Higher Physics Our Dynamic Universe Notes... · Newton’s Law of Universal Gravitation Gravitation...

Higher Physics

Our Dynamic Universe

Notes

Name_______ Class__

Previous Knowledge

Gravitation 2

This section builds on the knowledge from the following key areas from

Dynamics and Space Booklet 2 - Forces

Newton’s Laws

Learning Outcomes At the end of this section you should be able to :

o State Newton’s Universal Law of Gravitation

o Use Newton’s Universal Law of Gravitation to calculate the force

between two masses separated by a distance, r

o Compare the gravitational force between objects on different

scales

o Everyday objects

o Planets

o On a subatomic level

o Explain how the slingshot effect is used to travel in space

o Describe lunar and planetary orbits.

Gravitational Field

Gravitation 3

A gravitational field is a place where there is a force on a mass.

The gravitational field strength ‘g’ is defined as the force per unit mass.

We often call the gravitational force acting on an object its weight.

W = mg

We can calculate that the value for ‘g’ is different in different places.

Place Gravitational Field Strength (Nkg-1)

Earth 9.8

Moon 1.6

Mars 4

Jupiter 25

The force of gravity pulls objects towards the centre of the planet. It

has an effect over a large distance. The Moon orbits Earth due to the

force of gravity acting on it.

Newton formulated a law of universal gravitation. His theory was that the

force of gravitational attraction is dependent on the masses of both

objects and is inversely proportional to the square of the distance that

separates them.

We experience the force due to gravity because of the mass of the

planet.

W = weight (Newton – N)

m = mass (kilogramme – kg)

g = gravitational field strength (Nkg-1)

weight

Newton’s Law of Universal Gravitation

Gravitation 4

F = G m1m2

r2

1. Force between everyday objects

F= Force of attraction (N)

G= Gravitational constant (Nm2kg-2)

m1= mass of object 1 (kg)

m2= mass of object 2 (kg)

r = distance between objects (m)

Gravitational constant = 6.67 x 10-11 Nm2kg-2 (in data sheet)

Example 1

Calculate the force between an apple of mass 0.1kg and an orange of

mass 0.15kg, sitting on a worktop, separated by 0.2m.

F = G m1m2 = 6.67 x 10-11 x 0.1 x 0.15 = 2.5 x 10-11 N

r2 0.22

Calculate the force due to the Earth on the apple

Mass of Earth – 5.97 x 1024 kg

Radius of Earth – 6.38 x 106 m

F = G m1m2 = 6.67 x 10-11 x 0.1 x 5.97 x 1024

r2 (6.38 x 106) 2

= 0.978 N

W = mg = 0.1 x 9.8 = 0.98 N

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pic

0.2 m


Gravitation 5

2. Subatomic Scale

3. Force of attraction on a planetary scale

Example 2

Calculate the force of attraction due to gravitation between a proton

and a neutron.

Mass of a proton = 1.67 x 10-27 kg

Mass of a neutron = 1.67 x 10-27 kg

Radius of proton : radius of neutron = 0.84 x 10-15m

F = G m1m2 = 6.67 x 10-11 x 1.67 x 10-27 x 1.67 x 10-27

r2 (0.84 x 10-15) 2

= 2.64 x 10-34 N

Example 3

A satellite orbits a planet at a distance of 5.0 x 107 m from the centre

of the planet.

The mass of the satellite is 3.5 x 104 kg.

The mass of the planet is 6 x 1024 kg.

a) Calculate the gravitational force acting on the satellite due to

the planet is

(2013 SQA Revised Higher Q4 adapted)

F = G m1m2 = 6.67 x 10-11 x 3.5 x 104 x 6 x 1024

r2 (5.0 x 107) 2

= 5.6 x 103 N

b) The radius is now doubled. What effect does this have on the

force observed on the planet?

It is quartered because the force is proportional to 1/r2


Gravitation 6 ODU Problem booklet 2

P2 Q 1 - 6

Example 4

Two small asteroids are 12 m apart.

