A Level Physics: Astronomy and Cosmology — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Astronomy and Cosmology revision notes

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Section A

1. Distinguish between luminosity and radiant flux intensity. [2]

2. Explain what is meant by a standard candle and why Type Ia supernovae qualify. [3]

3. State Hubble’s law and explain what it implies about the universe. [3]

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Section B

4. A star has a peak emission wavelength of 480 nm and a luminosity of 4.6 × 10²⁷ W. (Wien constant = 2.9 × 10⁻³ m K; σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴)

(a) Calculate the surface temperature. [2]

(b) Calculate the radius of the star. [3]

(c) Explain why Wien’s law must be applied before Stefan’s law. [2]

5. A galaxy shows a spectral line at 660.4 nm which has a laboratory wavelength of 656.3 nm. (c = 3.00 × 10⁸ m s⁻¹; H₀ = 2.3 × 10⁻¹⁸ s⁻¹)

(a) Calculate the recession velocity. [3]

(b) Calculate the distance to the galaxy. [2]

(c) Estimate the age of the universe from H₀. [2]

6. Almost every galaxy observed shows redshift, and the redshift increases with distance.

(a) State the two conclusions that follow. [2]

(b) A student concludes that the Earth must be at the centre of the universe. Explain why this is wrong. [3]

(c) Give two further pieces of evidence for the Big Bang, stating what each demonstrates. [4]

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Section C

7. A standard candle has luminosity 4.0 × 10²⁶ W and is measured to have flux 1.0 × 10⁻¹² W m⁻² at Earth.

(a) Starting from F = L ÷ (4πd²), show how this can be rearranged to find the distance d. [2]

(b) Calculate the distance to the standard candle. [2]

(c) Explain why measuring flux alone, without knowing the object is a standard candle, is not sufficient to determine its distance. [2]

8. Different measurement techniques for the Hubble constant give values that disagree by several percent, even though all cluster around 70 km s⁻¹ Mpc⁻¹.

(a) State what this disagreement implies about using 1/H₀ to estimate the age of the universe. [2]

(b) A galaxy has an independently measured distance of 1.2 × 10²⁴ m and a recession velocity of 2.76 × 10⁶ m s⁻¹. Calculate the value of H₀ implied by this single galaxy. [2]

(c) State one reason why combining measurements from many galaxies gives a more reliable estimate of H₀ than using just one. [1]

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Answers

1. Luminosity is the total power radiated by the star in all directions [1]; radiant flux intensity is the power received per unit area at the observer [1].

2. An object of known (or reliably standardisable) luminosity [1], so that measuring its flux gives its distance via the inverse square law [1]. Type Ia supernovae detonate at a similar critical mass, so they reach approximately the same peak luminosity — real supernovae show some intrinsic variation, but this can be corrected for (e.g. from how quickly the brightness declines), making them standardisable candles rather than perfectly identical ones [1].

3. v = H₀d — recession velocity is proportional to distance [1]. This implies the universe is expanding [1], and therefore was smaller and denser in the past [1].

4. (a) T = 2.9 × 10⁻³ ÷ (480 × 10⁻⁹) [1] = 6042 K [1].

(b) L = 4πr²σT⁴, so r = √(L ÷ (4πσT⁴)) [1] T⁴ = 6042⁴ = 1.333 × 10¹⁵ r = √(4.6 × 10²⁷ ÷ (4π × 5.67 × 10⁻⁸ × 1.333 × 10¹⁵)) [1] = 2.20 × 10⁹ m [1].

(c) Stefan’s law contains two unknowns — radius and temperature [1]. Wien’s law gives the temperature from the peak wavelength, leaving only one unknown in Stefan’s law [1].

5. (a) Δλ = 660.4 − 656.3 = 4.1 nm [1] v = c × (Δλ ÷ λ) = 3.00 × 10⁸ × (4.1 ÷ 656.3) [1] = 1.87 × 10⁶ m s⁻¹ [1].

(b) d = v ÷ H₀ = 1.87 × 10⁶ ÷ 2.3 × 10⁻¹⁸ [1] = 8.15 × 10²³ m [1].

(c) age ≈ 1 ÷ H₀ = 1 ÷ 2.3 × 10⁻¹⁸ [1] = 4.35 × 10¹⁷ s (≈ 13.8 billion years) [1].

6. (a) The galaxies are receding from us [1], and more distant galaxies recede faster [1].

(b) It is space itself that is expanding, not galaxies moving through space [1]. On large, unbound scales, every point recedes from every other point [1] — this does not apply to gravitationally bound systems like galaxies, solar systems or galaxy clusters, which are held together and do not expand — so an observer in any (unbound, large-scale) galaxy would see exactly the same relationship between distance and recession speed [1].

(c) Cosmic microwave background radiation [1] — the cooled remnant of radiation from the hot dense early universe, with a black-body spectrum at about 2.7 K [1]. Relative abundance of hydrogen and helium [1] — the observed ratio matches that predicted by nucleosynthesis in the first minutes after the Big Bang [1].

7. (a) Multiplying both sides by 4πd² gives 4πd²F = L, so d² = L ÷ (4πF), and therefore d = √(L ÷ (4πF)) [2].

(b) d = √(4.0 × 10²⁶ ÷ (4π × 1.0 × 10⁻¹²)) [1] = 5.64 × 10¹⁸ m [1].

(c) Flux depends on both luminosity and distance, so the same measured flux could come from a more luminous source further away or a less luminous source closer in [1]. Only when the luminosity is already known — because the object is a standard candle — can the flux equation be solved uniquely for distance [1].

8. (a) The few-percent-level disagreement between techniques means H₀ itself is known only to a few percent, not to an order of magnitude [1]; separately, 1/H₀ is only a rough age estimate even for a perfectly known H₀, because it assumes a constant expansion rate rather than accounting for how the expansion rate has changed over cosmic history [1].

(b) H₀ = v ÷ d = 2.76 × 10⁶ ÷ 1.2 × 10²⁴ [1] = 2.3 × 10⁻¹⁸ s⁻¹ [1].

(c) Combining many galaxies averages out the individual scatter and measurement error in any one galaxy’s distance or velocity, giving a statistically more reliable value [1].

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Where marks are usually lost

• Confusing luminosity with radiant flux.
• Applying Stefan’s law before Wien’s, leaving two unknowns.
• Forgetting the 4π in the inverse square law or in Stefan’s law.
• Concluding that redshift places Earth at the centre.
• Naming Big Bang evidence without saying what it shows.
• Treating the Hubble constant as a precisely known, single fixed value rather than an order-of-magnitude estimate that varies between measurement techniques.
• Quoting a distance found from flux without first confirming the object is a genuine standard candle of known luminosity.