Module 5: C20 - Cosmology (The Big Bang)

Question 1

What is the Cosmological Principle

Answer 1

⚫ There are three assumptions:

⚫ The universe is homogeneous (it’s density is the same everywhere)
⚫ The universe is isotropic (it’s the same in all directions)
⚫ The laws of physics are universal (all laws of physics on Earth can be applied to other places in the universe)

Question 2

What is an Astronomical Unit (AU)

Answer 2

Astronomical unit (AU) is the average distance from the Earth to the Sun = 1.50x10^11m

(most often used to describe the distances from planets to the Sun).

Question 3

What is a Light-year (ly)

Answer 3

The Light-year (ly) is the distance travelled by light in a vacuum in a time of one year = 9.46x10^15m

(most often used to describe the distances between stars in our galaxy)

Question 4

What is a Parsec (pc)?

Answer 4

The Parsec (pc) is the distance that gives a parallax angle of 1 second = 3.0857×10^16 m

(most often used to measure the distances between stars and galaxies)

Question 5

Example Question:

The parallax angle, p, for a star is 0.0238 arcseconds. What is the distance, d, in metres?

Answer 5

Step 1: Substitute values into the equation
d = 1/p
d = 1/0.0238

Step 2: Calculate answer in parsecs
d = 42.016 806 parsecs

Step 3: Convert to metres
d = 42.016806 x 3.1x10^16 m
d = 1.3025210x10^18
d = 1.30x10^18 m

Question 6

Calculate the distance to the object in the specified unit:

0.0420 arc seconds in parsecs

Answer 6

d = 1/p
d = 1/0.0420
d = 23.809523 pc
d = 23.8 pc (3sf)

Question 7

Calculate the distance to the object in the specified unit:

0.0317 arc seconds in metres

Answer 7

d = 1/p
d = 1/0.0317
d = 31.545741 pc
d = 31.545741 x 3.1x10^16
d = 9.7791798 x 10^17 m
d = 9.78x10^17 m (3sf)

Question 8

Calculate the distance to the object in the specified unit:

0.735 arcseconds in light years

Answer 8

d = 1/p
d = 1/0.735
d = 1.3605442 pc
d = 1.3605442 x 3.1x10^16 / 9.46x10^15
d = 4.458442997 ly
d = 4.46 ly (3sf)

Question 9

What do professional astronomers prefer to measure angles with

Answer 9

They prefer to measure angles not in degrees, but arcminutes and arc seconds. There are 60 arcminutes in 1°, and 60 arc seconds in each arcminute. Therefore, 1 arcsecond = (1/3600)°

Question 10

What is Stellar Parallax used for?

Answer 10

Stellar parallax is a technique used to determine the distance to stars that are relatively close to the Earth, at distances less than 100pc.

Question 11

What is parallax

Answer 11

Parallax is the allarent apparent shift in the position if a relatively close star against the backdrop of much more distant stars as the Earth orbits the Sun.

Question 12

What equation gives the distance to a nearby star in parsecs (+ what is the equation limited to)

Answer 12

d = 1/p
(distance = d, parallax angle = p)

This technique is limited to stars less than 100pc from the Earth, because as d increases, the parallax angle decreases, eventually becoming to small to measure accurately)

Question 13

What did Edwin Hubble discover

Answer 13

Edwin Hubble observed that the pattern of dark lines in light from distant galaxies is shifted towards the red end of the spectrum. This red shift suggests that distant galaxies are moving away from Earth and supports the idea of an expanding Universe.

Question 14

Example of the Doppler Effect and Red Shift

Answer 14

When an ambulance drives past you, its siren sounds higher pitched as it approaches, and lower pitched as it moves away. This is the Doppler effect. The same thing happens to the light emitted by very fast moving objects, such as distant stars, and can be seen in their spectra. This is red shift.

Question 15

Doppler Effect Definition

Answer 15

The Doppler effect is an increase (or decrease) in the frequency of sound, light, or other waves as the source and observer move towards (or away from) each other.