The masses of the asteroids are 2.0 x 103kg and 0.050 x 10 3 kg. The

gravitational force acting between the asteroids is

F = G m1m2 = 6.67 x 10-11 x 2.0 x 103 x 0.050 x 10 3

r2 12 2

= 4.6 x 10-8 N

Example 5

What is the gravitational pull of a 5 kg mass on a 3 kg mass when their

centres are 0.15 m apart? What is the force of the 3 kg mass on the

5 kg mass?

F = G m1m2 = 6.67 x 10-11 x 3 x 5

r2 0.152

= 4.4 x 10-8 N

The force of the 3 kg mass on the 5 kg mass is the same magnitude

(4.4 x 10-8 N) but in the opposite direction.

SQP Q4 adapted

Example 6

One of the boys in a physics class turns to the girl sitting next to him

and says ‘I feel a force of attraction towards you’. Explain, in terms of

physics, whether or not he is correct, calculating a value for the force.

Estimate the mass of the pupils to be 50 and 65kg, with a distance of

30cm between them.

F = G m1m2 = 6.67 x 10-11 x 50 x 65

r2 0.302

= 2.4 x 10-6 N

Although it is a force of attraction it would be too small to feel the

effect of. Possibly biology rather than physics?

Special Relativity

Special Relativity 7

Learning Outcomes o Describe the motion of an object in terms of an observer’s frame

of reference.

o State that the speed of light in a vacuum is the same for all

observers in all reference frames.

o Explain how the constancy of the speed of light led Einstein to

derive his theory of Special Relativity.

o Use the time dilation and length contraction equations to analyse

real and observed times and lengths.

o Explain that relativistic effects are only observed when objects

are moving with velocities close to the speed of light.

o Describe examples which illustrate Einsteins postulates

o Explain an example of time dilation

o Use the equation for time dilation to calculate the new time

o Explain an example of length contraction

o Use the equation for length contraction to calculate the new length

o Use relativistic effects to explain the observation that more

muons are found at sea level than expected

o Carry out calculations to calculate the half life of muons when

travelling close to the speed of light

o Carry out calculations to find the length contraction for muons

o Explain situations using special relativity

o Twin’s Paradox

o Muons

o Ladder

o Light

Frames of Reference


How you describe the motion of an object depends on how you observe it.

1. Two buses travelling at 60 miles per hour in opposite directions.

If you were sitting next to the window of a bus how would the following

observers describe your motion?

Observer Location Observation

1 Sitting next to you on

the bus

You are stationary

2 A person standing on the

pavement as the bus

passes.

You are travelling to the

right at 60 miles per hour.

3 A person sitting beside

the window on the bus

travelling to the left at

60 miles per hour


right at 120 miles per hour.

All of these are possible.

2.Two spacecraft travelling at 2 x 108 ms-1 in opposite directions.

Observer Location Observation

1 Sitting next to you on

the spacecraft

You are stationary

2 A person standing on the

pavement as the

spacecraft passes.


right at 2 x 108 ms-1

3 A person sitting beside

the window on the

spacecraft travelling to

the left at 2 x 108 ms-1


right at 4 x 108 ms-1.

Observations 1 and 2 are possible, but observation 3 is not because you

cannot exceed the speed of light.

Einstein’s Postulates

Special Relativity 9 ODU Problem booklet 2

P3 Q 1 - 11

1. When two observers are moving at constant speeds relative to one

another, they will observe the same laws of physics

2. The speed of light (in a vacuum) is the same for all observers,

regardless of their motion relative to the light source.

Speed = distance

time

Since speed is constant, then either distance or time must alter.

Special relativity describes the behaviour of objects travelling at

very high speeds. It is ‘special’ relativity because it is the ‘special’

case where the motion between observers is uniform

Time Dilation


The observer on the platform sees the ball travel much further than an

observer inside the train – but this all takes place over the same time

interval.

Thought Experiment 1

The experiment is repeated on a spaceship travelling at velocity v. A

beam of light detected by a photodiode replaces the ball. The path taken

by the light can be represented by the following diagram.

A ball is fired from the

floor of a railway carriage,

hits the roof, then falls

back to the ground again.

1 2

1

3 4

1

5

1

6

1

7

1

An observer standing on the platform films the train pass, then plays

back the film frame by frame. The position of the ball is shown in the

frames below.

