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The nature of the universe

Chapter 18

Looking out at a clear night sky, you might see a

few hundred stars if you were lucky. You might

also see the Moon and, if you knew where to look,

a planet or two. The naked-eye view from the Earth

allows us to see just a tiny fraction of the universe

in which we live.

The universe is all the matter and energy

which we can observe, or which we might in

principle be able to observe. Here, we use theword observe rather than see because there is

much out there that we cannot see with our eyes

or through telescopes cold objects that do not

emit much visible light but emit other forms of

electromagnetic radiation outside the visible part of

the electromagnetic spectrum.

The cosmological principle

Todays telescopes allow us to observe far beyond

our local region of the universe and across the

entire spectrum. Figure 18.1shows a view of distant

galaxies taken by the Hubble Space Telescope.

All observations have to be interpreted. Is that

speck of light in the night sky a star or a planet?

Why does a certain stars position in the sky seem

to wobble very slightly? Does that pattern of stars

really represent an ancient hero called Orion? Someinterpretations are better than others, but every idea

about the nature of the universe must be tested by

further observations.

Fortunately for us, it seems that distant regions

of the universe are not very different from our own

region. The light from distant galaxies is not a

different kind of light; faraway stars seem similar to

those nearby. This makes it easier to understand the

universe as a whole, and so we can hope to develop

ideas about the structure of the universe and how it

has developed.The idea that the universe has the same large-

scale structure when observed from any point

within it is known as the cosmological principle.

This important principle has three facets:

The universe is homogeneous. This means thaton a large scale the universe is the same at all

places its density is the same everywhere.

The universe is isotropic. This means thatthe universe is the same in all directions.

Strong support for this comes from the cosmic

microwave background radiation, which has the

same intensity in all directions (see Chapter 19).

The laws of physics are universal. This meansthat the same tried and tested laws of physics

on the Earth can be applied to other places in

the universe.

Figure 18.1 A view of several distant galaxies,

taken by the Hubble Space Telescope. Many of

these galaxies appear blue because they are young;

blue light is characteristic of stars forming.

continued

e-Learning

Objectives
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Chapter 18: The nature of the universe

262

Most stars live for a very long time millions

or even billions of years. We do not have scientic

records going back that far, so we have to rely on the

fact that we can see vast numbers of stars. We must

assume that those that we see represent stars at all

stages of their lives. This means that we can deduce the

life history of stars from the evidence gathered overthe last century or two. (This is a bit like observing the

population of a town. You would see smaller people

and bigger ones, and it would not take you long to

deduce how people grow up, get older and die.)

The birth, life and death of the Sun

We will start by focusing on the Sun since it is a

fairly ordinary star. Then we will consider how the

life cycles of other stars might differ.

Stars like the Sun form from clouds of interstellar

dust and gas. The main elements are the gaseshydrogen and helium, together with small amounts

of other elements such as iron, silicon and carbon.

This is material that is scattered thinly throughout

the galaxy. Where it is denser, its own gravity causes

material to pull together and contract to form a denser

mass. This has a stronger pull, so that more matter

is pulled in, and so on. This process is known as

gravitational collapse.

Although space is very cold, the interstellar dust

and gas heats up as it collapses. This is because it

is losing gravitational potential energy and gaining

kinetic energy. The particles collide with each other,

sharing out their energy and getting hotter in the

process. In effect, they form a gas whose internal

energy is increasing. (Recall that, in Chapter 7, in the

section Temperature and molecular kinetic energy,

we saw that the internal energy of a gas is directly

proportional to its thermodynamic temperature.)

The life of starsWhat is out there? There are many billions of

galaxies, each a large cluster of billions of stars, held

together by their mutual gravitational attraction. If

there are about 1011stars in the average galaxy and

about 1011galaxies in the universe, that makes a

grand total of about 10

22

stars in the universe. Suchvast numbers are beyond out everyday imaginings.

Spread amongst the galaxies are electromagnetic

radiation, of various sorts, fast-moving particles and

clouds of dust.

