(i) Using the data in (c), calculate, in parsecs, the distance from Earth to Gomeisa.

(ii) Gomeisa has a radius four times that of the Sun. Use the data in (c) to show that the ratio

\[\frac{{{\rm{luminosity of Gomeisa}}}}{{{\rm{luminosity of Sun}}}}\]

is about 200.

Gomeisa, Luyten’s star and the Sun are main sequence stars. On the grid of the Hertzsprung–Russell (HR) diagram, identify the position of

(i) Gomeisa, with the letter G.

(ii) Luyten’s star, with the letter L.

(i) \(2.9 =  - 0.7 + 51{\rm{g}}\left( {\frac{d}{{10}}} \right)\);
\(\frac{d}{{10}} = {10^{\frac{{{\rm{3.6}}}}{{\rm{5}}}}}\);
52 (pc);
Award [2 max] ECF if magnitudes are reversed giving 1.9 (pc).
Award [2 max] if data for Lutyen’s star is used and no credit for the distance of 4 (pc) has already been given in (c)(i).
Award [3] for a bald correct answer.
(ii) \(\frac{{{L_{\rm{G}}}}}{{{L_{\rm{S}}}}} = {\left[ {\frac{{{R_{\rm{G}}}}}{{{R_{\rm{S}}}}}} \right]^2}{\left[ {\frac{{{T_{\rm{G}}}}}{{{T_{\rm{S}}}}}} \right]^4}\);
\( = {4^2} \times {\left[ {\frac{{11000}}{{5800}}} \right]^4}\);
=210; (must see this answer to better than 1 significant figure)
Approximate answer of 200 is given in the question so correct steps in the working are required to award any marks.

(i) G correct within region shown;

(ii) L correct within region shown;