Y

X Z

2d ½ ct’

X

Y

Z X, Z

Y

½ vt ½ vt ½ vt

½ ct’

Time Dilation


P5 Q 1 - 9

On the left is the path seen by the person on the train. On the right is

the path seen by the observer on the platform watching the train pass.

t = time measured on the platform by the observer on the

platform

t’ = time measured on the train by the observer on the train

v = speed the object is moving at (ms-1)

c = speed of light (ms-1)

t = 2d (for the observer on the train)

c

The horizontal distance travelled by the train = vt’.

By forming a right angled triangle the following relationship can be

calculated.

(½ ct’)2 = (½ ct)2 + (½ vt’)2

(ct’)2 = (ct)2 + (vt’)2

c2t’2 = c2t2 + v2t’2

(c2 –v2)t’2 = c2t2

(1 – v2/c2)t’2 = t2 (dividing both sides by c2)

t’ =

Example 7

A rocket is travelling at a constant 2.7 x 108 ms-1 compared to an

observer on Earth. The pilot measures the journey as taking 240

minutes. How long did the journey take when measured from Earth?

t = 240 minutes

v = 2.7 x 108 ms-1

c = 3 x 108 ms-1

t’ = ?

t’ =

t’ = 550 minutes

Length Contraction


P7 Q 1 - 9

Thought Experiment 2

Length contraction is only observed when objects travel at a

speed close to the speed of light and in a direction parallel to the

direction in which the observed body is travelling.

l = length measured on the platform by the observer

l’ = length measured on the train by the observer

v = speed the object is moving at (ms-1)


l’ = l

For the observer on

the train the ball goes

from one end of the

train to the other and

back

To the observer on the

platform the ball travels to

the end of the carriage, but it

has moved forwards, so the

total distance travelled is less.

1 2

Example 8

A rocket has a length of 10m when at rest on the Earth. An observer

on Earth watches the rocket passing at a constant speed of

1.5 x 108ms-1. Calculate the length of the rocket as measured by the

observer.

l = 10m

v = 1.5 x 108 ms-1 = 0.5c

c = 3 x 108 ms-1

t’ = ?

= l

= 10

l’ = 8.7m

Lorentz Factor (γ)


The Lorentz factor takes into account the speed of the object.

γ =

This allows us to re-write both the time dilation equation and the length

contraction equation as shown below.

t’ = t γ =

For small speeds (less than 0.1c) the Lorentz factor is approximately 1

and relativistic effects are negligibly small.

Thought Experiment 3 – The Twins Paradox

One twin stays at home, the other goes on a journey through space

travelling close to the speed of light. What happens?

Time runs more slowly for the twin who goes into space, so when they

return they should be younger than their twin who stayed at home.

However – space travel requires acceleration. This can only be dealt with

using General Relativity, which is beyond this course.

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Speed (multiples of c)

Muons


Muons are created in the upper atmosphere. The half life of the muon is

1.56 x 10-6 s and they travel at a speed of 0.98c. If a million muons start

off at a height of 10km we should find very few muons at sea level,

however substantial numbers are detected – what is the reason?

Time dilation Length Contraction

We see many more muons than we would expect because, travelling at

0.98c, they experience relativistic effects. From the muon’s

perspective the 10km is 2km because of length contraction.

Alternatively the half life of 1.56 μs is increased to 7.84 μs due to

time dilation.

Either of these situations has the effect of allowing more muons to

reach sea level.

1,000,000 muons

?

muons

Time from muon’s perspective

1.56 x 10-6 s

Length from muon’s perspective

l’ = l

= 10

= 2 km

Length from our perspective

10 km

Time from our perspective

Non-relativistic calculation

t = distance = 10,000

speed (0.98 x 3 x 108)

=3.5 x 10-5 s

This is equivalent to 21.8 half

lives, meaning we would expect

only 0.3 muons at ground level.

t’ =

= 7.84 x 10-6 s

This is equivalent to approx. 4

half lives, which predicts that

roughly 50,000 muons would be

observed.

t = distance = 2,000

speed (0.98 x 3 x 108)

=6.8 x 10-6 s

Again this is equivalent to

approx. 4 half lives, predicting

50,000 muons at ground level.

