(i) State Hubble’s law.

(ii) State why Hubble’s law cannot be used to determine the distance from Earth to nearby galaxies, such as Andromeda.

(i) Show that \(\frac{1}{{{H_0}}}\)  is an estimate of the age of the universe, where H₀ is the Hubble constant.

(ii) Assuming H₀ = 80 km s⁻¹Mpc⁻¹, estimate the age of the universe in seconds.

(i) recessional speed of a galaxy is directly proportional to distance from Earth/ v=H₀d with symbols defined;

(ii) local velocity of Andromeda relative to Earth greater than (recessional) speed due to expansion of universe / OWTTE;

(i) relative speed between two points in universe separated by distance d is \(v = \frac{d}{T}\) where T is the age of the universe;
\(v = \frac{d}{T}\)=H₀d therefore \(T = \frac{1}{{{H_0}}}\);

(ii) \(T = \frac{1}{{80}} \times \frac{{{{10}^6} \times 3.26 \times 9.46 \times {{10}^{15}}}}{{1000}} = 4 \times {10^{17}}\left( {\rm{s}} \right)\);
Do not deduct unit mark if seconds not given, as question asks for answer in seconds.