The luminosity of a star is proportional to the surface area times the energy radiated per square meter (σ is the Stefan-Boltzmann constant):
Dividing the expressions for the luminosities of a star and the Sun allows us to compare them:
Snapshot 1: A star the same size as the Sun but about half as hot is much less luminous than the Sun.
Snapshot 2: A star about half as hot as the Sun but 20 times larger is nearly 29 times more luminous than the Sun.
Snapshot 3: A star the same size as the Sun that is about 4 times hotter is over 345 times more luminous than the Sun.
Snapshot 4: A star 20 times the size of the Sun and about 4 times hotter is over 138,000 times more luminous than the Sun.
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