Muons


P9 Q 1 - 9

Summary

Property Speed Measured by

observer on

spaceship

Measured by

observer on

planet

Length – L Rest L L

Close to c L Less than L

Time – T Rest T T

Close to c T Greater than T

Example 9

Muons are sub-atomic particles produced when cosmic rays enter the

atmosphere about 15km above the surface of the Earth. Muons have

a mean lifetime of 2.2 x 10-6 s in their frame of reference. Muons

are travelling at 0.999c relative to an observer on Earth.

a) Show that the mean distance travelled by the muons in their

frame of reference is 660m

b) Calculate the mean lifetime of the muons as measured by the

observer on Earth

c) Explain why a greater number of muons are detected on the

surface of the Earth than would be expected if relativistic

effects were not taken into account.

a) d = vt = (3 x 108 x 0.999) x 2.2 x 10-6 = 660m

b) t’ =

= 4.9 x 10-5s

c) For an observer on Earth’s frame of reference the mean

life of the muon is much greater

OR

The distance in the muon frame of reference is shorter.

SQA SQP Q4 (adapted)

The Expanding Universe

The Expanding Universe 16

This section builds on the knowledge from the following key areas from

Dynamics and Space Book 3 – Space

Cosmology

Learning Outcomes At the end of the section you should be able to

o Describe the Doppler Effect in terms of the changing frequencies

of sound and light for moving objects

o Use the Doppler Effect equation for calculations involving the

sound emitted by moving objects

o Understand that light from distant galaxies is red-shifted because

they are moving away from the Earth

o Carry out calculations involving the red-shift and the recession

velocity of a distant galaxy

o State that the Doppler Effect equations used for sound cannot be

used with light from fast moving galaxies because relativistic

effects need to be taken into account

o State that, for slow moving galaxies, redshift is the ratio of the

velocity of the galaxy to the velocity of light.

o Explain Hubble’s Law as the relationship between the recession

velocity of a galaxy and its distance from the observer

o Use Hubble’s Law in calculations involving recession velocity and

distance from observer

o Understand how Hubble’s Law can be used to estimate the age of

the universe.

o Describe evidence for the expansion of the universe

o Describe that the orbital speed of the Sun and other stars gives a

way of determining the mass of our galaxy

o Define the term ‘dark matter’.

o Explain the evidence for dark matter in terms of measurements of

the mass of our galaxy and others.

o Define the term ‘dark energy’.

Explain the evidence for dark energy in terms of measurements of the

expansion rate of the Universe and the concept of something that

overcomes the force of gravity.

The Expanding Universe


o Explain that the temperature of a stellar object is related to the

distribution of wavelengths of emitted radiation

o Describe that the peak wavelength emitted is related to the

temperature of the object – the greater the temperature, the

shorter the wavelength.

o Understand the qualitative relationship between the temperature

of a star and the intensity of radiation – the greater the

temperature, the greater the intensity of radiation.

o Understand what is meant by the cosmic microwave background and

how this relates to the peak wavelength of the radiation

o Provide evidence to justify the model of the Big Bang for the

beginning and evolution of the universe.

Doppler Effect


The Doppler Effect is the change in pitch observed as something making

a sound moves towards you, passes you and then travels away from you.

Stationary Source

A stationary source of sound producing waves at a

constant frequency will have wavefronts travelling in

all directions from the source .

All observers will hear the same sound, which is

equal to the actual frequency of the source, f.

Moving Source

If the source is moving to the right at a speed, v, wavefronts are

produced at the same rate as before, but each time a new wavefront is

produced the source has moved some distance to the right. This causes

the wavefronts on the left to be created further apart and the

wavefronts on the right to be created closer together.

NOTE – The frequency of the

source remains constant – it is the

observed frequency that changes.

This is why sounds seem to be higher

before something reaches you, then

lower when it has passed. You only hear

the true frequency when it is opposite

you.

This is used to check the speed of motorists and to measure blood

pressure by detecting the speed of blood flow in the body.

