Question

A small spinning asteroid is in a circular orbit around a star, much like the earth's motion around our sun. The asteroid has a surface area of 9.50 m2. The total power it absorbs from the star is 4400 W. Assuming the surface is an ideal absorber and radiator, calculate the equilibrium temperature of the asteroid (in K).

Answer 1

T = 300.6K

Step-by-step explanation:

In this problem, since the asteroid is an ideal absorber, we can approximate it to a black body, and use Stefan's law

P = σ A e T⁴

where P is the absorbed power, A the area of ​​the asteroid, and the emissivity that for a black body is worth 1 and sigma the Stefan_boltzmann constant 5,670 10⁻⁸ W / m² K⁴

they ask us for the temperature of the asteroid

T =
`\sqrt[4]{(P / \sigma A e)}`

let's calculate

T = (4400 / (5,670 10⁻⁸ 9.50 1)

T =(81.6857 108)

T = 3,006 102 K

T = 300.6K