OCR A Level Physics A: Distances, redshift, Hubble's law and the Big Bang (H556)

This guide covers section 5.5.3 (Cosmology), statements (a) to (o), of the OCR Advanced GCE in Physics A specification (H556), Version 3.0 (March 2026), for first assessment in 2017. H556 is the full A level. It belongs to module 5 (Newtonian world and astrophysics). Stellar evolution, the Hertzsprung-Russell diagram, spectra, Wien’s law and Stefan’s law are separate units, so they are not repeated here.

Related pages: revision notes, practice questions, OCR A Level Physics hub, printable checklist and the free 10-minute diagnostics.

What you must be able to do

Statement	Content
5.5.3(a)	Use the astronomical unit, light-year and parsec
5.5.3(b), (c)	Explain stellar parallax; use p = 1/d
5.5.3(d)	State the Cosmological principle
5.5.3(e), (f)	Describe the Doppler effect for light; use Δλ/λ ≈ Δf/f ≈ v/c
5.5.3(g), (h)	Use Hubble’s law; explain how galactic red shift supports an expanding universe
5.5.3(i)	Give H0 in km s⁻¹ Mpc⁻¹ and in s⁻¹
5.5.3(j) to (l)	Big Bang theory; microwave background at 2.7 K; expansion of space-time
5.5.3(m)	Estimate the age of the universe, t ≈ 1/H0
5.5.3(n), (o)	Evolution of the universe; dark energy, dark matter and ordinary matter

Distances: AU, light-year and parsec (5.5.3(a))

Metres are far too small for astronomy, so three units are used.

• The astronomical unit (AU) is the mean distance from the Earth to the Sun, 1.50 × 10¹¹ m.
• The light-year (ly) is the distance light travels in a vacuum in one year, about 9.46 × 10¹⁵ m.
• The parsec (pc) is the distance at which a star shows a parallax of one second of arc, about 3.09 × 10¹⁶ m.

Useful links: 1 pc is about 3.26 ly, and 1 Mpc is 10⁶ pc. The light-year is a distance, not a time. Use the unit that keeps numbers sensible: AU inside the Solar System, ly or pc between stars, Mpc between galaxies.

Worked example 1. A star is 4.2 ly away. Give its distance in metres and in parsec.

Distance = 4.2 × 9.46 × 10¹⁵ = 3.97 × 10¹⁶ m. In parsec: 3.97 × 10¹⁶ / 3.09 × 10¹⁶ = 1.29 pc.

The specification links this statement to small-angle work (M4.6). One second of arc is 1/3600 of a degree, which is 4.85 × 10⁻⁶ rad. If 1 AU subtends this angle, the distance is 1.496 × 10¹¹ / 4.85 × 10⁻⁶ = 3.09 × 10¹⁶ m. That is where the parsec comes from.

Stellar parallax (5.5.3(b), (c))

Parallax is the small change in direction in which a close star is seen, compared with far more distant stars, as the Earth moves round its orbit. You observe the star twice, six months apart, when the Earth is at opposite ends of its orbit. The parallax angle p is half the total angular shift. Equivalently, it is the angle subtended at the star by a line of one AU, the Earth-Sun distance.

For p in seconds of arc and d in parsec:

p = 1/d

so a star with a parallax of 0.5 seconds of arc is 2 pc away. The smaller the angle, the greater the distance.

Worked example 2. A star has a parallax of 0.0625 seconds of arc. Find its distance in pc, ly and m.

d = 1/p = 1/0.0625 = 16.0 pc. In ly: 16.0 × 3.09 × 10¹⁶ / 9.46 × 10¹⁵ = 52.3 ly. In m: 16.0 × 3.09 × 10¹⁶ = 4.94 × 10¹⁷ m.

Parallax angles are tiny, so the method works only for relatively nearby stars. For very distant stars the angle falls below what can be measured.

The Cosmological principle (5.5.3(d))

On a large enough scale the universe is:

• homogeneous: it has the same average density and structure everywhere
• isotropic: it looks the same in every direction from any position
• governed by the same laws of physics everywhere (the laws are universal).

“Large enough” means averaging over huge volumes. Galaxies and clusters are clumpy, but at scales of hundreds of Mpc the clumps average out. The principle means no place is special and there is no centre. It is an assumption that observations are tested against.

Doppler effect and Doppler shift (5.5.3(e), (f))

When a source and observer move relative to each other, the observed wavelength and frequency change. A source moving away gives a longer wavelength and lower frequency (red shift). A source moving towards you gives a shorter wavelength and higher frequency (blue shift). For light the shift is read from known spectral lines, comparing the wavelength measured on Earth with the wavelength measured from a laboratory source.

For a source moving at speed v much less than c:

Δλ/λ ≈ Δf/f ≈ v/c

Δλ is the change in wavelength, λ the emitted wavelength, and c the speed of light, 3.00 × 10⁸ m s⁻¹. This approximation fails at speeds close to c.

Worked example 3. A hydrogen line of wavelength 656.3 nm is measured as 659.6 nm in the light of a galaxy. Find the speed of recession.

Δλ = 659.6 − 656.3 = 3.3 nm. v = c × Δλ/λ = 3.00 × 10⁸ × 3.3 / 656.3 = 1.5 × 10⁶ m s⁻¹.

The shift is positive, so the galaxy is receding. Keep Δλ and λ in the same unit; they cancel.

