Find the radius rrigel of the star rigel, the bright blue star in the constellation orion that radiates energy at a rate of 2.7×1031w and has a surface temperature of 11,000 k. assume that the star is spherical. use σ=5.67×10−8w/m2⋅k4 for the stefan-boltzmann constant and express your answer numerically in meters to two significant figures.

Explanation:

The Stefan–Boltzmann law for a black body (as stars are treated) can be written as , where is the total energy radiated per unit surface area across all wavelengths per unit time, the absolute temperature and is the Stefan–Boltzmann constant.

If we multiply by the surface area of the star we get the total energy radiated across all wavelengths per unit time, which is the total power radiated, so we can write:

where we have used the formula for the surface area of a sphere

Solving for r we have:

the closer the planet is to the sun, the larger the gravity

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2