Our own galaxy is the Milky Way. Our Sun is just

one star in this galaxy, part way out along one of its

spiral arms (Figure 18.2). The solar system consists

of the Sun together with everything held within its

gravitational eld the eight planets, the minor

planets, natural planetary satellites such as the Moon,

comets, asteroids and so on.

This principle allows us to make observations of

parts of the universe and then extrapolate them to

the whole universe. If this were not the case if

distant regions consisted entirely of clusters of

black holes orbiting under a previously unknown

force we would nd it hard to develop any

general theories of the universe.

In this chapter, you will learn a bit about scientists

current view of the nature of the universe, based on

observations. Then, in Chapter 19, we will look at

ideas about how the universe has evolved and come

to be as it is today, and how it may end up.

Figure 18.2 A spiral galaxy very similar to the

Milky Way.
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to radiation pressure from the photons released by

the star fusion reactions.

The gravitational collapse of the interstellar dust

and gas results in a spinning star with a small fractionof the material (< 1%) orbiting around the star. Again,

gravity is at work, pulling matter together to form

planets, planetary satellites and the other objects that

orbit the star.

At the centre of this collapsing dust and gas cloud,

the material becomes very hot and dense. A star is

forming see Figure 18.3and Figure18.4. When its

temperature is high enough (~10

7

K), fusion reactionsstart, with hydrogen nuclei fusing to form helium

nuclei and nuclei of other light elements. The fusion of

hydrogen into helium is known as hydrogen burning,

representedby the following nuclear equation:

411 H42 He + 2

0+1 e + 2

The chance of four hydrogen nuclei interacting

to produce a helium nucleus is almost zero. The

equation above is really a summary of the proton

proton cycle:

11 H +

11 H

21 H +

0+1 e +

11 H +

21H

32 He +

32 He +

32 He

42 He + 2

11 H

(In these equations, is a gamma-ray photon and

is a neutrino.) The fusion reactions release energy

as mass is converted into energy in accordance with

Einsteins massenergy equation E= mc2. This

increases the temperature of the stellar material even

more rapidly than if the collapse was entirely due to

gravitational forces. Once this happens, the star will

glow for millions or billions of years.

A star reaches a steady temperature when the

power released by fusion reactions is equal to the

power radiated away from the star. The star has

a stable size because of equilibrium between the

attractive gravitational forces and outward forces due

gravitational collapse of

interstellar dust cloud

GPE decreasing, KE increasing

fusion starts

A star is born.temperature increasing

Figure 18.3 Stages in the formation of a star.

Figure 18.4 A computer simulation of star

formation. It is impossible to photograph such an

event as the material is cold and dark, but this image

generated by a computer model shows how it might

look. Several stars are forming from a cloud of

interstellar matter.

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Venus and possibly Earth. Figure 18.6gives an idea

of the relative sizes of a Sun-like star and a red giant.

The core continues to collapse. Its density and

temperature increase. The helium nuclei in the outer

shell reach a temperature of about 108K and start

to fuse together at a phenomenal rate. In a process

known as the helium fash, the material surrounding

the core is ejected away as a planetary nebula

(Figure 18.7). Note that the term planetary nebula

can be misleading it has nothing to do with the

formation of planets as was once thought.

A bright central core is left behind. This remnant is

known as a white dwarf. It gradually cools and dims

over a period of millions of years. Here are some

characteristics of a white dwarf:

No fusion of hydrogen occurs in a white dwarf.It glows because photons produced by fusionreactions in the past are still leaking away from it.

It is very dense. A teaspoon of white dwarfmaterial will have a mass of 5 tonnes.

As the material of the star becomes morecompressed, electrons are no longer attached to

individual atoms but move freely throughout the

star in the state of matter called plasma.

The ageing Sun

The Sun is thought to have existed for about 4.5 billion

years, as has the Earth. It is likely to go on shining

for at least as long again, but eventually its store of

hydrogen fuel will start to run low. The description

below describes the evolution of the Sun or of any star

with a mass less than about 3 solar masses.

As the temperature and pressure of the innermost

parts of a star increase, more complex fusion

reactions can occur and these produce other elements

such as carbon, silicon and iron. Figure 18.5shows

the typical structure of the core of an ageing star.

