Redshift of distant galaxies and its cause, the redshift formula, Hubble's law relating distance and recession velocity, and estimating the age and size of the Universe.

What this dot point is asking

Edexcel statements 16.1 to 16.6 want you to know that galaxies beyond the Local Group show redshift, that redshift is caused by galaxies receding, to use the redshift formula $\dfrac{\lambda - \lambda_0}{\lambda_0} = \dfrac{v}{c}$, to use Hubble's law $v = H_0 d$ (including reading a gradient), and to estimate the age and size of the Universe from the Hubble constant.

Redshift and its cause

Redshift is the central observation of cosmology: nearly every distant galaxy is moving away, and the shift in its spectral lines measures how fast. The cause is recession (statement 16.2), ultimately because space itself is expanding and carrying the galaxies apart, so we are not at a special centre. Galaxies in the Local Group can show blueshift (Andromeda is approaching), but beyond it the expansion dominates and everything recedes.

The redshift formula

This is a key calculation. Find the change in wavelength ($\lambda - \lambda_0$), divide by the emitted wavelength $\lambda_0$ to get the fractional redshift, then multiply by $c$ to get the velocity. The wavelength units cancel as long as they are the same top and bottom. The formula is on the data sheet, so the marks are for correct substitution and rearrangement.

Hubble's law

Hubble's law is the quantitative statement that the Universe is expanding uniformly: double the distance, double the recession speed. The proportionality is what you calculate with ($v = H_0 d$, rearranged as needed) and what you read from a graph (the gradient gives $H_0$, statement 4c). Combined with a redshift-derived velocity, it gives the distance to a galaxy, extending the distance ladder to the farthest galaxies.

The age and size of the Universe

The estimate works by imagining the expansion reversed: if galaxies are flying apart at speeds proportional to their distances, they were all together a time $\approx 1/H_0$ ago, which is the age of the Universe. This is statement 16.6. The value of $H_0$ therefore directly controls the estimated age, which is why measuring it precisely matters so much in cosmology.

How Edexcel examines this

This is telescopic Paper 2 content and a major calculation point. Two calculations recur: the redshift formula (find $\lambda - \lambda_0$, divide by $\lambda_0$, multiply by $c$ for the velocity) and Hubble's law ($v = H_0 d$, rearranged to find a distance or velocity), both from the data sheet. You may also read $H_0$ as the gradient of a velocity-distance graph. The redshift cause (recession) and Hubble's law (more distant galaxies recede faster) are tested by explanation, and the age of the Universe by the $1/H_0$ idea (running the expansion backwards), with a larger $H_0$ meaning a younger Universe. Synoptic links run to standard candles for the distances (Topic 13) and to the Big Bang evidence (next dot point). The commonest errors are reversing the redshift direction and mismatching units in Hubble's law, so keep redshift as increased wavelength and the units consistent.

Try this

Q1. State what the redshift of a distant galaxy tells us about its motion. [1 mark]

• Cue. It is moving away from us (receding); a greater redshift means a faster recession.

Q2. State Hubble's law in its formula form. [1 mark]

• Cue. $v = H_0 d$ (recession velocity equals the Hubble constant times distance).