Astrophysics and cosmology

What the syllabus demands

• —Interpret black-body spectra and connect peak wavelength, surface temperature and emitted power.
• —Use Stefan–Boltzmann and inverse-square relationships to distinguish a star's luminosity from received intensity.
• —Explain distance measurements using parallax and standard candles.
• —Read Hertzsprung–Russell diagrams and connect stellar temperature, luminosity and evolution.
• —Use Doppler shifts, cosmological redshift and Hubble's relationship with appropriate units and approximations.
• —Discuss how uncertainty in expansion and the amount of gravitating matter affects cosmological models.

Definitions that earn marks

Clear definitions to practise — check your course mark scheme

Luminosity, L

A source's total radiant power, measured in watts. It describes the source itself, rather than the power received by one detector.

Received intensity, I

Radiant power received per unit area, measured in W/m². For the same source it decreases as distance increases.

Black body

An ideal object that absorbs all incident electromagnetic radiation and emits a thermal spectrum determined by its temperature.

Standard candle

An astronomical source whose luminosity can be established, allowing its distance to be inferred from its received intensity.

Stellar parallax

The apparent shift of a nearby star against more distant stars when viewed from different positions in Earth's orbit.

Redshift, z

The fractional wavelength increase: observed minus emitted wavelength, divided by emitted wavelength. It is dimensionless.

The equations

More equations to practise: the Edexcel IAL formula sheet.

Where the marks die

Common mistakes to check

1. 01

   Substituting degrees Celsius into T⁴. Convert to kelvin first. A small temperature error can have a large effect because the luminosity depends on the fourth power.

2. 02

   Using πR² as the emitting area of a star. That is the area of its projected disc; the complete spherical surface has area 4πR². The much larger 4πd² describes how the radiation spreads before reaching a detector.

3. 03

   Calling a dim-looking star low-luminosity without considering distance. A luminous source far away can deliver less intensity than a weak source nearby. A standard candle is useful because its luminosity is established independently.

4. 04

   Reading an H–R diagram as if temperature rises to the right. Conventionally it decreases to the right; luminosity increases upward. Giants are luminous despite relatively cool surfaces because they are large, while white dwarfs can be hot but faint because they are small.

5. 05

   Using the full six-month parallax displacement as p. The parallax angle is half that shift. A smaller parallax means a greater distance, and the measurement becomes harder as that angle shrinks.

6. 06

   Dividing a wavelength change by the observed wavelength. The redshift definition uses the emitted, laboratory wavelength. Apply v ≈ cz only when the small-redshift approximation is appropriate.

7. 07

   Inverting H₀ in km/s/Mpc and labelling the answer seconds. Convert the megaparsec to kilometres first, or convert the whole constant to s⁻¹. A quoted numerical value without its units is not enough.

One worked example, done properly