As the rate of fusion reactions slows down, the

core of the star starts to collapse under gravitational

attraction. The thin shell of helium nuclei surrounding

the core of the star start to fuse to produce beryllium,

carbon and oxygen nuclei. A thin layer of thehydrogen shell surrounding the helium-rich core

becomes sufciently hot to fuse hydrogen nuclei

again. The increased power production from the

helium shell causes the outer shell of the star to

expand due to radiation pressure. The size of the

star increases and its surface temperature drops. It

becomes a red giant. When our Sun becomes a red

giant, it will engulf the closest planets Mercury,

Figure 18.5 The tiny core of an old star shows layers where elements are made by fusion reactions.

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when further collapse would require two or more

electrons to exist in the same quantum state.

The maximum mass of a white dwarf is about1.4 solar masses. This upper limit for the mass of

a white dwarf is known as the Chandrasekhar

limit, named after the Indian-American

astrophysicist Subrahmanyan Chandrasekhar who

rst predicted this in 1930 (Figure 18.8).

More massive stars

A star that is more massive than the Sun (typically,

more than 3 solar masses) behaves differently.

Approaching the end of its life, it swells to become a

super red giant. When it collapses to form a white

dwarf, provided its mass is still more than 1.4 solar

masses, its gravity is strong enough to cause it to

collapse even further. The gravitational pressures

are enormous and overcome the Fermi pressure.

The electrons combine with the protons to produce

neutrons and neutrinos. The neutrinos escape and the

central core of the star is now made entirely of closely

packed neutrons. The outer shells surrounding the

A white dwarf is prevented from further gravitational collapse by electron degeneracypressure (also known as Fermi pressure). This

comes about as follows. There is a law called

Paulis exclusion principle which states that no

two electrons can exist in the same quantum state.

(This is why only two electrons can occupy any

energy level in an atom.) As gravity tries to cause

the star to collapse further, a limit is reached

The Sun today.

hydrogen-burning

shell

helium

core

The Sun as a red giant.

Figure 18.6 The Sun as it is today, and as a red giant

in the future.

Figure 18.7 The Cats Eye nebula lies around 3600

light years from Earth in the constellation Draco.

At the centre, you can see a white dwarf.

Figure 18.8 Subrahmanyan Chandrasekhar

(19101995), Indian-US astrophysicist.

Chandrasekhars main work was in showing that

the fate of a star is dependent on its mass.

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neutron core collapse violently and rebound against

the solid neutron core. This generates a shockwave

which explodes the surface layers of the star as a

supernova. A supernova blasts off heavier elements

like carbon, oxygen, and iron into the galaxy. These

become incorporated into future stellar systems. In

fact, the carbon in our bodies and the oxygen we

breathe originated from explosive supernovae.

Supernova events are rather rare they only occur

about once every 50 years in our galaxy. However,

they are very bright, so bright that for a few days they

can outshine an entire galaxy. A supernova has the

intensity equivalent to about 1011stars. This means

that quite distant supernovae can be readily observed.

What remains of the core of the star depends on

its mass.

For lighter stars, the core is entirely made up of neutrons, as described above. The result is aneutron star, a remnant with an extremely high

density, roughly 1018kg m3.

For even heavier stars, the supernova leaves aneutron star that is so massive that it continues to

collapse inwards under its own gravity to form a

black hole.

A black hole forms when matter collapses almost

to a point (a singularity). The gravitational eld

within a few kilometres of the point is so strong

that not even light can escape from it that is whyit appears black. While we cannot see a black hole,

we can see its effects. For example, some stars seem

to be orbiting around an invisible partner, which is

probably a black hole.

Now look at Worked example 1.

Increasingm

ass

stable star red giant

super red

giant

supernovablack

hole

neutron

star

white

dwarf

star

forming

Mass < 3

solar masses

Mass > 3

solar masses

Figure 18.9 The life-history of a star depends on its mass.

Figure 18.9summarises the possible life-histories

of stars.

The density of a particular neutron star is

2.01017kg m3and it has a mass of 6.0 1030kg.

Calculate the radius of this neutron star.

Step 1 Write down the information given.

density= 2.01017kg m3

mass m = 6.01030kg

Step 2 Use the equation for density to calculate

the volume of the star.

