Astronomy and Cosmology

This guide covers Topic 25, Astronomy and cosmology, in full — subtopics 25.1 Standard candles, 25.2 Stellar radii and 25.3 Hubble’s law and the Big Bang theory — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is the final A Level topic, completing the full 9702 syllabus, and draws on radiation and wave concepts from earlier in the course.

Before studying this

This resource assumes the electromagnetic spectrum from Waves: Progressive Waves, the Doppler Effect and Polarisation, and photon energy from Quantum Physics.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — A Level, Topic 25

25.1 Standard candles — understanding that a standard candle is any astronomical object that has a known luminosity; understanding that the luminosity of an object may be determined using the Stefan-Boltzmann law; understanding that the luminosity of a star may be estimated by assuming it is a standard candle; recalling and using the inverse square law for radiant flux intensity F = L/(4πd²) in relation to standard candles.

25.2 Stellar radii — using Wien’s law λₘₐₓT = constant to estimate the peak surface temperature of a star; recalling and using the Stefan-Boltzmann law L = 4πr²σT⁴, combined with Wien’s law, to estimate the radius of a star, given its luminosity and temperature.

25.3 Hubble’s law and the Big Bang theory — recalling that the Doppler effect may be used to determine the recession speeds of galaxies; recalling and using Δλ/λ ≈ Δf/f ≈ v/c for the redshift of electromagnetic radiation from a receding source; recalling and using Hubble’s law v = H₀d; understanding that the Hubble constant and Hubble’s law are consistent with the Big Bang theory for the origin of the universe.

Luminosity and standard candles

A star’s luminosity L is the total power it radiates, related to its radius r and surface temperature T by the Stefan-Boltzmann law:

L = 4πr²σT⁴

where σ is the Stefan-Boltzmann constant. A standard candle is any astronomical object whose luminosity is already known (or can be reliably assumed), so that measuring how bright it appears from Earth allows its distance to be calculated.

Radiant flux intensity and distance

The radiant flux intensity F (how bright an object appears, i.e. power received per unit area) falls off with the square of distance:

F = L / (4πd²)

If an object’s luminosity L is known (it is a standard candle) and its flux F can be measured from Earth, this equation can be rearranged to find its distance d — the basis of the standard-candle distance-measurement method used throughout astronomy.

Worked example. A standard candle has luminosity 4.0 × 10²⁶ W and is measured to have flux 1.0 × 10⁻¹² W m⁻² at Earth. Its distance:

d = √(L / 4πF) = √(4.0 × 10²⁶ / (4π × 1.0 × 10⁻¹²)) ≈ 5.64 × 10¹⁸ m

Stellar radii

Wien’s law relates a star’s peak emission wavelength λₘₐₓ to its surface temperature:

λₘₐₓT = constant

Measuring a star’s spectrum gives λₘₐₓ, and hence its temperature T via Wien’s law. Combining this temperature with the star’s luminosity (determined, for example, via the standard-candle method) in the Stefan-Boltzmann law, L = 4πr²σT⁴, allows the star’s radius r to be calculated — a two-step method connecting the two laws covered in this topic.

The Doppler effect and redshift

Light from a receding astronomical source is shifted to longer wavelengths (redshift), an application of the Doppler effect to electromagnetic waves:

Δλ/λ ≈ Δf/f ≈ v/c

where v is the recession speed of the source and c is the speed of light. Measuring the redshift of light from a distant galaxy therefore gives its recession speed.

Hubble’s law and the Big Bang

Hubble’s law states that a galaxy’s recession speed is proportional to its distance from Earth:

v = H₀d

where H₀ is the Hubble constant. Its value is not precisely known, but it is of the order of 2.3 × 10⁻¹⁸ s⁻¹ — the syllabus expects the constant in this base SI form, though it is often quoted in astronomy as roughly 70 km s⁻¹ Mpc⁻¹ (the two are equivalent: 70 km s⁻¹ Mpc⁻¹ converts to base units via 1 Mpc = 3.086 × 10²² m). Because more distant galaxies recede faster, Hubble’s law is direct observational evidence that the universe is expanding — and running this expansion backward in time implies the universe originated from an extremely small, dense state at a finite time in the past, consistent with the Big Bang theory. (As background beyond what the syllabus requires: the reciprocal of the Hubble constant, 1/H₀, gives an order-of-magnitude estimate for the age of the universe.)

Common mistakes

• Confusing luminosity (total power radiated, in watts) with radiant flux intensity (power received per unit area at a given distance, in W m⁻²) — these are related by the inverse square law but are not the same quantity.
• Applying Wien’s law and the Stefan-Boltzmann law independently without connecting them — finding a stellar radius requires combining temperature from Wien’s law with luminosity in the Stefan-Boltzmann law.
• Treating the Hubble constant as a precisely known, fixed number — the syllabus explicitly notes it is not well known, only of the order of 2.3 × 10⁻¹⁸ s⁻¹ (about 70 km s⁻¹ Mpc⁻¹).
• Assuming redshift implies motion through space in the everyday sense rather than the large-scale expansion of space itself — a subtlety beyond what is required at this level, but worth being aware of conceptually.

Quick revision checklist

• L = 4πr²σT⁴ (Stefan-Boltzmann law, stellar radii) and F = L/(4πd²) (inverse square law, standard candles)
• Combining Wien’s law (λₘₐₓT = constant) with the Stefan-Boltzmann law to find stellar radius
• Δλ/λ ≈ v/c for redshift, and v = H₀d for Hubble’s law
• Hubble’s law as evidence for universal expansion and the Big Bang theory

Related resources

• Medical Physics — the previous A Level topic
• Cambridge AS & A Level Physics hub — the complete syllabus, now fully covered

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.