Classification by Luminosity — Quick Summary

Mr Toogood's Physics · Astrophysics

AQA 3.9.2.1 / 3.9.2.2
1 pc = 3.26 ly
Parsec definition
θ = 1AU/D
Parallax angle
I = L/4πr²
Inverse square law
m−M=5log(d/10)
Distance modulus

Distance units

  • Light year: distance light travels in 1 year = 9.46×10¹⁵ m.
  • Parsec: distance at which 1 AU subtends a parallax angle of exactly 1 arcsec = 3.26 ly = 3.09×10¹⁶ m.

Parallax

Diagram showing how a nearby star's parallax angle is measured from opposite points in Earth's orbit

A nearby star shifts against distant background stars as Earth orbits the Sun.

Observing a nearby star from two points in Earth's orbit (6 months apart) against the fixed background of distant stars gives the parallax angle, θ:

θ = 1AU / D  (small-angle approx., θ in radians)
Limitation: atmospheric distortion limits ground-based parallax to θ ≳ 0.01 arcsec, i.e. distances up to ~100 pc. Space telescopes improve on this.

The magnitude scale

  • Apparent magnitude (m): how bright a star appears from Earth (Hipparcos scale: 1 = brightest, 6 = dimmest visible to the naked eye). Lower m = brighter.
  • Each step of 1 magnitude = a brightness ratio of 100^(1/5) ≈ 2.51.
Diagram of the inverse square law showing intensity falling off with distance from a star

Intensity falls off as 1/r² as radiation spreads over an expanding sphere.

Luminosity (L) = total power output of a star (W) — its true, intrinsic brightness, independent of distance.

Absolute magnitude & distance modulus

Absolute magnitude (M): the apparent magnitude a star would have if viewed from exactly 10 pc — lets astronomers compare true luminosities directly.

Distance modulus, m−M: if m < M the star is closer than 10 pc; if m > M it's further than 10 pc. Rearranging m−M=5log(d/10) gives the distance.

Standard candles

Light curve of a Cepheid variable star, showing its periodic brightness variation

Cepheid variables: period of brightness variation links directly to peak absolute magnitude.

  • Cepheid variables: period–luminosity relationship gives M from the measured period; used by Hubble to prove other galaxies exist.
  • Type 1a supernovae: always the same peak absolute magnitude (M≈−19) — a "standard candle" bright enough to measure vast, galaxy-scale distances.

Exam essentials

Key equations

  • 1pc=3.26ly=3.09×10¹⁶m
  • θ=1AU/D
  • m−M=5log(d/10)
  • I=L/4πr²

Interpreting m and M

  • Comparing m and M for two stars tells you about relative distance, not just brightness.
  • Similar apparent magnitude but very different absolute magnitude → very different distances.

Common slips

  • Lower magnitude = brighter — the scale is inverted, don't assume "bigger number = brighter."
  • Keep d in parsecs in the distance modulus equation.
  • Don't round intermediate steps (e.g. m−M) before the final log calculation.