Question 19N.3.SL.TZ0.10

stars in a cluster are gravitationally bound OR in constellation are not ✔

stars in a cluster are the same/similar age OR in constellation are not ✔

stars in a cluster are close in space/the same distance away OR in constellation are not ✔

stars in a cluster originate from same gas cloud OR in constellation do not ✔

stars in a cluster appear much closer in night sky than in a constellation ✔

Notes: Take care to reward only 1 comment from a given marking point for MP1 to MP5.

«$T=\frac{2.9\times {10}^{-3}}{490\times {10}^{-9}}$»

5900 K ✔

NOTE: Answer 6000 K is given in the question.
Answer must be to at least 2 s.f. OR correct working.

«from b∝ L∝ R² T⁴»

realization that $R^2\propto \frac{b}{T^4}$ «for binary stars which are same distance away» ✔

$\frac{R_{\mathrm{A}}}{R_{\mathrm{B}}}=\sqrt{\frac{\left({\displaystyle \frac{1.1\times {10}^{-9}}{5.4\times {10}^{-11}}}\right)}{{\left({\displaystyle \frac{5900}{4100}}\right)}^4}}$ ✔

$\frac{R_{\mathrm{A}}}{R_{\mathrm{B}}}=2.2$ ✔

NOTE: Award [2] for answer 0.46 from inverted ratio.

«use of $L=4\mathrm{\pi }{d}^{2}b$»

$L=4\mathrm{\pi }\times {\left(1.8\times {10}^{17}\right)}^2\times 1.1\times {10}^{-9} «=4.48\times {10}^{26} \mathrm{W}»$✔

$L=1.2 L_{\odot }$ ✔

approximately correct position on the main sequence as shown, within highlighted region ✔

main sequence star
OR
type F or G star ✔

$\frac{M}{M_{\odot }}=1.2^{\frac{1}{3.5}}=1.05$ ✔

mass of the «remnant» star $<1.4M_{\odot }$ OR Chandrasekhar limit
OR
mass OR luminosity similar to the Sun ✔

the final stage is white dwarf ✔