Cosmology

What you'll learn

How astronomers measure huge distances using AU, light-years and parsecs.
How stellar parallax gives distances to nearby stars.
How Doppler redshift and Hubble’s law support an expanding Universe.
Why the Big Bang theory is supported by the 2.7 K microwave background radiation.

1. Astronomical distance scales

In cosmology, ordinary metres are often inconvenient because distances are enormous. Astronomers use larger distance units depending on the scale being discussed.

Definition

Astronomical distance units

The astronomical unit, AU, is the mean Earth-Sun distance: 1 AU is approximately $1.50 \times 10^{11}\ \text{m}$ .
A light-year, ly, is the distance light travels in one year: 1 ly is approximately $9.46 \times 10^{15}\ \text{m}$ .
A parsec, pc, is the distance at which 1 AU subtends an angle of 1 arcsecond. 1 pc is approximately $3.09 \times 10^{16}\ \text{m}$ , or about 3.26 ly.
A megaparsec, Mpc, is $pc10^6\ \text{pc}$ and is commonly used for galaxy distances.

An arcsecond is a tiny angle: there are 3600 arcseconds in 1 degree.

Example

Converting parsecs into light-years and metres

A star is 12 pc from Earth. Find its distance in light-years and metres.

Convert parsecs into light-years using 1 pc is about 3.26 ly:

12\ \text{pc} \times 3.26\ \text{ly pc}^{-1} = 39.1\ \text{ly}

Convert parsecs into metres using $m1\ \text{pc} = 3.09 \times 10^{16}\ \text{m}$ :

12\ \text{pc} \times 3.09 \times 10^{16}\ \text{m pc}^{-1} = 3.71 \times 10^{17}\ \text{m}

Quote sensible significant figures:

\approx 39\ \text{ly} \approx 3.7 \times 10^{17}\ \text{m}

2. Stellar parallax

Stellar parallax is the apparent shift in the position of a nearby star against a background of very distant stars, caused by the Earth moving around the Sun.

We observe the star six months apart, when Earth is on opposite sides of its orbit. The nearby star appears to shift slightly. The parallax angle, $p$ , is half the total angular shift.

Stellar parallax diagram showing Earth six months apart, 1 AU baseline, parallax angle p, and distance d in parsec

For OCR, the key equation is:

\frac{1}{d}

where $p$ is the parallax in seconds of arc and $d$ is the distance in parsec.

Common Mistake

Using the wrong angle

The parallax angle $p$ is half the total apparent shift measured between observations six months apart. The equation $p = 1/ d$ uses $p$ in arcseconds and $d$ in parsecs; do not put $p$ in degrees or radians for this equation.

Example

Finding distance from parallax

A nearby star has a parallax angle of 0.20 arcseconds. Calculate its distance in parsecs and light-years.

Rearrange the parallax equation:

\frac{1}{p}

Substitute $p = 0.20$ arcseconds:

\frac{1}{0.20} = 5.0\ \text{pc}

Convert into light-years:

5.0\ \text{pc} \times 3.26\ \text{ly pc}^{-1} = 16.3\ \text{ly}

So the star is about 5.0 pc, or 16 ly, away.

3. The Cosmological principle

The Cosmological principle is an assumption about the Universe on very large scales.

Key Idea

Cosmological principle

On large enough scales, the Universe is homogeneous meaning it has the same average structure everywhere, isotropic meaning it looks the same in every direction, and the laws of physics are universal meaning the same physical laws apply throughout the Universe.

This does not mean every local region is identical. Stars, galaxies and clusters clearly exist. The principle applies when you average over extremely large cosmic distances.

4. Doppler shift of electromagnetic radiation

The Doppler effect is the change in observed wavelength or frequency when a source and observer move relative to one another.

For electromagnetic radiation:

Redshift means the observed wavelength is longer than the emitted wavelength. This indicates the source is moving away.
Blueshift means the observed wavelength is shorter. This indicates the source is moving towards the observer.

For speeds much smaller than the speed of light, use the approximate Doppler equation:

\frac{\Delta \lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}

where $Δλ\Delta \lambda$ is the change in wavelength, $Δf\Delta f$ is the change in frequency, $v$ is the relative speed, and $c$ is the speed of light in vacuum.