=m

V

V=m

=6.01030

2.01017

= 3.01013m3

Step 3 Now calculate the radius of the star using

V =4

3r3

4

3r3= 3.01013

r=3

33.01013

4 1.9104m

The radius of the neutron star is about 19 km.

Compare this with the radius of our Sun, which is700 000 km.

Worked example 1

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It is useful to remember that the distance to the Sun is

approximately 150 million km.

For measuring distances between stars in our

galaxy, astronomers tend to use light-years(ly),

which is a much bigger distance.

We can easily determine the light-year by multiplying

the speed of light in a vacuum (3.0 108m s1) by

the time of one year in seconds (see SAQ 4). The

distance to the nearest star from the Sun is about

4.2 ly. The radius of the solar system is roughly 2.0 ly.

For measuring distances between stars and

galaxies, astronomers tend to use the parsec

(pc). The parsec is dened from a technique that

astronomers have used to measure the distance to

other stars nearby in our galaxy. These stars showparallax; that is, their apparentposition against the

background of other, more distant stars alters when

they are observed at different times during the year.

This is a consequence of the Earths orbiting around

the Sun. Figure 18.10shows the Earth at opposite

ends of its orbit (E1and E2). If the star 61 Cygni is

observed from these two positions, it is observed to

move through an angle 2p. The anglepis called the

parallaxof the star, and it is such a small angle that it

is measured in seconds of arc.

SAQ

a1 In Figure 18.9, which part shows the life-

history of the Sun?

Explain why the Sun willb

never become a black hole.

a2 When a star forms, what force causes a cloud

of dust and gas to collapse inwards?

State the force that causes planets to formb

around a new star.

State the force that causes a massivec

neutron star to become a

black hole.

3 A neutron star consists of a vast number of

neutrons, closely packed together.

a Use the following data todetermine the density of

a neutron.

mass of neutron = 1.71027kg

radius of neutron = 1.31015m

b A particular neutron star has a mass of

4.01030kg. Using your answer to part a,

estimate the radius of the neutron star.

c The material of a neutron star consists of

spherical neutrons with small gaps between

them. Explain whether this means that your

answer to part bis an underestimate or anoverestimate.

d The mass of the Sun is 2.0 1030kg; its radius

is 7.0108m. Explain why the neutron stars

radius is so different from that

of the Sun.

Measuring the universeIn science, we generally use SI units. However,

because of the vast scale of the universe, other

units have come into use which can give a better

impression of the distances involved. We will look

at three of these units, their denitions, and their

relationships to the metre, the SI unit of distance.

For measuring distances in our solar system, it is

convenient to use the astronomical unit(AU). For

example, the planet Uranus is 19.2 AU from the Sun.

The astronomical unit (AU) is the average

distance of the Earth from the Sun.

1 AU = 1.4961011m 1.51011m

The light-year (ly) is the distance travelled by

light through a vacuum in one year.

1 ly 9.461015m 9.51015m

There are 60 arc seconds in a minute of arc, and

60 arc minutes in a degree. Hence:

1 arc second =1

3600degrees

Answer

Answer

Hint

Answer

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268

The term parsec comes from the wordsparallax

andsecond.

Clearly, stars with smaller values ofpare at greater

distances, so:

distance (pc) =1

parallax (arc seconds)

or

d(pc) =1

p(arc second)

For 61 Cygni,p= 0.3 arc seconds, so its distance

from the Sun is 1/0.3 = 3.3 pc.

From the denition of the parsec, it can be shown

that (as in Worked example 2):

1 pc 3.11016m 3.3 ly

Sun

p

p

E1

E2

2p

61 Cygni

orbit of Earth

distant stars

apparent position

of 61 Cygni from E1

apparent position

of 61 Cygni from E2

1 AU

1 AU

Figure 18.10 Measuring the parallaxpof a nearby star.

Show that a parsec (1 pc) is equal to 3.11016m.

Step 1 For a star at a distance of 1 pc, we can

draw a triangle similar to Figure 18.10. The side

of the triangle opposite to the star has a length of

1 AU see Figure 18.11.

Worked example 2

starSun1 pc

1 arc second

1 AU

Earth

Figure 18.11 This triangle denes the parsec;

note that it is notdrawn to scale the page would

have to be at least 1 km wide.

