The sun radiates approximately as a blackbody at a temperature of about 6000 K a

Question

The sun radiates approximately as a blackbody at a temperature of about 6000 K and subtends an angle of 0.52o at the distance of Earth, A satellite forming a sphere 1 m in diameter orbits the Sun at the distance of Earth. The satellite receives radiation from the Sun and at the same time radiates this energy as a blackbody. Assuming that there is no internal generation of energy in the satellite and no mechanism for energy loss other than via blackbody radiation, what is the temperature of the satellite? (Hint: Find the power absorbed by the satellite from the Sun, as well as the power radiated if the satellite is at a temperature T. The two powers are equal at equilibrium.)

Explanation / Answer

power recieved by the satellite = 1361 watt/m2 ( solar constant )

radius = 0.5 meter

area of satellite = 0.5^2 * 3.14 = 0.785 m2

hence power recieved= areafacing sun( pi * r^2) * solar constant = 1068 watt

power recieved = power given out

use

q = ? T4 A         (1)

where

q = heat transfer per unit time (W)

? = 5.6703 10-8 (W/m2K4) - The Stefan-Boltzmann Constant

T = absolute temperature Kelvin (K)

A = area of the emitting body (m2)

we have 1068 = 5.6703 10-8 (W/m2K4) * ( area of sphere ( 4 pi r^2 )) * t^4

we get T = 278 Kelvin

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