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Medical physics and astronomy (A Level)

25. Astronomy and Cosmology

5 min read 9 parts Lesson 22 of 22 Unit quiz

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25. Astronomy and Cosmology — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Use luminosity, standard candles, Wien's and Stefan–Boltzmann laws, redshift and Hubble's law to find distances, temperatures, radii and the age of the …

  • Luminosity L
  • Radiant flux F
  • Difference
  • Spreading of light
  • Assumptions
  • Use of distance

Section 1 of 9Luminosity and radiant flux

  • Luminosity L = the total power radiated by a star, in watts.
  • Radiant flux F = the power per unit area received normally at the observer, in W m−2.
  • Difference
    • luminosity is the whole output at the star, while the radiant flux is the small fraction reaching a unit area on Earth after spreading out.

Section 2 of 9Inverse square law of flux

  • Spreading of light
    • the star's radiation spreads evenly over a sphere of surface area 4πd2, where d is the distance to the star.
  • Equation
    • F = L/(4πd2).
    • A star twice as far away gives one quarter of the flux.
    • A larger measured F means the star is closer.
  • Assumptions
    • uniform radiation and no absorption between the star and Earth.
  • Use of distance
    • d is the distance to the star, not the star's radius.

Section 3 of 9Standard candles and stellar distances

  • Standard candle = an astronomical object whose luminosity is known because of a characteristic property of its class.
  • Cepheid variable stars
    • pulsating stars whose brightness varies periodically, with a period related to their luminosity.
  • Type 1a supernovae
    • explosions of a white dwarf in a binary pair that always reach the same peak luminosity.
  • Method
    • measure the flux F received, use the known L and calculate d from the inverse square law.
  • Distance ladder
    • parallax works only for nearby stars, so overlapping standard-candle methods, each covering a range, build the scale out to distant galaxies.
  • Comparison
    • type 1a supernovae are far more luminous than Cepheids, so they are visible and usable in the most distant galaxies.

Section 4 of 9Wien's displacement law

  • Black body = an object that absorbs all radiation falling on it, reflecting and transmitting none, and is a good emitter.
    • Stars are the best approximation, and the spectrum depends only on temperature.
  • Wien's law
    • the peak wavelength is inversely proportional to the surface temperature, λmaxT = 2.9 × 10−3 m K.
    • A hotter body has a shorter peak wavelength and a greater intensity at every wavelength.
    • Temperature must be in kelvin.
  • Colour and temperature
    • hotter stars are blue or white and cooler stars are yellow or red, such as Betelgeuse in Orion.
ColourTemperature / K
Blueabove 33 000
Blue-white10 000 – 30 000
White7500 – 10 000
Yellow-white6000 – 7500
Yellow5000 – 6000
Orange3500 – 5000
Redbelow 3500

Section 5 of 9Stefan–Boltzmann law and stellar radii

  • Stefan–Boltzmann law = the total energy emitted per unit area per second by a black body is proportional to the fourth power of its absolute temperature.
  • Luminosity
    • L = 4πr2σT4, where r is the star's radius and σ = 5.67 × 10−8 W m−2 K−4.
    • Luminosity depends on both surface temperature and radius, so a cool star can be very luminous if it is huge.
  • Finding a radius:
  1. Use Wien's law to find the surface temperature from the peak wavelength.
  2. Find the luminosity, from the inverse square law if flux and distance are given.
  3. Rearrange to r √[L/(4πσT4)].

Section 6 of 9Spectra of stars and galaxies

  • Information
    • astronomers study space only through the radiation arriving from it, including emission and absorption spectra.
  • Absorption lines
    • hydrogen and helium in a star absorb particular wavelengths, giving characteristic lines.
  • Distant galaxies
    • the same pattern of lines appears but shifted to longer wavelengths towards the red end.
    • The pattern identifies the element and the shift gives the speed.

Section 7 of 9Doppler redshift

  • Doppler effect = the apparent change in wavelength or frequency of radiation caused by relative motion of source and observer.
  • Redshift
    • the source is receding, so the wavelength increases and the frequency decreases.
  • Blueshift
    • the source is approaching.
  • Equation (non-relativistic)
    • Δλ/λ ≈ Δf/f ≈ v/c.
  • Wording
    • the wavelengths of spectral lines increase towards the red end, and the lines do not literally "become red".

Section 8 of 9The expanding universe and Hubble's law

  • Expansion
    • nearly all galaxies are receding, which suggests the space between them is expanding.
    • The expansion stretches light waves on their way to us, producing the redshift.
    • The more redshifted the light, the faster the galaxy recedes.
  • Balloon analogy
    • dots on an inflating balloon move apart because the rubber stretches, as galaxies are carried apart by stretching space and not by moving through it.
  • Hubble's law = the recession speed of a galaxy is proportional to its distance from Earth, v = H0d.
    What the symbols mean: v = recession speed of the galaxy (km s−1) · H0 = Hubble constant (km s−1 Mpc−1) · d = distance (Mpc)
    • Hubble found speeds from redshift and distances from standard candles.
    • H0 is the Hubble constant (the expansion rate, in s−1), the gradient of a v–d graph.
    • Further galaxies recede faster.

Section 9 of 9Big Bang and the age of the universe

  • Big Bang theory
    • running the expansion backwards, all matter was at the same point in the past, in a hot, dense singular point that began expanding very quickly.
    • Redshift and expansion are key evidence.
  • Age of the universe
    • assuming a constant expansion rate, t0 = 1/H0.
  • Estimates
    • current estimates are 13 to 14 billion years, and obtaining an accurate H0 is a high priority for cosmologists.

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