Step 2 Use the triangle to determine the parsec.

1 AU = 1.4961011m

= 1 arc second = 1/3600 degrees

tan =1 AU

1 pc

1 pc =1 AU

tan=

1.496 1011

tan (1/3600)

3.11016m

continued

The parsec is dened as the distance that gives a

parallax angle of 1 arc second.

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a Copy Table 18.1and complete the last two

columns of the table as follows: Calculate d

in pc using the conversion 1 pc = 3.3 ly; then

calculatepd.

b Explain signicance of the

last column.

Star p/arc

sec

d/ly d/pc pd/pc

arc sec

Altair 0.20 16

Arcturus 0.090 36

Capella 0.073 45

Sirius 0.38 8.7

Vega 0.12 26

Table 18.1 See SAQ 7.

SAQ

4 Given that the speed of light in a vacuum is

c= 299 792 458 m s1and that 1 year = 365.25636

days, show that 1 light-year is

approximately 9.461015m.

5 The nearest star (other than the Sun) is Proxima

Centauri. It has a parallax of 0.76 seconds of arc.

Calculate its distance from Earth:

a in parsecs

b in light-years

c in metres.

6 The Moons average distance from the Earth is

4.0105km. What is this distance

in astronomical units (AU)?

7 The distance d of a star can be determined from its

parallaxp. Table 18.1shows details of some of the

brightest stars in our night sky. The parallaxp is in

arc seconds and the distance dis in light years.

Isaac Newton (16421727) suggested that theuniverse must be innitely large and roughly

uniform in its composition. In other words, the

universe has stars scattered throughout it and it goes

on for ever, in all directions. He thought it must be

innite because he realised that a nite universe

would collapse under the pull of its own gravity. An

innite universe has no centre and so it would not

collapse. (In a nite universe, every star is pulled

towards the centre of gravity of the universe; in an

innite universe, every star is pulled equally in all

directions so that there is no resultant force on it.)

This idea was challenged in 1826 by Heinrich

Olbers. He pictured a universe that was:

inniteuniformstatic.

Static means neither expanding nor contracting.

He had the idea that, if we lived in such a universe,

Olbers paradox

the sky would always be brightly lit, even at night.He argued this by saying that, in no matter what

direction you looked, your line of sight would

eventually reach a star. So every point in the sky

would be lit by a star. Although the most distant stars

are very dim, there must be large numbers of them,

which would compensate for their dimness. The

universe would be full of starlight and the surface of

the Earth would be as hot as the surface of a star.

There is another mathematical argument which

also suggests that the night sky ought to be bright.

In an innite universe with an innite number

of stars:

the number of stars increases with the squareof the distance. (Imagine a sphere of radius r

sprinkled with stars. The number of stars in this

shell will be proportional to the surface area of

the shell; that is 4r2.)

continued

Answer

Answer

Answer

Answer

Extension

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270

The expanding universeEdwin Hubble (Figure 18.12) was an American

astronomer working in the early decades of the

twentieth century. This was a time when big

telescopes were being constructed, which allowed

many thousands of distant and dim galaxies to be

observed. Hubble photographed many galaxies and

made a catalogue of them, classifying them according

to their different shapes. He also became expert in

measuring the distances to galaxies.

These modern telescopes were tted with

spectrometers which made it possible to record the

spectra of light from individual stars or galaxies.

The lines in the spectra can be interpreted to identify

the elements present in the star. (Every atom of a

particular element produces a line spectrum and the

wavelengths of the lines are characteristic of the

element; see Chapter 20 inPhysics 1.)

Another American, Vesto Slipher, had noticed an

interesting phenomenon when he looked at the spectraof other galaxies. Although they showed the same

patternof lines (indicating that the same elements

were present as in our own galaxy), the lines were

slightly out of position. The entire spectrum was

shifted, either towards the red end of the spectrum

or towards the blue end. For most galaxies, the lines

were shifted towards the red end of the spectrum. In

other words, their wavelengths were slightly increased

by an amount called the redshift. Figure 18.13shows

spectra for four galaxies with increasing redshifts.

