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

These notes condense section 5.5.3 (Cosmology) of the OCR Advanced GCE in Physics A specification (H556), Version 3.0 (March 2026), first assessment 2017. Read the full study guide for explanations, then test yourself with the practice questions. Course links: OCR A Level Physics hub, printable checklist and free 10-minute diagnostics.

Units of distance (5.5.3(a))

Unit	Meaning	Value
Astronomical unit (AU)	Mean Earth-Sun distance	1.50 × 10¹¹ m
Light-year (ly)	Distance light travels in a vacuum in one year	9.46 × 10¹⁵ m
Parsec (pc)	Distance at which a star has a parallax of 1 second of arc	3.09 × 10¹⁶ m

• 1 pc ≈ 3.26 ly; 1 Mpc = 10⁶ pc ≈ 3.09 × 10²² m.
• 1 second of arc = 1/3600 degree = 4.85 × 10⁻⁶ rad. Small-angle idea: 1 AU / 4.85 × 10⁻⁶ rad gives 1 pc.
• A light-year is a distance, never a time.

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

Method in steps:

1. Record the star’s position against distant background stars.
2. Record it again six months later, at the opposite side of the Earth’s orbit.
3. Halve the total angular shift to get the parallax angle p.
4. Convert to seconds of arc, then use d = 1/p to get d in parsec.

Quantity	Unit
p = 1/d	p in seconds of arc, d in pc

• Small p means a large d. Only relatively nearby stars have a measurable p.
• Worked reminder: p = 0.20 seconds of arc gives d = 5.0 pc, which is 16 ly (5.0 × 3.26 = 16.3).

Cosmological principle (5.5.3(d))

On a large scale the universe is homogeneous (same average everywhere), isotropic (same in all directions) and obeys the same physical laws everywhere. No place is special, so expansion has no centre.

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

Result	Meaning
Δλ/λ ≈ Δf/f ≈ v/c	For v much less than c
Positive Δλ	Source receding: red shift
Negative Δλ	Source approaching: blue shift

Method in steps:

1. Identify a known spectral line and its laboratory wavelength λ.
2. Find Δλ = observed minus laboratory wavelength.
3. Compute v = c × Δλ/λ with c = 3.00 × 10⁸ m s⁻¹.

Worked reminder: a line at 486.1 nm is observed at 488.5 nm. Δλ = 2.4 nm, so v = 3.00 × 10⁸ × 2.4 / 486.1 = 1.5 × 10⁶ m s⁻¹, receding.

Hubble’s law and H0 (5.5.3(g), (h), (i))

Result	Meaning
v ≈ H0 d	Recession speed proportional to distance
Graph of v against d	Straight line through the origin, gradient H0
H0 in km s⁻¹ Mpc⁻¹	Typical value used here: 70
H0 in s⁻¹	Divide by km per Mpc (3.09 × 10¹⁹)

• Worked reminder: 70 km s⁻¹ Mpc⁻¹ is 70 / 3.09 × 10¹⁹ = 2.27 × 10⁻¹⁸ s⁻¹.
• Expanding universe: all distant galaxies are red-shifted, more so the further away they are. The pattern is the same from any galaxy, so there is no centre. Balloon analogy: dots on a balloon move apart as it inflates.
• Fit a straight line through the origin through the data points. Do not join the end points.

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

• Theory: the universe began about 14 billion years ago in a tiny, very hot, very dense state and has been expanding and cooling since. It is not an explosion into existing space. Space-time itself expands.
• Evidence 1: galactic red shift and Hubble’s law (expansion).
• Evidence 2: the cosmic microwave background, observed from all directions at a temperature of 2.7 K, matching the prediction for radiation left from the hot early universe, stretched to longer wavelength by expansion.
• Acceptance grew as the CMB was found and the theory’s predictions were tested.

Age of the universe (5.5.3(m))

Result	Condition
t ≈ 1/H0	H0 in s⁻¹; assumes constant expansion rate

Method: convert H0 to s⁻¹, take the reciprocal, divide by 3.16 × 10⁷ s per year. A larger H0 gives a younger universe. It is an estimate only.

