The big idea: Sort a pile of light bulbs by how much power they draw and what colour they glow, and they cluster into families — dim warm ones here, bright white ones there. Astronomers sort stars the same way on the Hertzsprung-Russell (H-R) diagram, a graph of luminosity against surface temperature.
Where a star sits tells you what type of star it is, and lets you compare stars' temperatures, sizes and brightnesses at a glance.
One odd thing to remember: temperature runs backwards — hot stars are on the left, cool ones on the right.
The Hertzsprung-Russell (H-R) diagram. Watch the axes: temperature runs the WRONG way — hot on the LEFT, cool on the right; luminosity increases UPWARD. Most stars sit on the diagonal main-sequence band; cool-but-bright red giants and supergiants are top-right, and hot-but-dim white dwarfs are bottom-left. The Sun is an ordinary main-sequence star.
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New words, plainly: Luminosity (L) = the total power a star radiates, in watts. (Not how bright it looks from Earth — that also depends on distance.)
Main sequence = the diagonal band where ordinary stars, fusing hydrogen, spend most of their lives. The Sun is on it.
Red giant / supergiant = a huge, cool, very luminous star (top-right). White dwarf = a tiny, hot, dim leftover core (bottom-left).
| Where it sits on the diagram | Star type | What that tells you |
|---|---|---|
| On the diagonal band through the middle | Main-sequence star (like the Sun) | Fusing hydrogen; hotter ones are brighter |
| Top-right (cool but very bright) | Red giant | Cool surface, but huge → still very luminous |
| Very top (extremely bright) | Supergiant | Enormous and the most luminous of all |
| Bottom-left (hot but very dim) | White dwarf | Hot surface, but tiny → very low luminosity |
How to read a position: Left ↔ right tells you the temperature (left = hotter).
Up ↔ down tells you the luminosity (up = brighter).
Off the main sequence? Top-right means big and cool (a giant); bottom-left means small and hot (a white dwarf).
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A star's position fixes its size too. Two stars with the same luminosity but different temperatures must have different radii — the cooler one has to be bigger to radiate just as much power.
Hot star (left side)
- High surface temperature T
- Each square metre glows fiercely (L per area = σT⁴)
- For a given luminosity it can be small
Cool star (right side)
- Low surface temperature T
- Each square metre glows faintly
- To match the same luminosity it must be much bigger
- luminosity — total power the star radiates (W)
- Stefan-Boltzmann constant, 5.67 × 10⁻⁸ W m⁻² K⁻⁴ (given constant)
- surface area of the star, 4πr² for a sphere (m²)
- surface (absolute) temperature of the star (K)
- radius of the star (m)
Comparing to the Sun — the shortcut: Since L = 4πr²σT⁴, for two stars the σ and 4π cancel, so L ∝ r²T⁴.
Compare any star to the Sun and rearrange for the radius:
Rstar / Rsun = (Tsun / Tstar)² × √(Lstar / Lsun)
Work in units of the Sun (L in Lsun, T in K) and you never need σ at all.
A red giant has luminosity L = 8100 Lsun and surface temperature T = 2900 K. The Sun's surface temperature is 5800 K. Determine how many times bigger than the Sun this star is. (Use Rstar/Rsun = (Tsun/Tstar)² × √(Lstar/Lsun).)
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How this is tested — the H-R diagram appears on both papers:
Paper 1A
- Identify / determine: read two stars' positions and compare their temperature, luminosity and radius.
- Or calculate the ratio of two radii from their L and T using L ∝ r²T⁴.
Paper 2
- State / sketch: state a star's type from its position.
- Or sketch where a star sits relative to the Sun, given its radius and temperature.
The classic trap: The temperature axis runs backwards (hot on the LEFT). And a star being far up (luminous) does not make it hot — red giants are cool but bright because they are huge.
Two stars are plotted on an H-R diagram. Star X has luminosity 6400 Lsun and surface temperature 4350 K. Compared with the Sun (temperature 5800 K), determine the radius of Star X as a multiple of the Sun's radius. (Use Rstar/Rsun = (Tsun/Tstar)² × √(Lstar/Lsun).)
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On an H-R diagram, Star P sits at the bottom-left (hot, very low luminosity) and Star Q sits at the top-right (cool, very high luminosity). (a) State the type of each star. (b) State which star has the larger radius, with a reason.
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