Betelgeuse is a star in the constellation Orion. It radiates heat at the rate of 2.70 × 10³⁰ W and has a surface temperature of 3000 K. Assuming that it is a perfect emitter, what is the radius of Betelgeuse? The Stefan-Boltzmann constant is 5.67 × 10^-8 W/(m²∙K⁴).

Question

Quizplus · Accepted Answer

The luminosity of a star is given by the Stefan-Boltzmann Law: L = 4πR²σT⁴. Solving for R, we get R = √(L / (4πσT⁴)). Substituting the given values, R = √(2.70 × 10³⁰ / (4π × 5.67 × 10⁻⁸ × 3000⁴)) ≈ 2.16 × 10¹¹ m.

Betelgeuse Is a Star in the Constellation Orion