Common Mistake

Wavelength and frequency change oppositely

For redshift, wavelength increases but frequency decreases. In many A-Level calculations, $Δλ/λ\Delta \lambda / \lambda$ and $Δf/f\Delta f / f$ are treated as magnitudes, so use the size of the fractional shift unless the question explicitly asks for a sign.

Example

Calculating speed from redshift

A spectral line has a laboratory wavelength of 486.1 nm. In light from a distant galaxy, the same line is observed at 487.6 nm. Calculate the galaxy’s recessional speed.

Find the change in wavelength:

\Delta \lambda = 487.6\ \text{nm} - 486.1\ \text{nm} = 1.5\ \text{nm}

Calculate the fractional wavelength shift:

\frac{\Delta \lambda}{\lambda} = \frac{1.5\ \text{nm}}{486.1\ \text{nm}} = 3.09 \times 10^{-3}

Use the Doppler equation with $\times 10^8\ \text{m s}^{-1}$ :

\approx c\frac{\Delta \lambda}{\lambda} = 3.00 \times 10^8\ \text{m s}^{-1} \times 3.09 \times 10^{-3}

\times 10^5\ \text{m s}^{-1}

Interpret the shift:

The wavelength is longer, so the galaxy is receding at about $9.3 \times 10^5\ \text{m s}^{-1}$ , or $s−1930\ \text{km s}^{-1}$ .

5. Hubble’s law and the expanding Universe

Observations show that light from most distant galaxies is redshifted. This means those galaxies are receding from us.

Hubble’s law states that, for receding galaxies:

\approx H_0 d

where $v$ is the recessional speed, $d$ is the distance to the galaxy, and $H_0$ is the Hubble constant.

Galactic redshift, expansion of space, and Hubble law graph with gradient H0

On a graph of recessional speed against distance, the gradient is $H_0$ . The law supports the model of an expanding Universe: more distant galaxies recede faster because space itself is expanding.

Common Mistake

Nearby galaxies can be awkward

Hubble’s law is a large-scale trend. Nearby galaxies can have local motions due to gravitational interactions, so they may not fit the straight-line pattern neatly.

The Hubble constant is often quoted in $Mpc−1\text{km s}^{-1}\ \text{Mpc}^{-1}$ , because galaxy speeds are often in kilometres per second and distances in megaparsecs. In SI units, $H_0$ has unit $s−1\text{s}^{-1}$ because it is speed divided by distance.

Example

Using Hubble’s law and estimating the age

Take $Mpc−1H_0 = 70\ \text{km s}^{-1}\ \text{Mpc}^{-1}$ . A galaxy is 150 Mpc away. Estimate its recessional speed and the age of the Universe.

Use Hubble’s law for the galaxy:

\approx H_0 d = 70\ \text{km s}^{-1}\ \text{Mpc}^{-1} \times 150\ \text{Mpc}

\times 10^4\ \text{km s}^{-1}

Convert $H_0$ into $s−1\text{s}^{-1}$ . Since $km1\ \text{Mpc} = 3.09 \times 10^{19}\ \text{km}$ :

H_0 = \frac{70\ \text{km s}^{-1}}{3.09 \times 10^{19}\ \text{km}} = 2.27 \times 10^{-18}\ \text{s}^{-1}

Use the estimate for the age of the Universe:

\approx H_0^{-1} = \frac{1}{2.27 \times 10^{-18}\ \text{s}^{-1}} = 4.41 \times 10^{17}\ \text{s}

Convert seconds into years using $s1\ \text{year} \approx 3.16 \times 10^7\ \text{s}$ :

\frac{4.41 \times 10^{17}\ \text{s}}{3.16 \times 10^7\ \text{s year}^{-1}} = 1.40 \times 10^{10}\ \text{years}

So this gives an estimated age of about 14 billion years.

6. Big Bang theory

Definition

Big Bang theory

The Big Bang theory says that the Universe began in a very hot, dense state and has expanded and cooled over time. It was not an explosion into pre-existing space; it gave rise to the expansion of space-time itself.

The galactic redshift evidence fits this model: if the Universe is expanding now, then in the past it was smaller, hotter and denser.