Shorter wavelength

Higher frequency

Longer wavelength

Lower frequency

Doppler Effect

The Expanding Universe 19 ODU Problem booklet 2

P11 Q 1 - 18

Example 11

A source of sound waves of

frequency 50 Hz is travelling

away from an observer at 10 ms-1.

Calculate the frequency heard by

the observer.

Example 10

A source of sound waves of

frequency 10 Hz is travelling

towards an observer at 40 ms-1.

Calculate the frequency heard

by the observer.

Where fo = frequency heard by the observer (Hz)

fs = frequency of the source of the sound (Hz)

v = velocity of the sound waves (ms-1)

vs = velocity of the source (ms-1)

Moving away from Observer

Frequency decreases

Moving towards Observer

Frequency increases

fo = fs

fo = fs

fo = fs

= 10

= 11.3

= 11 Hz

fo = fs

= 50

= 48.6

= 49 Hz

Example 12

The siren on a fire engine is emitting sound with a constant frequency

of 1000Hz. The fire engine is travelling at a constant speed of 20 ms-1

as it approaches and passes a stationary observer. The speed of sound

in air is 340 ms-1.

Which row in the table shows the frequency of the sound heard by the

observer as the ambulance approaches and as it moves away from the

observer? Frequency as fire engine

approaches (Hz)

Frequency as fire engine

moves away (Hz)

A 1000 1000

B 1063 944

C 944 1000

D 1063 1000

E 944 1063

SQA SQP Q6 adapted

B

Red Shift


P14 Q 19 - 20

The Doppler Effect affects light as well as sound. Astronomers have

observed that the characteristic line spectra for different elements

appeared to expand and are shifted towards the longer wavelengths at

the red end of the spectrum. This is known as Red Shift. It also suggests

that the universe is expanding.

If light is travelling towards an observer the wavelength would appear to

contract and move towards the ‘blue’ end of the spectrum – hence Blue

Shift.

Redshift is more often observed as a spectral tracing as shown in this

diagram

Changes in the frequency is also observed as a change in the wavelength

(remember that v = fλ) This can be observed in both stars and galaxies.

Redshift (z) can be calculated using the equation

Where z = red shift (no units)

Δλ = λobserved – λsource

λobserved = wavelength measured by the observer (Hz)

λsource = wavelength measured at source (Hz)

vg = velocity of galaxy (ms-1)


Line spectrum at rest

Moving towards observer – blueshift λo<λs

Moving away from observer – redshift λo>λs

z = λobserved – λsource = Δλ = vg remember z has no units

λsource λ c

Re

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ift

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From:

http://www.faculty.umb.edu/gary_zabel/

Courses/Parallel%20Universes/Texts/Re

mote%20Sensing%20Tutorial%20Page%2

0A-9.htm (12th June 2014)

Wavelength (nm)

Redshift spectral tracing

http://www.faculty.umb.edu/gary_zabel/Courses/Parallel%20Universes/Texts/Remote%20Sensing%20Tutorial%20Page%20A-9.htm




Red Shift


P14 Q 19 - 20

Earth

Sun

Nearby

star Distant

stars

Parallax angle

Measuring Distances in Space

1. Parallax Distant objects appear to be located at a different angle relative to near

objects depending on where you position when you make the observation. This is

called parallax. This is used to calculate astronomical distances.

One Parsec (pc)

The distance to a star that subtends an angle of 1 second at an arc of length 1

astronomical unit (the distance from Earth to the Sun)

2. Comparison of absolute to apparent luminosity

Cephid variable stars have a predictable variation of luminosity (the amount of

electromagnetic energy radiated per second). The absolute luminosity is

converted to apparent luminosity, which can then be used to calculate the

distance using the inverse square law

Example 13

An astronomer observes the spectrum of light from a star. The

spectrum contains the emission lines for hydrogen.

The astronomer compares this spectrum with the spectrum from a

hydrogen lamp. The line, which has a wavelength of 656 nm, from the

lamp is found to be shifted to 663 nm in the spectrum from the star.

