Astronomy and Cosmology · revision map · A-Level 9702, Topic 25
TOPIC 25 · ASTRONOMY AND COSMOLOGY
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
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ASTRONOMY & COSMOLOGY25
Standard Candles
A known brightness gives a distance.
- Luminosity L: total power radiated by a star (W).
- Radiant flux intensity F: power per unit area reaching us (W m−²).
- A standard candle has a known L, so measuring F fixes the distance d to its galaxy.
- Examples: Cepheid variables and type Ia supernovae, whose L is known from their behaviour.
F = L / (4πd²)
inverse-square law
F is also written as intensity
F is also written as intensity
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's law fixes T from the peak wavelength λmax.
- Stefan-Boltzmann links L, radius r and T, so L and T give r.
- σ is the Stefan-Boltzmann constant; L treats the star as a sphere of area 4πr².
λmax T = constant
L = 4πσr²T⁴
Hubble's Law & the Big Bang
Galaxies recede; the Universe expands.
- Spectral lines from galaxies are redshifted: λ is stretched, so the galaxy moves away.
- The fractional shift gives the recession speed v (for v much less than c).
- Recession speed v rises in proportion to distance d (Hubble's law).
- Reverse the expansion: a hot, dense origin, the Big Bang, of age ≈ 1 / H₀.
Δλ/λ ≈ v/c
v = H₀d
H₀ is Hubble's constant, the gradient of the v against d line
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 Hubble's constant for the age of the Universe.
Light carries the numbers, luminosity, spectrum and redshift, that measure the Universe.
each rung calibrates the next, from nearby candles to distant redshifts