As a star runs out of hydrogen to fuel nuclear fusion in its core, changes within the star usually cause it to leave the main sequence, expanding and cooling as it does so. Would a star with a radius 12 times that of the Sun, but a surface temperature 0.3 times that of the Sun, be more, or less luminous than the Sun?

Show and explain your reasoning.

You may assume the surface area of a sphere is A = 4?r².

(Hint: you will need to consider the proportional effect on stellar luminosity of both the change in the surface area and the change in surface temperature of a star, as implied by Equation 4.2 (see Topic 10: Section 4.1.2). It isn't necessary to input actual values.)

Understanding the luminosity of stars is basically as simple as this - the rate at which a star emits energy depends on its physical size and temperature. While the physics behind this is rather complex, the equation governing this relation is relatively simple: L & ATA Egn. 4.2 where L is the luminosity of the star, A is the surface area of the star and 7 is its temperature. So, at a fixed temperature, the greater the surface area of the star, the more power it will emit - and vice versa - and also, for a fixed area, the amount of power emitted from a star depends very sensitively on its temperature. How much more luminous would a star be than the Sun if it had twice the surface area and was three times as hot? Hide