(i) On the axes, sketch a graph to show how the recessional speed v of a galaxy varies with distance d from the Earth.

(ii) Outline how the graph in (a)(i) can be used to determine the age of the universe.

Astronomers use the factor z to report the red-shift of an object relative to Earth where

\[z = \frac{{{\rm{shift in wavelength detected by Earth observer}}}}{{{\rm{wavelength of light emitted by object}}}}\]

Quasar 3C273 is thought to be the closest quasar to Earth and has z=0.18. Assuming that the Hubble constant is 70 kms^–1 Mpc^–1, determine the distance of this object from Earth.

(i) straight line that passes through the origin (or would do so if extrapolated);

(ii) gradient is H₀/Hubble’s constant;
age of universe is \(\frac{1}{{{H_0}}}\) or age is \(\frac{1}{{{\rm{gradient}}}}\);

v=(0.18×c=)5.4×10⁷(ms^-1) or 5.4×10⁴(kms^-1);
\(d = \frac{v}{{70}} = 770\left( {{\rm{Mpc}}} \right)\) or 2.4×10²⁵(m);
Award [1 max] if v is correctly calculated but left in ms^–1, giving an answer of 770 000 (Mpc).
Award [1 max] ECF for an incorrect value of v used correctly in kms^–1.
Award [0] for an incorrect value of v and failure to convert to kms^–1.
Award [2] for a bald correct answer.