suggest that the
Universe did in fact begin with a big bang.
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[Total 5 marks]
5.
The ultimate fate of the Universe is not yet clear. The figure below shows
a graph where the size of the Universe is represented from the big bang
B to the present day P. The graph has been extended into the future by
the dotted line (– – – – –).
size
measure of
Universe
P
B
0
(i)
time
Calculate a value for the age of the Universe in years. Assume the
Hubble constant to be 75 km s–1 Mpc–1.
age = …..……………… years
[3]
(ii)
Describe and explain what final fate for the Universe is represented
in the figure above.
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[2]
(iii) The mass of the Universe may be significantly greater than that
assumed in the first paragraph of this question.
Taking this to be case, sketch a second graph on the figure above
using the same scales to show the future evolution of the Universe.
[2]
(iv) Comment upon the implications of your graph for the future of the
Universe.
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[1]
[Total 8 marks]
6.
Describe how the fate of the Universe depends upon its mean density
and explain why this ultimate fate is not yet known.
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[Total 5 marks]
7.
The future of the Universe may be open, closed or flat. Explain the
meaning of the terms in italics, using a graph to illustrate your answer.
'size measure'
of Universe
age of Universe
.....................................................................................................................
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[Total 4 marks]
8.
Why is our understanding of the very earliest moments of the Universe
unreliable?
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[Total 2 marks]
9.
The mean density of the Universe, 0, is thought to be approximately
1 × 10–26 kg m–3.
Calculate a value for the Hubble constant H0.
H0 = ...........................s–1
[Total 2 marks]