The second major piece of evidence is the cosmic microwave background radiation, often shortened to CMB. This is microwave radiation detected from all directions in space, corresponding to a temperature of about 2.7 K.

Key Idea

Microwave background evidence

The 2.7 K cosmic microwave background is interpreted as leftover radiation from the early hot Universe, stretched to microwave wavelengths as space expanded. Its discovery and measurement were crucial in the scientific community’s acceptance of the Big Bang theory.

This is a good example of how scientific theories become accepted: a model makes sense of existing evidence, survives testing, and gains support when new observations match its predictions.

7. Evolution of the Universe

You do not need a detailed particle-physics timeline, but you should know the broad story.

Soon after the Big Bang, the Universe was extremely hot and dense. As space-time expanded, the Universe cooled. Particles formed, then simple nuclei, and later atoms. Once atoms formed, radiation could travel more freely; this early radiation is now observed as the CMB.

Over much longer timescales, gravity caused matter to clump into stars and galaxies. Stars produced heavier elements, galaxies evolved, and the Universe continued expanding to the present day.

8. What is the Universe made of?

Current ideas suggest the Universe contains:

Ordinary matter: atoms, ions, electrons, stars, gas, dust, planets and living things. This is only a small percentage of the total.
Dark matter: matter that does not emit or absorb electromagnetic radiation in the usual way, but has gravitational effects.
Dark energy: a component associated with the large-scale expansion of the Universe.

A common approximate breakdown is about 5% ordinary matter, 25% dark matter and 70% dark energy.

Exam technique

In the exam

For parallax, check that $p$ is in arcseconds and $d$ is in parsecs before using $p = 1/ d$ .
For Doppler shift, longer wavelength means redshift and recession; calculate speed using the fractional shift times $c$ .
For Hubble calculations, use $\approx H_0 d$ , remember the graph gradient is $H_0$ , and convert $H_0$ into $s−1\text{s}^{-1}$ before using $\approx H_0^{-1}$ .

Self review

Check yourself

A star has parallax 0.050 arcseconds. What is its distance in parsecs?
A spectral line shifts from 500 nm to 505 nm. Is the source approaching or receding, and what speed would you estimate?
Why is the 2.7 K microwave background radiation strong evidence for the Big Bang theory?

What you'll learn

How astronomers measure huge distances using AU, light-years and parsecs.
How stellar parallax gives distances to nearby stars.
How Doppler redshift and Hubble’s law support an expanding Universe.
Why the Big Bang theory is supported by the 2.7 K microwave background radiation.

1. Astronomical distance scales

In cosmology, ordinary metres are often inconvenient because distances are enormous. Astronomers use larger distance units depending on the scale being discussed.

Definition

Astronomical distance units

The astronomical unit, AU, is the mean Earth-Sun distance: 1 AU is approximately $1.50 \times 10^{11}\ \text{m}$ .
A light-year, ly, is the distance light travels in one year: 1 ly is approximately $9.46 \times 10^{15}\ \text{m}$ .
A parsec, pc, is the distance at which 1 AU subtends an angle of 1 arcsecond. 1 pc is approximately $3.09 \times 10^{16}\ \text{m}$ , or about 3.26 ly.
A megaparsec, Mpc, is $pc10^6\ \text{pc}$ and is commonly used for galaxy distances.

An arcsecond is a tiny angle: there are 3600 arcseconds in 1 degree.

Example

Converting parsecs into light-years and metres

A star is 12 pc from Earth. Find its distance in light-years and metres.

Convert parsecs into light-years using 1 pc is about 3.26 ly:

12\ \text{pc} \times 3.26\ \text{ly pc}^{-1} = 39.1\ \text{ly}

Convert parsecs into metres using $m1\ \text{pc} = 3.09 \times 10^{16}\ \text{m}$ :

12\ \text{pc} \times 3.09 \times 10^{16}\ \text{m pc}^{-1} = 3.71 \times 10^{17}\ \text{m}

Quote sensible significant figures:

\approx 39\ \text{ly} \approx 3.7 \times 10^{17}\ \text{m}

2. Stellar parallax

Stellar parallax is the apparent shift in the position of a nearby star against a background of very distant stars, caused by the Earth moving around the Sun.

