Ten original structured questions in the style of Paper 4, covering the whole of Astronomy and cosmology: luminosity and the inverse square law, standard candles, Wien's law and the Stefan-Boltzmann law for stellar radii, redshift, Hubble's law and the age of the Universe. The last questions build the full distance ladder. Each is tagged with its lessons; attempt them all, then reveal the worked solutions.
The Sun has a luminosity of 3.83 × 10²⁶ W. The Earth orbits at a distance of 1.50 × 10¹¹ m.
(a) State what is meant by the luminosity of a star. [1]
(b) State what is meant by radiant flux intensity. [1]
(c) Calculate the radiant flux intensity received at the Earth. [3]
(d) State two assumptions made in using F = L / (4πd²). [2]
A type Ia supernova has a known luminosity of 1.0 × 10³⁶ W. In a distant galaxy, one is observed with a radiant flux intensity of 2.0 × 10⁻¹⁵ W m⁻².
(a) State what is meant by a standard candle. [1]
(b) Calculate the distance to the galaxy, in metres. [3]
(c) Convert this distance to megaparsecs (Mpc). [2]
(d) Suggest why standard candles are needed to find the distances to far galaxies. [1]
Two stars, A and B, have the same luminosity. Star A is at distance d and star B is at distance 3d.
(a) Calculate the ratio Fₐ / F₮ of the fluxes received from them. [2]
(b) State which star appears brighter, and why. [2]
(c) A third pair have equal luminosity, but one appears 100 times brighter than the other. Find the ratio of their distances. [2]
The continuous spectrum of a star peaks at a wavelength of 480 nm.
(a) State Wien's displacement law. [1]
(b) Calculate the surface temperature of the star. [2]
(c) A second star appears red, with a peak at 700 nm. Calculate its surface temperature. [2]
(d) State which star is hotter, and how the colour tells you. [2]
A star has a luminosity of 4.0 × 10²⁸ W and a surface temperature of 1.0 × 10⁴ K.
(a) State the Stefan-Boltzmann law. [1]
(b) Calculate the power radiated per unit area of the star's surface. [2]
(c) Calculate the radius of the star. [3]
(d) Express this radius as a multiple of the Sun's radius. [2]
Two stars, X and Y, have the same radius. Star X has a surface temperature of 12000 K and star Y of 3000 K.
(a) Calculate the ratio of their peak wavelengths, λ₧/λₖ. [2]
(b) Calculate the ratio of their luminosities, L₧/Lₖ. [2]
(c) Comment on which star is more luminous and the role of temperature. [2]
A spectral line that has a laboratory wavelength of 434 nm is observed at 442 nm in the light from a galaxy.
(a) State what is meant by redshift. [1]
(b) Calculate the fractional shift Δλ/λ. [2]
(c) Calculate the speed of recession of the galaxy. [2]
(d) State the direction of motion of the galaxy and how the spectrum shows it. [2]
The galaxy in question 7 recedes at 5.5 × 10⁶ m s⁻¹. Take H₀ = 2.3 × 10⁻¹⁸ s⁻¹.
(a) State Hubble's law. [1]
(b) Calculate the distance to the galaxy, in metres. [2]
(c) Convert this distance to megaparsecs. [2]
(d) Describe the graph of recession speed against distance for many galaxies, and state what its gradient represents. [3]
Observations show that almost all galaxies are receding, with v = H₀d. Take H₀ = 2.3 × 10⁻¹⁸ s⁻¹.
(a) Explain how Hubble's law supports the idea of an expanding Universe and the Big Bang. [2]
(b) Estimate the age of the Universe, in seconds. [2]
(c) Convert this age into years. (1 year ≈ 3.16 × 10⁷ s) [2]
(d) State one assumption made when using 1/H₀ as the age. [2]
Astronomers build a "distance ladder" using several methods together.
(a) State how each of standard candles, Wien's law and redshift contributes to studying a distant galaxy. [3]
(b) A Cepheid variable places a galaxy at 15 Mpc. Using H₀ = 70 km s⁻¹ Mpc⁻¹, calculate the expected recession speed. [2]
(c) A type Ia supernova in the same galaxy has a known luminosity and a measured flux. Explain how this independently confirms the distance. [2]
(d) Suggest why redshift, rather than standard candles, is used for the most distant galaxies. [2]
Mark this once you have attempted all ten questions and checked your working against the solutions. Revealing the solutions alone does not count.