Physics 9702 · syllabus 25
Cambridge A Level Physics 9702 — Astronomy and cosmology topical past papers
Measuring the Universe: luminosity, standard candles and the inverse square law, stellar temperatures and radii, redshift, Hubble's law and the Big Bang.
- Questions
- 27
- Years
- 2022–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 27
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What Astronomy and cosmology covers
A star's luminosity is the total power it radiates. Spread over a sphere, that power gives a radiant flux intensity F = L/(4πd²) at a distance d, so if you know an object's luminosity, which makes it a standard candle, measuring F gives its distance. Standard candles such as Cepheid variable stars and type Ia supernovae are how distances to other galaxies are found.
A star's spectrum peaks at a wavelength inversely proportional to its surface temperature, which is Wien's displacement law, λₘₐₓ ∝ 1/T. The Stefan–Boltzmann law, L = 4πσr²T⁴, links luminosity, radius and temperature, so combining it with Wien's law lets you estimate the radius of a star far too distant to be seen as a disc.
Spectral lines from distant galaxies appear at longer wavelengths than in the laboratory. This redshift, Δλ/λ ≈ v/c, shows that the galaxies are receding, and Hubble's law, v ≈ H₀d, shows that more distant galaxies recede faster: evidence that the Universe is expanding from a hot, dense beginning, the Big Bang. This A Level topic is examined on Paper 4, with the Hubble constant used in SI units, s⁻¹.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 25 Astronomy and cosmology
- 25.1 Standard candles
- 25.2 Stellar radii
- 25.3 Hubble's law and the Big Bang theory
What you should be able to do
- Use F = L/(4πd²) to find a distance from a standard candle's luminosity
- Explain what a standard candle is and how standard candles give the distances to galaxies
- Use Wien's displacement law to estimate a star's surface temperature
- Combine the Stefan–Boltzmann law with Wien's law to estimate the radius of a star
- Calculate a recession speed from redshift using Δλ/λ ≈ Δf/f ≈ v/c
- Use Hubble's law and explain how redshift supports an expanding Universe and the Big Bang theory
Key ideas
- Radiant flux intensity F = L/(4πd²) (W m⁻²)
- Wien's displacement law λₘₐₓ ∝ 1/T, so λₘₐₓT is constant (about 2.9 × 10⁻³ m K)
- Stefan–Boltzmann law L = 4πσr²T⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
- Redshift Δλ/λ ≈ Δf/f ≈ v/c
- Hubble's law v ≈ H₀d, with H₀ in s⁻¹
How Astronomy and cosmology has been examined
From 2022 to 2026, Astronomy and cosmology was on Paper 4 · A Level Structured Questions in 11 of 11 exam series, worth about 8% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 4 · A Level Structured Questions | 27 | 8% | 11 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 9.
Filed in Momentum under: Astronomy & Cosmology.
A worked example
A star's spectrum peaks at a wavelength of 290 nm and its luminosity is 2.0 × 10²⁸ W. Taking Wien's constant as 2.9 × 10⁻³ m K, estimate the star's surface temperature and radius.
- Wien's law: T = 2.9 × 10⁻³ / 290 × 10⁻⁹ = 1.0 × 10⁴ K
- Stefan–Boltzmann law: L = 4πσr²T⁴, so r = √(L / 4πσT⁴)
- 4πσT⁴ = 4π × 5.67 × 10⁻⁸ × (1.0 × 10⁴)⁴ = 7.13 × 10⁹ W m⁻²
- r = √(2.0 × 10²⁸ / 7.13 × 10⁹) = √(2.81 × 10¹⁸) = 1.7 × 10⁹ m
Answer: Surface temperature 1.0 × 10⁴ K; radius 1.7 × 10⁹ m, about 2.4 times the Sun's
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Using the observed wavelength as λ in Δλ/λ — λ is the emitted wavelength, as measured in the laboratory, and Δλ is the shift
- Forgetting the fourth power of T, or the square of r, in L = 4πσr²T⁴ — a star twice as hot with the same radius is sixteen times as luminous
- Mixing distance units in Hubble's law — with H₀ in s⁻¹, d must be in metres and v in m s⁻¹
- Confusing radiant flux intensity with luminosity — luminosity is the star's total power output; flux intensity is the power arriving per square metre at the observer
Exam technique
- When estimating a radius, find T from Wien's law first, then rearrange L = 4πσr²T⁴ for r before substituting
- In 'explain how redshift supports the Big Bang' answers, go in order: lines are redshifted, so galaxies recede; recession speed is proportional to distance, so the Universe is expanding; running the expansion backwards points to a hot, dense beginning
- Keep large powers of ten in standard form, and compare a stellar radius with the Sun's, about 7 × 10⁸ m, as a check on the order of magnitude
Practising in Momentum
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