Question 16

What will happen to the absorption lines on a spectrum where a galaxy is moving towards the earth?

Answer 16

If the galaxy is moving towards the Earth the absorption lines will be blue-shifted - they move towards the blue end of the spectrum, because the wavelength appears shorter.

Question 17

What will happen to the absorption lines on a spectrum where a galaxy is moving away the earth?

Answer 17

If the galaxy is moving away from the Earth, the absorption lines will be red-shifted - they all move towards the red end of the spectrum, because the wavelengths appears stretched.

Question 18

What formula can be used to calculate the amount of red shift?

Answer 18

z = Δλ / λ

z = v / c

(Z - red shift
Δλ - difference between the observed and emitted wavelengths
λ - emitted wavelength
v - relative velocity
c - speed of light)

Question 19

What is Hubble’s Law?

Answer 19

Hubble found that the speed of a receding galaxy is directly proportional to its distance from the Earth. This became Hubble’s law.

v = Ho x d

(Where H0 is known as Hubble’s constant.)

Question 20

What were 2 key observations Hubble made before creating Hubble’s Law?

Answer 20

1. He confirmed earlier observations that the light from the vast majority of galaxies was red-shifted, that is, they had a relative velocity away from the Earth.
2. He found that in general, the further away the galaxy was, the greater the observed red shift and so the faster the galaxy was moving.

Question 21

Worked Example: Speed of a galaxy

In the laboratory an absorption line of hydrogen is observed at a wavelength of 656.4nm. In a distant galaxy the same absorption line is observed at 658.1nm. Calculate the speed of the galaxy and state whether it is moving towards or away from the Earth.

Answer 21

Step 1: Calculate the change in wavelength
Δλ = 658.1 - 656.4 = 1.7nm

The wavelength observed from the galaxy is longer than the wavelength in the labatory, so the galaxy must be receding. The spectral line has been red-shifted.

Step 2: The Doppler equation Δλ/λ ≈ v/c can be rearranged to give cΔλ/λ ≈ v.

Therefore:
v ≈ cΔλ/λ ≈ (3.00x10^8 x 1.7x10^-9) / 656.4x10^-9 = 7.76x10^5

≈ 780kms^-1

Question 22

How can you use Hubble’s Constant to estimate the age of the Universe

Answer 22

Time = Distance/Speed

Time = 1/Ho

(Ho = Hubble’s Constant)

Using Ho = 2.2x10^-18 s^-1 gives the age as 4.5x10^17 s (~14 billion years)

Question 23

What is Cosmic Microwave Background Radiation?

Answer 23

Cosmic Microwave Background Radiation is radiation remaining from the Big Bang expansion and fills the whole of the Universe. This is key evidence for the Big Bang theory.

Question 24

What are the 2 pieces of key evidence for the Big Bang theory

Answer 24

• Hubble’s Law
• Microwave Background Radiation

Question 25

Why did the Big Bang theory become the most widely accepted theory on the origin of the Universe

Answer 25

None of the competing theories has predicted or could explain the origin of the microwave background radiation, so the Big Bang theory become the most widely accepted theory on the origin of the Universe.

Question 26

What two ways can Background Microwave Radiation be explained by (involving the Big Bang)

Answer 26

- When the Universe was young and extremely hot, space was saturated with high-energy gamma photons. The expansion of the Universe means that space itself was stretched over time. This expansion stretched the wavelength of these high-energy photons, so we now observe this primordial electromagnetic radiation as microwaves. - The Universe was extremely dense and got when it was young. Expansion of space over billions of years has reduced that that temperature to around 2.7K. The Universe may be treated as a black-body radiator - at this temperature the peak wavelength would correspond to about 1mm, in the microwave region of the spectrum.

Question 27

What is currently the best accepted hypothesis to explain the how the expansion of the Universe is accelerating

Answer 27

The acceleration of the Universe’s expansion needed a source of energy, one which has never been detected. We use the term ‘dark energy’ to describe a hypothetical form of energy that permeates all space. Dark energy is currently the best accepted hypothesis to explain the accelerating rate of expansion.

