State what is meant by a main sequence star.

Show that the mass of Theta 1 Orionis is about 40 solar masses.

The surface temperature of the Sun is about 6000 K. Estimate the surface temperature of Theta 1 Orionis.

Determine the distance of Theta 1 Orionis in AU.

Discuss how Theta 1 Orionis does not collapse under its own weight.

The Sun and Theta 1 Orionis will eventually leave the main sequence. Compare and contrast the different stages in the evolution of the two stars.

stars fusing hydrogen «into helium»

[1 mark]

$M = {M_ \odot }{\left( {4 \times {{10}^5}} \right)^{\frac{1}{{3.5}}}} = 39.86{M_ \odot }$

«$M \approx 40{M_ \odot }$»

Accept reverse working.

[1 mark]

$4 \times {10^5} = {13^2} \times \frac{{{T^4}}}{{{{6000}^4}}}$

$T \approx 42\,000$ «K»

Accept use of substituted values into $L = \sigma$4$\pi$R²T⁴.

Award [2] for a bald correct answer.

[2 marks]

$4 \times {10^{ - 11}} = 4 \times {10^5} \times \frac{{1{\text{A}}{{\text{U}}^2}}}{{{d^2}}}$

$d = 1 \times {10^8}$ «AU»

Accept use of correct values into $b = \frac{L}{{4\pi {d^2}}}$.

[2 marks]

the gravitation «pressure» is balanced by radiation «pressure»

that is created by the production of energy due to fusion in the core / OWTTE

Award [1 max] if pressure and force is inappropriately mixed in the answer.

Award [1 max] for unexplained "hydrostatic equilibrium is reached".

[2 marks]

the Sun will evolve to become a red giant whereas Theta 1 Orionis will become a red super giant

the Sun will explode as a planetary nebula whereas Theta 1 Orionis will explode as a supernova

the Sun will end up as a white dwarf whereas Theta 1 Orionis as a neutron star/black hole

[3 marks]