You can see that each line in the spectrum has been

progressively shifted to longer wavelengths and that

the effect is greater for some galaxies than for others.

Slipher explained these redshifts in terms of the

Doppler effect (see Chapter 17). Electromagnetic

waves (such as light) emitted by a source that is

moving away from the observer are stretched out,

increasing their wavelength fromto+ see

Figure 18.14. The faster the source is receding, the

the intensity of light from these stars decreasesaccording to the inverse square with distance.

These two effects cancel each other and hence the

night sky ought to be bright!

Because we know that the sky at night is dark,

Olbers said that at least one of his assumptions

about the universe must be incorrect. It must be

nite or non-uniform or expanding/contracting, or

some combination of these.

This is Olbers paradox:

Olbers paradox is an example of how big

conclusions (in this case, about the nature of the

universe) can be drawn from simple observations.

Before Olbers, everyone knew that the night sky is

dark, but no-one had realised what that observation

can tell us about the nature of the universe.

In the next section, we will look at evidence that

was gathered in the early twentieth century which

helped to give an answers to Olbers paradox.

For an innite, uniform and static universe,

the night sky should be bright because of light

received in all directions from stars.

Figure 18.12 Edwin Hubble in front of the 2.5 m

telescope at Mount Wilson Observatory. He

was the rst astronomer to measure the distance

to another galaxy, conrming the existence of

galaxies beyond our own.
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Hubbles law

Hubbles great achievement was to combine his

measurements of the distances of the galaxies with

measurements of their speeds of recession, deduced

from their redshifts. He plotted a graph showing the

recessional speed vof each galaxy against its distance

xfrom us. A more up-to-date version of this is shown

in Figure 18.15. The pattern is clear. The greater

the distancexto a galaxy, the greater its speed of

recession v:

speed of recession of galaxy distance of galaxy

vx

This relationship is known as Hubbles law. We can

write it as an equation:

v=H0x

greater the redshift. The speed of recession vof a

galaxy (or other source) can be deduced from the

fractional change in wavelength. We can show that:

=

v

c

where cis the speed of light. Note that this only tells

us the component of the galaxys velocity along the

line joining the galaxy to the observer, i.e. directly

away from or towards the observer. The galaxy may

have another component of velocity at right angles

to this, across the observers eld of view. The

equation above is known as the Doppler equation

and can only be applied to a galaxy travelling slowly

compared with the speed of light (that is, v c).

Sliphers measurements made it possible to calculate

the speed of recession of galaxies beyond our own,and the technique was also applied to determine the

motion of individual stars in our own galaxy. (A few

galaxies were found to have blueshifts; characteristic

wavelengths in their spectra were found to be

shortened, indicating that they are moving towards us.)

galaxy A

galaxy B

galaxy C

galaxy D

H+K

Source emits 1 complete wave in time .a

As it does so, the source moves distance

v .

v

b

So the wavelength is stretched by v .

+ (v )

c

c

c

c

c

c

The change in wavelength is = .v

c

Figure 18.13 Redshifts in the spectra from distant

galaxies. The upper and lower traces are reference

spectra, for comparison. The arrows indicate

how a pair of lines (H + K) are redshifted by

different amounts.

Figure 18.14 Explaining the Doppler origin of the

redshift. The wavelength increases by an amount

equal to the distance moved by the source as it emits

one wave.

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strip of universe has expanded. An observer at A will

conclude that all the other galaxies have moved away

from him, with the distance to H having increased the

most. At the same time, an observer at H will conclude

that all of the galaxies are moving away from him.

Equally, an observer at D will see galaxies AC

moving away to the left and EH moving away to the

right. For each observer, all galaxies are receding and

the further the galaxy, the faster it is receding.

This is an example of the cosmological principle

(seepage 261). Each observer will observe the sameeffect. There is no special place in the universe from

which you could observe anything different.

SAQ

A distant galaxy has a redshift8

of 0.085. Calculate its

speed of recession.