Hubble’s law and the expanding universe (5.5.3(g), (h), (i))

Hubble found that light from distant galaxies is red-shifted, and that the further away the galaxy, the greater the red shift. Interpreting the shift as a recession speed:

v ≈ H0 d

where v is the recession speed, d is the distance and H0 is the Hubble constant. The law applies to receding galaxies. A graph of v against d is a straight line through the origin with gradient H0.

H0 is quoted in km s⁻¹ Mpc⁻¹. This guide uses 70 km s⁻¹ Mpc⁻¹ unless data are given.

Worked example 4. Using H0 = 70 km s⁻¹ Mpc⁻¹, find (i) the speed of a galaxy 120 Mpc away and (ii) the distance of a galaxy receding at 15 000 km s⁻¹.

(i) v = 70 × 120 = 8400 km s⁻¹. (ii) d = v/H0 = 15 000 / 70 = 214 Mpc.

Converting H0 to s⁻¹. Kilometres and megaparsecs are both lengths, so H0 reduces to a rate. Convert Mpc to km: 1 Mpc = 3.09 × 10²² m = 3.09 × 10¹⁹ km.

H0 = 70 / 3.09 × 10¹⁹ = 2.27 × 10⁻¹⁸ s⁻¹.

Worked example 5 (using data). Five galaxies give these results.

d / Mpc	50	100	150	200	250
v / km s⁻¹	3600	7300	10 800	14 500	17 900

Each v/d is close to 72 (72, 73, 72, 72.5, 71.6). A best-fit line through the origin has gradient 72 km s⁻¹ Mpc⁻¹, so H0 ≈ 72 km s⁻¹ Mpc⁻¹. Do not simply join the first and last points when fitting a line to scattered data.

Why this supports an expanding universe. Every distant galaxy recedes, and the speed is proportional to distance. This is just what a uniform expansion of space gives: the gaps between galaxies grow, and a more distant galaxy has more space between it and us to stretch. Because the Cosmological principle says no place is special, an observer in any galaxy would see the same pattern. Expansion therefore has no centre. Picture dots on an inflating balloon: from any dot, all others move away, faster for those farther away. The red shift is better described as the stretching of light’s wavelength as space expands, though at A level it is analysed with the Doppler equation.

The Big Bang theory and its evidence (5.5.3(j), (k), (l))

If galaxies are moving apart now, they were closer in the past. Running time backwards, all matter and energy were once in a tiny, very hot, very dense state. The Big Bang theory says the universe began from such a state about 14 billion years ago and has been expanding and cooling since. It is not an explosion into pre-existing empty space. The Big Bang gave rise to the expansion of space-time: space itself (together with time) expands, carrying galaxies with it.

Evidence:

• Galactic red shift and Hubble’s law: the universe is expanding, as above.
• Cosmic microwave background (CMB) radiation: radiation reaching us equally from all directions, with a spectrum corresponding to a temperature of 2.7 K, in the microwave region. It is the radiation released when the early universe became transparent. As space expanded, its wavelength stretched from a much shorter wavelength and the equivalent temperature fell, so it was predicted to be a cold relic of the hot early universe. Its detection, and its near-uniformity in every direction, matched the prediction.

Scientific acceptance of the theory grew as predictions were tested, with the CMB a major turning point. A different, steady-state idea had no natural explanation for the CMB.

Age of the universe (5.5.3(m))

If galaxies have always moved at constant speed, a galaxy now at distance d travelling at v = H0 d took t = d/v to arrive:

t ≈ 1/H0

with H0 in s⁻¹ (an order-of-magnitude estimate, as the specification’s M1.4 reference suggests).

Worked example 6. For H0 = 70 km s⁻¹ Mpc⁻¹: 1/H0 = 1 / 2.27 × 10⁻¹⁸ = 4.41 × 10¹⁷ s. With 1 year = 3.16 × 10⁷ s, t = 1.40 × 10¹⁰ years, about 14 billion years. A larger H0 gives a younger universe. The estimate ignores any change in expansion rate, so it is an estimate only.

Evolution of the universe, and what it is made of (5.5.3(n), (o))

In outline, from the Big Bang to now:

1. Very early: extreme temperature and density; space-time begins expanding rapidly.
2. Within seconds: the universe cools; quarks combine into protons and neutrons.
3. After a few minutes: nuclear fusion forms light nuclei, mainly hydrogen and helium.
4. After a few hundred thousand years: cooled enough for electrons to join nuclei and form atoms. Radiation travels freely: this is the CMB.
5. After hundreds of millions of years: gravity pulls gas into the first stars and galaxies. Later stars make heavier elements.
6. About 4.6 billion years ago: the Solar System forms. Today: about 13.8 billion years after the Big Bang.

Current ideas say the universe is roughly 68% dark energy, 27% dark matter and 5% ordinary matter (the matter of stars, planets and people). Dark matter does not emit light but has gravitational effects, for example galaxies rotating faster than visible matter alone can explain. Dark energy is a name for whatever is making the expansion accelerate. Neither is yet explained.

Common errors

• Writing a light-year as a time, or using 1 pc = 1 ly.
• Using p = 1/d with p in degrees or radians. It needs seconds of arc and parsec.
• Using the full Earth-orbit angle as p instead of half.
• Saying the galaxies move through space away from a central point. The expansion has no centre.
• Forgetting to convert Mpc to km before finding H0 in s⁻¹.
• Calling the Big Bang an explosion in space.

Official syllabus

OCR Advanced GCE in Physics A (H556), Version 3.0 (March 2026), first assessment 2017, published by OCR. Section 5.5.3, Cosmology.