Question 28

What do we know about Dark Matter, and where could it be in the Universe

Answer 28

Not much is known about dark matter. We do know that it cannot be seen directly with telescopes and that it neither emits nor absorbs light. There are exotic speculations as to what it could be: black holes, gravitinos, weakly interacting massive particles (wimps), axions, Q-ball, e.t.c. The truth is that dark energy and dark matter remain a mystery waiting to be solved.

Question 29

Timeline of the Universe: What happened at the point of the Big Bang

Answer 29

Time and space are created The Universe is a singularity - it is infinitely dense and hot.

Question 30

Timeline of the Universe: What happen at 10^-35 seconds into the Universe

Answer 30

The Universe expands rapidly, including a phase of incredible acceleration known as inflation. There is no matter in the Universe - instead it is full of electromagnetic radiation in the form of high-energy gamma photons. The temperature is about 10^28 K.

Question 31

Timeline of the Universe: What happened at 10^-6 seconds into the Universe

Answer 31

The first fundamental particles (quarks, leptons, etc.) gain mass through a mechanism that is not fully understood but involves the Higgs Boson (discovered in 2013).

Question 32

Timeline of the Universe: What happened at 10^-3 seconds into the Universe

Answer 32

The quarks combine to form the first hadrons, such as protons and neutrons. Most of the mass in the Universe was created within the first second through the process of pair production (high-energy photons transforming into particle-antiparticle pairs).

Question 33

Timeline of the Universe: What happened 1 second into the Universe

Answer 33

The creation of matter stops after about 1s, once the temperature has dropped to about 10^9 K.

Question 34

Timeline of the Universe: Summary of what happened in the first second of the Universe

Answer 34

- Time and space are created - The Universe is a singularity (infinitely hot and dense) - The Universe expands rapidly including a phase of incredible acceleration (known as inflation) - There is no matter, just electromagnetic radiation in the form of high-energy gamma photons. - The first fundamental particles (quarks, leptons, etc.) gain mass through a mechanism that is not fully understood but involves the Higgs Boson - The quarks combine to for the first hadrons, such as protons and neutrons - Most of the mass in the Universe was created within the first second through the process of pair production (high-energy photons transforming into particle-antiparticle pairs) - The creation of matter stops after around 1 second, once the temperature has dropped to about 10^9 K.

Question 35

Timeline of the Universe: What happens 100s into the Universe

Answer 35

Protons and neutrons fuse together to form deuterium and helium nuclei, along with a small quantity of lithium and beryllium. The expansion of the Universe is so rapid that no heavier elements are created. During this stage, about 25% of the matter in the Universe is helium nuclei (known as primordial helium).

Question 36

Timeline of the Universe: What happened 380,000 years after the Big Bang

Answer 36

The Universe cools enough for the first atoms to form. The nuclei capture electrons. The electromagnetic radiation from this stage of the Universe is what can be detected as microwave background radiation.

Question 37

Timeline of the Universe: What happened 30 million years after the Big Bang

Answer 37

The first stars appear. Through nuclear fusion in these stars, the first heavy elements (beyond lithium) begin to form.

Question 38

Timeline of the Universe: What happened 200 million years after the Big Bang

Answer 38

Our galaxy, the Milky Way, forms as gravitational forces pull clouds of hydrogen and existing stars together.

Question 39

Timeline of the Universe: What happened 9 billion years after the Big Bang

Answer 39

The Solar System forms from the nebula left by the supernova of a larger star. After the Sun forms the remaining material forms the Earth and other planets (around 1 billion years later). It is though that around 1 billion years after the formation of the Earth (11 billion years after the Big Bang) primitive life begins on Earth.

Question 40

Timeline of the Universe: What happened 13.7 billion years after the Big Bang (now)

Answer 40

Around 200,000 years ago the modern humans evolve, and eventually study physics. The temperature of the Universe is 2.7K.