LucidSTEM
A-LEVEL 9702 · A2 · TOPIC 25
Astronomy and cosmology
The chain of the topic: a star's luminosity plus the inverse-square law turns a standard candle into a distance; its spectrum, through Wien's law and Stefan-Boltzmann, fixes its radius; and the redshift of distant galaxies feeds Hubble's law, the expanding Universe and the Big Bang. Around the hexagon are the three ideas; above is what it builds on, below is where it leads.
TOPIC 25: ASTRONOMY AND COSMOLOGY
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T22 Photons & spectra T7 Waves & the Doppler shift T13 Gravitation & stellar mass 25.1
25.2
25.3
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TOPIC 25
ASTRONOMY
& COSMOLOGY
1 · STANDARD CANDLES
Known brightness gives distance.
Luminosity L: total power radiated by a star (W).
Radiant flux F: power per unit area reaching us.
A standard candle has a known L, so measuring F
fixes the distance d to its galaxy.
F = L / (4πd²)
inverse-square law
L
power spreads over a sphere 4πd²
so flux F falls as 1 / d² with distance d
2 · STELLAR RADII
The spectrum reveals temperature, then size.
A star radiates as a black body; the peak shifts
to shorter λ as the surface gets hotter.
Wien fixes T; Stefan-Boltzmann links L, r and T.
Knowing L and T then yields the radius r.
λmax ∝ 1 / T
L = 4πσr²T⁴
intensity
λ
hotter
cooler
peak λ moves left as T rises
3 · HUBBLE'S LAW & THE BIG BANG
Galaxies recede; the Universe expands.
Spectral lines from galaxies are redshifted: λ is
stretched, so the galaxy is moving away.
Recession speed v rises with distance d (Hubble).
Reverse the expansion: a hot, dense origin, the
Big Bang, of age ≈ 1 / H₀.
Δλ/λ ≈ Δf/f ≈ v/c
v = H₀d
v
d
gradient = H₀
4 · MEASURING THE UNIVERSE
Chain the relations to reach cosmic scales.
From F and a known L get distance d (candle).
From the spectrum get T (Wien), then r (Stefan).
From redshift get v, then far d via v = H₀d.
Invert the constant for the age of the Universe.
d → r → v → H₀ → age
candle
radius
redshift
a distance ladder out to cosmic scales
LEADS TO
T23 Nuclear physics: fusion that powers a star's L T13 Gravitation: dark matter from orbital dynamics T22 Quantum: spectral lines identify the elements One thread runs through: light carries the numbers, luminosity, spectrum and redshift, that measure the Universe.
← Builds on IGCSE: Stars & the Universe