Hubble's law (A-level only) — AQA A-Level Physics

Hubble's law is a fundamental relationship in cosmology that describes the expansion of the Universe. It states that the recessional velocity of a galaxy is directly proportional to its distance from Earth, expressed as v = H0 d, where H0 is the Hubble constant. This law is crucial because it provides observational evidence for the Big Bang theory and allows astronomers to estimate the age of the Universe.

In the AQA A-Level Physics specification, Hubble's law is part of the optional Astrophysics unit. It builds on concepts of redshift, the Doppler effect, and standard candles such as Cepheid variables and Type Ia supernovae. Understanding Hubble's law helps students appreciate how astronomical distances are measured and how the Universe evolves over time.

• →Hubble's law: v = H0 d, where v is recessional velocity, H0 is the Hubble constant, and d is distance.
• →The Hubble constant H0 is the gradient of a velocity-distance graph and has units of s^-1 (or km s^-1 Mpc^-1).
• →Redshift: The observed increase in wavelength of light from receding galaxies, used to determine recessional velocity.
• →The age of the Universe is estimated as 1/H0, assuming a constant rate of expansion.
• →Hubble's law is only valid for distant galaxies, where cosmic expansion dominates over local gravitational motions.

• Hubble's law is v = Hd, where v is recession speed, d is distance and H is the Hubble constant.
• Redshift of spectral lines gives recession speed, often using Δλ/λ₀ = v/c for speeds much less than c.
• Distance is determined independently, for example using standard candles such as type Ia supernovae or Cepheid variables.
• The simple interpretation is that the universe is expanding uniformly, so more distant galaxies recede faster; Earth is not at the centre of expansion.
• Assuming H is constant, the age of the universe is estimated as t ≈ 1/H, obtained from time = distance/speed = d/(Hd).
• Unit conversion is essential: H in km s⁻¹ Mpc⁻¹ must be converted to s⁻¹ before calculating 1/H, using 1 Mpc ≈ 3.09 × 10¹⁹ km.
• States that the Universe is expanding and that the early Universe was much hotter and denser than it is now.
• Explains cosmological redshift qualitatively as stretching of photon wavelengths by expansion of space, not as a Doppler shift through a stationary medium.
• Identifies the CMBR as microwave radiation at about 2.7 K coming from all directions and interprets it as relic thermal radiation from the early Universe.
• Links the near-uniform temperature and small ripples in the CMBR to an initially hot, dense state that later cooled and clumped to form galaxies.
• Explains that Big Bang nucleosynthesis in the first minutes produced mainly hydrogen and helium, giving the observed relative abundance of about three parts hydrogen to one part helium by mass.
• Uses at least two independent pieces of evidence to support the Big Bang model rather than relying on a single observation.

• 💡Write down v = Hd and rearrange to H = v/d if you need to find H from a graph of recession speed against distance; the gradient is H.
• 💡When estimating the age of the universe, show the unit conversion for H clearly and state the final answer in years, using 1 year ≈ 3.15 × 10⁷ s.
• 💡Use the phrase expansion of space rather than galaxies flying through space to describe the simple interpretation.
• 💡If a graph is provided, read the gradient using a large triangle on the line of best fit to reduce uncertainty.
• 💡When asked for evidence, name the observation, state what is measured and explain how it supports the Big Bang model in one linked chain.
• 💡Use the phrase 'expansion of space' rather than 'galaxies moving through space' when explaining cosmological redshift.
• 💡For the CMBR, quote the approximate temperature 2.7 K and mention its near-uniformity and small ripples.
• 💡For hydrogen and helium abundance, give the approximate mass ratio three to one and link it to nucleosynthesis in the first minutes.
• 💡Always state the units of the Hubble constant as s^-1 or km s^-1 Mpc^-1, and show how you convert between them if necessary.
• 💡When describing Hubble's law, explicitly mention that it applies to distant galaxies and that the velocity is due to the expansion of space itself, not motion through space.
• 💡For calculation questions, write down the formula v = H0 d, substitute values with units, and give your final answer to an appropriate number of significant figures (usually 2 or 3).

• Using H directly in km s⁻¹ Mpc⁻¹ to find an age in seconds: correct by converting H to s⁻¹ first, for example by multiplying by 10³ m km⁻¹ and dividing by 3.09 × 10²² m Mpc⁻¹.
• Thinking that redshift means galaxies are moving through space away from a central point: correct by explaining that space itself expands and the recession is observed uniformly.
• Confusing the Hubble constant H with the age of the universe: correct by stating that age is estimated as 1/H only under the assumption that H has been constant.
• Forgetting that v = Hd applies to distant galaxies, not to objects bound within a galaxy: correct by noting that local gravitationally bound systems do not expand with the universe.
• Treating cosmological redshift as a simple Doppler shift through space; correct this by describing expansion of space stretching photon wavelengths.
• Describing the CMBR as coming only from the centre of the Universe or from a single direction; correct this by stating it is isotropic, arriving from all directions.
• Claiming that all helium was made in stars; correct this by explaining that the observed primordial abundance is too large for stellar production alone and matches Big Bang nucleosynthesis.
• Stating that the CMBR is the same as the light from the first stars; correct this by identifying it as thermal radiation released when the early Universe became transparent, long before stars formed.
• Students often think Hubble's law applies to all galaxies, including those in the Local Group. Correction: It is only valid for distant galaxies where the recessional velocity due to expansion is much larger than local peculiar velocities.
• Students sometimes confuse the Hubble constant with the age of the Universe. Correction: The age is approximately 1/H0, not H0 itself.
• Students may incorrectly use the gradient of a distance-velocity graph (with distance on y-axis) as H0. Correction: H0 is the gradient only when velocity is on the y-axis and distance on the x-axis.

1. 1Day 1-2: Review the definition of Hubble's law and the Hubble constant. Learn the equation v = H0 d and its units. Practice rearranging the equation.
2. 2Day 3-4: Study the evidence for the Big Bang from Hubble's law. Watch videos or read notes on redshift and the expanding Universe. Make a summary sheet.
3. 3Day 5-6: Work through calculation problems, including converting between units (e.g., Mpc to m, s^-1 to years^-1). Use past paper questions.
4. 4Day 7-8: Complete a 6-mark structured question on Hubble's law and the age of the Universe. Mark it using the official mark scheme and note where you lost marks.
5. 5Day 9-10: Revise common misconceptions and examiner tips. Create flashcards for key definitions and formulas. Test yourself with active recall prompts.

• 📋Calculation of distance or recessional velocity using v = H0 d. Advice: Ensure units are consistent and convert where necessary.
• 📋Explanation of how Hubble's law supports the Big Bang theory. Advice: Link the expanding Universe to the idea of a hot, dense origin and mention the age estimate.
• 📋Graph analysis: determining H0 from a velocity-distance graph. Advice: Identify the gradient, use a large triangle, and state the unit.
• 📋Estimation of the age of the Universe using 1/H0. Advice: Show the calculation and convert seconds to years correctly.