The redshift of the light from the star is

z = λobserved – λsource = 663 – 656 = 0.011

λsource 656

Hubble’s Law


P15 Q 1 - 13

Edwin Hubble noticed that the light from some distant galaxies was red

shifted. By examining the redshift of galaxies at different distances

from Earth he realised that the further away a galaxy was the faster it

was travelling.

v = H0 d

Distance (Mpc) 0

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The graph shows

the relationship

between the

velocity of a galaxy,

as it recedes from

us, and its distance

(Hubble’s Law).

v = recession velocity

H0 = Hubble constant

d = distance to galaxy

Current estimate for

H0 = 2.34 x 10-18 s-1

Example 14

An observatory collects information from a distant star which

indicates that a redshift has taken place. The wavelength of the light

from the source is 656 nm, while the wavelength of the observed light

is 676 nm.

(a) Calculate the recessional velocity of the star.

(b) If the recessional velocity of a distant galaxy is

1.2 x 107 ms-1, show that the approximate distance

to this galaxy is 5.2 x 1024 m. (SQA SQP Q6 adapted)

(a) z = λobserved – λsource = 676 – 656 = 0.03

λsource 656

z = v v = zc = 0.03 x 3 x 108 = 9 x 106 ms-1

c

(b) v = H0 d d = 1.2 x 107 = 5.2 x 1024 m

2.3 x 10-18

Estimating the Age of the Universe


Hubble’s Law can be rearranged to give an estimate for the age of the

universe.

Since H0 = v and time = d so time = 1

d v H0

Hubble’s Law suggests that galaxies further away from us are moving

away faster than galaxies closer to us, which suggests that the universe

is expanding.

Model of the Expanding Universe – the balloon analogy

The model is a good analogy

because

The model is not a good

analogy because

Distance between stars

expands

Stars do not expand at this

rate

Expansion is in more than one

dimension

Centre of the balloon is not

the centre of the universe

The bigger the gap the faster

the expansion.

This is a 2D representation of

a 3D model

Example 15

Calculate the age of the Universe given the estimate for the Hubble

constant is 2.3 x 10 -18 s-1.

time = 1 = 1 = 4.2 x 1017 s roughly 13.8 billion

years

H0 2.3 x 10 -18

Small balloon with

stars drawn on

Inflated balloon. Surface and

stars have expanded.

Importance of Expansion


Expansion or Explosion?

Explosion Expansion Different parts fly off at different

speeds

Expansion explains the large scale

symmetry we see in the distribution

of galaxies

Fast parts overtake slow parts Expanding space explains the

redshifts and the Hubble Law

Difficult to imagine a suitable

mechanism to produce the range of

velocities from 100kms-1 to almost

the speed of light

Expansion also explains redshifts

and the Hubble law even if we are

not at the centre of the universe

It seems likely that velocity would be

related to some physical property.

E.g. if given the same energy, less

massive galaxies would be moving

faster

Balloon analogy – every galaxy

moves away from every other as

the space expands

If this was the case a definite

correlation between mass and

velocity would be expected – this is

not observed.

No galaxy is located at the centre

Hubble’s law works well even if we

only plot data for galaxies of similar

mass

Not only are we not at the centre

of the universe, it doesn’t even

need to have a centre.

Faster galaxies would leave slower

ones behind, resulting in those near

the centre (start) being more closely

packed than those on the periphery

(finish), but this is not observed.

If the universe is expanding now then

Going backwards in time it must have been a lot smaller.

At one time everything in the universe must have been

concentrated at one spot (singularity) which had zero size and

infinite energy

This leads us to believe that the Universe started from a


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Temperature of Stellar Objects


P17 Q 1

Stars emit radiation from the entire electromagnetic spectrum, but we

can measure the temperature of a star by looking for a peak in the

wavelengths emitted.

Stars which have a higher temperature emit more radiation, with shorter

wavelength, than stars which are ‘colder’.

This can be used to help find the average temperature of the universe,

which in turn could help provide evidence for the Big Bang.

This is also called black body radiation.

If the Big Bang took place it should be possible to detect its effect by

measuring the thermal emission of radiation in the Universe. This

radiation should have a longer wavelength, with a peak corresponding to

the temperature the Universe has cooled to.

http://en.wikipedia.org/wiki/File:Wiens_law.svg

The thermal emission

peak graph on the left

shows the relationship

between the intensity of

radiation emitted from

stars of different

temperatures is related

to the wavelength of

the light emitted from

the star.