We observe the star six months apart, when Earth is on opposite sides of its orbit. The nearby star appears to shift slightly. The parallax angle, $p$ , is half the total angular shift.

Stellar parallax diagram showing Earth six months apart, 1 AU baseline, parallax angle p, and distance d in parsec

For OCR, the key equation is:

\frac{1}{d}

where $p$ is the parallax in seconds of arc and $d$ is the distance in parsec.

Common Mistake

Using the wrong angle

Example

Finding distance from parallax

A nearby star has a parallax angle of 0.20 arcseconds. Calculate its distance in parsecs and light-years.

Rearrange the parallax equation:

\frac{1}{p}

Substitute $p = 0.20$ arcseconds:

\frac{1}{0.20} = 5.0\ \text{pc}

Convert into light-years:

5.0\ \text{pc} \times 3.26\ \text{ly pc}^{-1} = 16.3\ \text{ly}

So the star is about 5.0 pc, or 16 ly, away.

3. The Cosmological principle

The Cosmological principle is an assumption about the Universe on very large scales.

Key Idea

Cosmological principle

This does not mean every local region is identical. Stars, galaxies and clusters clearly exist. The principle applies when you average over extremely large cosmic distances.

4. Doppler shift of electromagnetic radiation

The Doppler effect is the change in observed wavelength or frequency when a source and observer move relative to one another.

For electromagnetic radiation:

Redshift means the observed wavelength is longer than the emitted wavelength. This indicates the source is moving away.
Blueshift means the observed wavelength is shorter. This indicates the source is moving towards the observer.

For speeds much smaller than the speed of light, use the approximate Doppler equation:

\frac{\Delta \lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}

where $Δλ\Delta \lambda$ is the change in wavelength, $Δf\Delta f$ is the change in frequency, $v$ is the relative speed, and $c$ is the speed of light in vacuum.

Common Mistake

Wavelength and frequency change oppositely

Example

Calculating speed from redshift

A spectral line has a laboratory wavelength of 486.1 nm. In light from a distant galaxy, the same line is observed at 487.6 nm. Calculate the galaxy’s recessional speed.

Find the change in wavelength:

\Delta \lambda = 487.6\ \text{nm} - 486.1\ \text{nm} = 1.5\ \text{nm}

Calculate the fractional wavelength shift:

\frac{\Delta \lambda}{\lambda} = \frac{1.5\ \text{nm}}{486.1\ \text{nm}} = 3.09 \times 10^{-3}

Use the Doppler equation with $\times 10^8\ \text{m s}^{-1}$ :

\approx c\frac{\Delta \lambda}{\lambda} = 3.00 \times 10^8\ \text{m s}^{-1} \times 3.09 \times 10^{-3}

\times 10^5\ \text{m s}^{-1}

Interpret the shift:

The wavelength is longer, so the galaxy is receding at about $9.3 \times 10^5\ \text{m s}^{-1}$ , or $s−1930\ \text{km s}^{-1}$ .

5. Hubble’s law and the expanding Universe

Observations show that light from most distant galaxies is redshifted. This means those galaxies are receding from us.

Hubble’s law states that, for receding galaxies:

\approx H_0 d

where $v$ is the recessional speed, $d$ is the distance to the galaxy, and $H_0$ is the Hubble constant.

Galactic redshift, expansion of space, and Hubble law graph with gradient H0

On a graph of recessional speed against distance, the gradient is $H_0$ . The law supports the model of an expanding Universe: more distant galaxies recede faster because space itself is expanding.

Common Mistake

Nearby galaxies can be awkward

Hubble’s law is a large-scale trend. Nearby galaxies can have local motions due to gravitational interactions, so they may not fit the straight-line pattern neatly.

Example

Using Hubble’s law and estimating the age

Take $Mpc−1H_0 = 70\ \text{km s}^{-1}\ \text{Mpc}^{-1}$ . A galaxy is 150 Mpc away. Estimate its recessional speed and the age of the Universe.