9 A green line in the spectrum of

calcium has a wavelength of

527.0 nm when measured in a (stationary) laboratory

on Earth. In the spectrum of a distant star, its

wavelength is found to be 526.3 nm. State what

you can deduce about the motion of the star.

Support your answer with a

numerical value.

where the constant of proportionalityH0is known as

the Hubble constant. The measured value ofH0is:

H0 70 km s1Mpc1

This shows that a galaxy that is 1 megaparsec (Mpc)

distant from the Earth will have a speed

of recession of 70 km s1; at 2 Mpc, vwill be

270 = 140 km s1, and so on.

The implication of Hubbles law is that the

universe is expanding; the galaxies are moving away

from each other.

Interpreting Hubbles law

At rst sight, it might appear that Hubble had shown

that all the galaxies are moving away from the Earth,

and that this means that we are at the centre of

the universe. However, we are not so special!

Figure 18.16shows why.

We picture galaxies AH, equally spaced in an

expanding universe. After a time interval t, the whole

0 100 200x/Mpc

0

2000

4000

6000

8000

10 000

12 000

14 000

16 000

v/km s1

Time = t

At the start ...

Some time later ...

Points distance d apart

Time = t + t

Points distance d + dapart

Figure 18.15 Hubbles law graph, using modern

values of measurements of recessional speed vand

distancex. The gradient of the graph is equal to the

Hubble constant.

Figure 18.16 The fabric of space is represented by

the strip and the galaxies by the dots. An expanding

universe carries all galaxies apart from each other.

Hint

Answer

Hint

Answer

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The age of the universe

Now that we haveH0in SI units, we can deduce the

age of the universe:

age of universe 1

H0

age of universe =1

2.261018 4.431017s

Since there are roughly 3.16107s in one year,

we have:

age of universe 4.431017

3.16107 14109years

So we conclude that the universe is roughly 14

billion years old. Remember that this is based on the

assumption that the universe has been expanding

at a steady rate over this time. It also depends onthe accuracy of the various measurements which

contribute to the Hubbles law graph.

Because nothing can move faster than the speed of

light, it follows that we can only observe the universe

up to a distance of 14 billion light years from us. This

gives us an upper limit on the observable size of the

universe.

Efforts have been made over the last 50 years to

rene these measurements and to nd other ways of

approaching the question. You can check using the

internet to see the current range of possible valuesforH0and the implications these have for the age

of the universe.

Now we can re-visit Olbers paradox and

reconsider the model of the universe which he started

from. The Big Bang model (also known as the

standard model) of an expanding universe suggests:

The universe is not static it is expanding.The universe is (probably) not innite.The nite age of the universe and the nite speedof light means that light from the most distant

galaxies has yet to reach us.

As distant galaxies recede, their light is red-shifted. This means that it is less energetic and

so dimmer.

In this chapter, we have considered only some of the

experimental evidence for the idea that the universe is

expanding following a Big Bang. In Chapter 19, we

will look at the nature of the Big Bang and how the

universe may change in the future.

The birth of the universeHubbles law implies that, at present, the universe

is expanding. What does this suggest about the past

history of the universe? The fact that vxsuggests

that, at some time in the past, all of the galaxies

must have been concentrated together in a very

small space.

You can picture this as a movie of the history of the

universe. As we watch today, the galaxies are moving

further and further apart. Run the lm backwards and

they move closer and closer together.

Hubbles graph was the rst evidence that the

universe might have started from a Big Bang. The

universe is believed to have originated from a very hot

explosion from which space and time evolved. Since

the Big Bang, all the galaxies have been moving apart.

The gradient of the Hubbles law graph can tell usabout how long ago this event happened. If the gradient

is steep (H0large), it suggests that galaxies are moving

fast and that the universe must therefore be relatively

young. If the gradient is less steep (H0small), the

universe must be older. If the rate of expansion of the

universe has been constant, we can conclude that:

age of universe 1

Hubble constant

1

H0

Changing units

To use this relationship to estimate the age of the

universe, we need to convertH0to SI units. Distances

to galaxies are large so they are often given in mega-

parsecs or light-years rather than metres. However, it

is useful to be able to convert these to metres.