Cosmic Microwave Background Radiation


The diagram shows the

spectrum obtained by the

COsmic Background Explorer

(COBE) satellite over three

years. The results were exactly

in line with predicted values.

Cosmic Microwave Background (CMB) radiation:

is the dominant source of radiation in the Universe

is isotropic (spread uniformly throughout space)

shows the characteristics of black body radiation (as illustrated by

the results above)

has a temperature of approximately 3K due to cooling on expansion

corresponds to a redshift of 1000, so the early temperature of

this radiation was approximately 3000K

CMB radiation has been described as the ‘afterglow’ of the Big Bang,

cooled to a faint whisper in the microwave region of the electromagnetic

spectrum.

The Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001,

carried out a more sensitive measurement of the radiation. The picture

showing the temperature of the universe provides information on the

history of the universe and helps shape predictions for the future of the

universe.

http://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe#mediaviewer/

File:Ilc_9yr_moll4096.png

Additional Evidence for the Big Bang


Hydrogen and Helium (Nucleosynthesis)

If the Big Bang took place the lightest elements should have been formed

soon after the event.

Theory suggests that, fractions of a second after the Big Bang, the

Universe was very hot and filled with a mixture of particles. As it cooled

down Hydrogen, Helium and trace amounts of Lithium should be produced.

The proportion of Helium detected in the Universe (approximately 24%)

provides evidence for this aspect of the Big Bang Theory and helps

predict the rate of expansion of the Universe.

Heavier elements were not produced at this time because temperature

had fallen too far and most of the neutrons had been used up. These

elements were created in stars.

Olbers’ Paradox

The sky is full of stars. Stars emit light. Why are there dark bits in the

sky?

1. The light from any stars further than the age of the universe away

will not have had time to get to us.

2. There is a ‘dark horizon’ beyond which light from the stars can never

reach us because the Universe is expanding at the rate the light

travels towards us. The distance the light must travel is always

increasing..

How will it end?

The Expanding Universe 29 Updated 20140919 NH

The shape of the Universe depends on how much mass it contains because

this is related to the pull of gravity. There are three possible outcomes.

1. Closed Universe

If the mean density exceeds a critical value then the universe will

expand to a finite size and then begin to collapse back in on itself,

slowly at first, and then at an ever-increasing rate until all the

galaxies collide and the universe ends in a Big Crunch.

2. Open Universe

If the mean density is less than the critical value, gravity will slow

the rate of expansion towards a steady value and the expansion will

continue forever.

3. Flat Universe

If the mean density equals the critical value, the universe will be

able to expand forever with the recession velocities tending

towards zero.

The critical density is about 5 hydrogen atoms per m3.

Ω = actual density of the Universe

critical density for a flat Universe

Ω < 1 Open Universe – Big Chill

Ω = 1 Flat Universe – Big Chill

Ω > 1 Closed Universe – Big Crunch.

http://sci.esa.int/education/3

5775-

cosmology/?fbodylongid=1706

Big chill

Big crunch

How will it end?

The Expanding Universe 30 Updated 20140919 NH

1.Dark Matter

Problem – Calculation of the amount of matter in the galaxy suggests

there is more matter than astronomers can detect.

Evidence - Orbital speed of the Sun mass of galaxy inside its orbit

Speed of rotation of an object is determined by the size of

the force maintaining its rotation. For the Sun the central

force is due to gravity, which is determined by the amount of

matter inside the Sun’s orbital path.

Conclusion – There must be a significant amount of mass that we cannot

see.

This invisible matter has been termed dark matter.

2.Dark Energy

Problem – The universe is expanding at an increasing rate.

Evidence – Hubble’s Law and the evidence from red shift shows that

expansion is continuing to increase. A force must be acting

against the force of gravity, pushing matter apart.

Conclusion – Dark Energy is a source of energy, which produces the force

that acts against gravity.

Roughly 68% of the Universe is Dark Energy, Dark Matter makes up

about 27% and less than 5% is normal matter.

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