Use Hubble’s law for the galaxy:

\approx H_0 d = 70\ \text{km s}^{-1}\ \text{Mpc}^{-1} \times 150\ \text{Mpc}

\times 10^4\ \text{km s}^{-1}

Convert $H_0$ into $s−1\text{s}^{-1}$ . Since $km1\ \text{Mpc} = 3.09 \times 10^{19}\ \text{km}$ :

H_0 = \frac{70\ \text{km s}^{-1}}{3.09 \times 10^{19}\ \text{km}} = 2.27 \times 10^{-18}\ \text{s}^{-1}

Use the estimate for the age of the Universe:

\approx H_0^{-1} = \frac{1}{2.27 \times 10^{-18}\ \text{s}^{-1}} = 4.41 \times 10^{17}\ \text{s}

Convert seconds into years using $s1\ \text{year} \approx 3.16 \times 10^7\ \text{s}$ :

\frac{4.41 \times 10^{17}\ \text{s}}{3.16 \times 10^7\ \text{s year}^{-1}} = 1.40 \times 10^{10}\ \text{years}

So this gives an estimated age of about 14 billion years.

6. Big Bang theory

Definition

Big Bang theory

The galactic redshift evidence fits this model: if the Universe is expanding now, then in the past it was smaller, hotter and denser.

Key Idea

Microwave background evidence

This is a good example of how scientific theories become accepted: a model makes sense of existing evidence, survives testing, and gains support when new observations match its predictions.

7. Evolution of the Universe

You do not need a detailed particle-physics timeline, but you should know the broad story.

Over much longer timescales, gravity caused matter to clump into stars and galaxies. Stars produced heavier elements, galaxies evolved, and the Universe continued expanding to the present day.

8. What is the Universe made of?

Current ideas suggest the Universe contains:

Ordinary matter: atoms, ions, electrons, stars, gas, dust, planets and living things. This is only a small percentage of the total.
Dark matter: matter that does not emit or absorb electromagnetic radiation in the usual way, but has gravitational effects.
Dark energy: a component associated with the large-scale expansion of the Universe.

A common approximate breakdown is about 5% ordinary matter, 25% dark matter and 70% dark energy.

Exam technique

In the exam

For parallax, check that $p$ is in arcseconds and $d$ is in parsecs before using $p = 1/ d$ .
For Doppler shift, longer wavelength means redshift and recession; calculate speed using the fractional shift times $c$ .
For Hubble calculations, use $\approx H_0 d$ , remember the graph gradient is $H_0$ , and convert $H_0$ into $s−1\text{s}^{-1}$ before using $\approx H_0^{-1}$ .

Self review

Check yourself

A star has parallax 0.050 arcseconds. What is its distance in parsecs?
A spectral line shifts from 500 nm to 505 nm. Is the source approaching or receding, and what speed would you estimate?
Why is the 2.7 K microwave background radiation strong evidence for the Big Bang theory?

What you'll learn

1. Astronomical distance scales

2. Stellar parallax

3. The Cosmological principle

4. Doppler shift of electromagnetic radiation

5. Hubble’s law and the expanding Universe

6. Big Bang theory

7. Evolution of the Universe

8. What is the Universe made of?

Review Cosmology by teaching Genie

Remember key concepts with flashcards

Cosmology

What you'll learn

1. Astronomical distance scales

2. Stellar parallax

3. The Cosmological principle

4. Doppler shift of electromagnetic radiation

5. Hubble’s law and the expanding Universe

6. Big Bang theory

7. Evolution of the Universe

8. What is the Universe made of?

Review Cosmology by teaching Genie

Remember key concepts with flashcards

Cosmology

What you'll learn

1. Astronomical distance scales

2. Stellar parallax

3. The Cosmological principle

4. Doppler shift of electromagnetic radiation

5. Hubble’s law and the expanding Universe

6. Big Bang theory

7. Evolution of the Universe

8. What is the Universe made of?

Review Cosmology by teaching Genie

Remember key concepts with flashcards

Cosmology Revision Guide

Cosmology

What you'll learn

1. Astronomical distance scales

2. Stellar parallax

3. The Cosmological principle

4. Doppler shift of electromagnetic radiation

5. Hubble’s law and the expanding Universe

6. Big Bang theory

7. Evolution of the Universe

8. What is the Universe made of?

Review Cosmology by teaching Genie

Remember key concepts with flashcards

Cosmology Revision Guide