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Power output of a star

Stars emit massive amounts of energy per second and so the power of a star is enormous. We assume that a star behaves as a perfectly 'black body' in other words it is a perfect radiator of radiation at its surface temperature.

The Stefan- Boltzmann law states that the power emitted by a black body of surface area A and with a surface temperature T (K) is given by the equation:

Power = σAT4 where σ is a constant (5.7x10-8 Wm-2K-4).

(Note: we are assuming here that the temperature of the surroundings (deep space) has a temperature of 0 K)

If we assume that a star is roughly spherical then A = 4πr2 for a star of radius r.

The power of a star is therefore:

Power output of a star = 4πσr2T4 = 7.16x10-7r2T4

Consider our Sun. It is a star of surface temperature 6000 K, and a radius 6.96x108 m. Using the preceding equation we can calculate its power output:

Power output of the Sun = 7.16x10-7r2T4 = 7.16x10-7x[6.96x108]2x[60004] = 7.16x10-7x 4.84x1017x1.296x1015 = 4.5x1026 W

An alternative way of finding out the power output of the Sun is to use the solar constant.

See: Solar constant

It is interesting to compare this power output with that of Canopus (a Carinae). Canopus has a surface temperature of 7500 K and a radius of 2x1011 m. Using these figures it is possible to calculate its power output as being in the region of 9x1031 W, about 200 000 times greater than that of the Sun!

© Keith Gibbs 2020