Evolution and composition (5.5.3(n), (o))

Stage	What happens
Earliest moments	Extremely hot and dense; rapid expansion
Seconds	Quarks form protons and neutrons
Minutes	Fusion makes light nuclei (hydrogen, helium)
Hundreds of thousands of years	Atoms form; radiation travels freely (the CMB)
Hundreds of millions of years	First stars and galaxies
Billions of years	Heavier elements made in stars; Solar System forms about 4.6 billion years ago

Composition: roughly 68% dark energy, 27% dark matter, 5% ordinary matter. Dark matter has gravitational effects but gives out no light. Dark energy is associated with accelerating expansion. Ordinary matter is the smallest share, so most of the universe is not made of the atoms we know. Both dark components are current ideas rather than settled explanations, and a good answer says so. Do not claim to know what either one is.

Worked reminder: H0 = 68 km s⁻¹ Mpc⁻¹ is 68 / 3.09 × 10¹⁹ = 2.20 × 10⁻¹⁸ s⁻¹. Then 1/H0 = 4.55 × 10¹⁷ s, which is 1.44 × 10¹⁰ years (about 14 billion).

Answer templates for written questions

• Explain how red shift shows the universe is expanding: the light from distant galaxies has longer wavelength than the same lines measured on Earth; the shift increases with distance; so the speed of recession increases with distance, as a uniform expansion would produce; the pattern would be the same from any galaxy.
• Explain why the CMB supports the Big Bang: the early universe was hot and dense and full of radiation; expansion stretched the wavelengths and cooled it; the prediction is a uniform glow of microwaves from every direction at a low temperature, and 2.7 K is what is detected.
• Explain how parallax gives distance: observe at opposite points of the Earth’s orbit, find the angle p, then use d = 1/p.
• State the Cosmological principle: homogeneous, isotropic, laws of physics universal.

Must-know distinctions

• Parallax angle (half the shift) versus total shift.
• Doppler red shift of a moving source versus the stretching of wavelength by expanding space.
• Observable evidence (red shift, CMB) versus theory (Big Bang).
• Dark matter (extra gravity) versus dark energy (accelerating expansion).

Quick self-test

1. Give 2.5 ly in metres.
2. A star has a parallax of 0.40 seconds of arc. Find its distance in pc.
3. Find the parallax of a star 5.0 pc away.
4. A galaxy’s lines show Δλ/λ = 0.0072. Find its recession speed.
5. Use H0 = 70 km s⁻¹ Mpc⁻¹ to find the speed of a galaxy 30 Mpc away.
6. A galaxy 300 Mpc away recedes at 21 000 km s⁻¹. Find H0.
7. Convert 75 km s⁻¹ Mpc⁻¹ to s⁻¹.
8. Estimate the age of the universe, in years, if H0 = 2.0 × 10⁻¹⁸ s⁻¹.
9. State the Cosmological principle.
10. State the temperature of the CMB and say what it supports.
11. A line of 500 nm from a source receding at 6.0 × 10⁶ m s⁻¹: find Δλ.
12. Name the three components of the universe in order of share.

Answers

1. 2.5 × 9.46 × 10¹⁵ = 2.4 × 10¹⁶ m (2.37 × 10¹⁶ m).
2. d = 1/0.40 = 2.5 pc.
3. p = 1/5.0 = 0.20 seconds of arc.
4. v = 0.0072 × 3.00 × 10⁸ = 2.2 × 10⁶ m s⁻¹.
5. v = 70 × 30 = 2100 km s⁻¹.
6. H0 = 21 000 / 300 = 70 km s⁻¹ Mpc⁻¹.
7. 75 / 3.09 × 10¹⁹ = 2.4 × 10⁻¹⁸ s⁻¹.
8. 1/H0 = 5.0 × 10¹⁷ s; divided by 3.16 × 10⁷ gives 1.6 × 10¹⁰ years.
9. The universe is homogeneous and isotropic on a large scale, and the laws of physics are the same everywhere.
10. 2.7 K; it supports the Big Bang theory (hot early universe that has expanded and cooled).
11. Δλ = λ v/c = 500 × 6.0 × 10⁶ / 3.00 × 10⁸ = 10 nm.
12. Dark energy, dark matter, ordinary matter.

Where marks are usually lost

• Giving a light-year as a unit of time.
• Putting p in degrees, or quoting d in light-years, in p = 1/d.
• Using the whole shift instead of half for the parallax angle.
• Leaving Mpc unconverted when asked for H0 in s⁻¹, or forgetting that km also needs converting.
• Finding H0 from only the last data point when asked to use the whole graph.
• Saying “the galaxies are moving away from us” without saying the same would be seen from any galaxy.
• Describing the Big Bang as an explosion in space.
• Using t = 1/H0 with H0 still in km s⁻¹ Mpc⁻¹.
• Describing the CMB as a “cold spot” rather than radiation arriving from all directions.

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.