Red shift v = Hd Simple interpretation as expansion of universe;…

The idea

Hubble's law states that the recession speed v of a distant galaxy is proportional to its distance d from Earth: v = Hd, where H is the Hubble constant. Redshift of spectral lines provides v, and distance is found from standard candles such as type Ia supernovae or Cepheid variables. The simple interpretation is that space itself is expanding uniformly, so all distant galaxies recede and more distant ones recede faster; this is not because Earth is at a special centre. If H is assumed constant, the age of the universe is estimated as t ≈ 1/H, because a galaxy now at distance d has taken approximately d/v = d/(Hd) = 1/H to reach that separation. You should use consistent units, typically converting H from km s⁻¹ Mpc⁻¹ to s⁻¹ before finding 1/H in seconds or years.

What earns the marks

• 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.

Common mistakes and how to put them right

• Using H directly in km s⁻¹ Mpc⁻¹ to find an age in seconds.

  Put it right 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.

  Put it right by explaining that space itself expands and the recession is observed uniformly.

• Confusing the Hubble constant H with the age of the universe.

  Put it right 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.

  Put it right by noting that local gravitationally bound systems do not expand with the universe.

Exam tips

• 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.