Since 1 pc 3.11016m, we have

1 Mpc 3.11022m.

Now we can convert the units of the Hubble

constant to SI units; note that we have to include a

factor of 103to change km s1to m s1.

70 km s1Mpc1=70103m s1

3.11022m

= 2.261018s1 2.31018s1

The units reduce to s1. (This should not be written as

Hz, as it is not a frequency.)
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274

11 Figure 18.15is a Hubbles law graph, plotted using

recently obtained data. Use it to

estimate the age of the universe.

SAQ

10 One experiment to estimate the Hubble constant

gives a value of 78 km s1Mpc1.

a Determine a value for the Hubble constant in

s1. (1 pc = 3.11016m.)

b Estimate the age of the universe

both in seconds and in years.

Summary

The cosmological principle suggests that the universe is uniform; there are no special places in theuniverse. This principle is based on a universe that is homogeneous and isotropic and in which the laws of

physics are universal.

The universe contains matter in the form of stars, clustered into galaxies, and electromagnetic radiation.The solar system consists of the Sun and all the objects (planets, comets, etc.) held in its gravitational eld.Stars form when clouds of interstellar gas and dust contract under the pull of their own gravity.The Sun will evolve to become a red giant and then a planetary nebula and a white dwarf. A moremassive star will become a super red giant and then a supernova and either a neutron star or a black hole,

depending on its initial mass.

Astronomical distances may be measured in astronomical units (AU), light-years (ly) or parsecs (pc).1 AU 1.51011m 1 ly 9.51015m 1 pc 3.11016m

Olbers paradox: For an innite, uniform and static universe, the night sky should be bright because of

light received in all directions from stars. (The paradox is resolved because the universe is neither staticnor innite.)

Redshift is related to speed of recession by the Doppler equation:

=

v

c

Hubbles law: speed of recession of a galaxy distance of galaxy. An equation for Hubbles law is:v=H0x

The age of the universe is related to the Hubble constant

H0by the equation:

age 1

H0

The SI unit for the Hubble constant is s 1.

Answer

Answer

Glossary

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Questions

a1 Explain why a star like the Sun does not collapse as a result of its own

gravitational eld. [2]

Describe some of the characteristics of a red giant and suggest why it emitsb

greater power than a star like the Sun. [4]

Describe the evolution of a star that is much more massive than our Sun. [5]c

Explain why a white dwarf is technically not a star. [2]d

[Total 13]

2 The graphs below show the variation of intensity with wavelength for part of the

Suns spectrum and for the same part of the spectrum from a distant star.

119

Intensity

(Sun)

120 121

Wavelength/nm

119

Intensity

(Star)

120 121

Wavelength/nm

Explain how the stars motion causes corresponding minima of intensity toa

occur at different wavelengths. [2]

Use the graphs to calculate the velocity of the star. [4]b

OCR Physics A2 (2825/01) January 2006 [Total 6]

a3 Explain briey how the composition of a star is determined. [2]

b The distances to nearby stars may be determined byparallax, and are often

quoted inparsecs.

Explain the meaning of the termi parallax. [2] Explain how theii parsecis dened. A diagram may be helpful. [2]

OCR Physics A2 (2825/01) June 2003 [Total 6]

continued

Answer

Answer

Answer

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a4 Explain how Olbers paradox and the work of Hubble on the motions of galaxies

provide evidence for a nite universe. [6]

The Hubble constantb H0is given by the equation:

H0=v

r

where v is the speed of recession of a galaxy and ris the distance from theobserver to the galaxy.

Some observations indicate a value for the Hubble constanti H0= 70 km s1Mpc1.

Convert this value into s1. [3]

Hence estimate the age of the universe. [1]ii

Use your answer toiii iito estimate the maximum observable size for

the universe. [2]

State an assumption you have made in answeringc b. [1]

OCR Physics A2 (2825/01) January 2004 [Total 13]

a5 What is meant bystellar parallax? [2]

The rst recorded stellar parallax had a value of 0.314 arc seconds.b

Calculate the distance of the star from Earth, giving your answer in parsecs. [2]i

What is this distance in metres? [1]ii

OCR Physics A2 (2825/01) June 2007 [Total 5]

Hint

Answer

Answer

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