I have a question about \'satellite\' problem. 1. Real satellites are complicate

Question

I have a question about 'satellite' problem.

1. Real satellites are complicated objects (see photo above). To simplify the problem, suppose the satellite is a spherical black body with a 0.5 m radius. Suppose the satellite's electronics generated 4000 Watts. What would be the steady-state temperature, Teq, of the satellite?

2. In reality, most electronics cannot survive long if the temperature is much higher than about 50oC, so the ability to dissipate heat places a significant constraint on the satellite's "power budget". How much power can the electronics produce and still keep the temperature of the satellite less than T = 50oC?

3. Thus far we have implicitly neglected the effects of the satellite being heated by the sun. Again assume that the satellite is a black sphere of radius 0.5 m, that it is a distance R = 1.5 x 1011 m from the sun, and that the temperature and radius of the sun (which we will also treat as a "black body") are Ts = 5700 K and Rs = 7 x 108 m, respectively. How much of the sun's power is absorbed by the satellite?

I do not know even how to start.
Please, help me...
thank you !

Explanation / Answer

1. Thermal power (P) radiated by the satellite = 4000 W Radius (r) of the satellite = 0.5 m Let us assume the satellite is a spherical black body. So emissivity of the satellite is e = 1 And surface area (A) of the satellite is A = 4(pi)r^2 = 4(pi)(0.5 m)^2 = 3.1416 m^2 Then according to the Stefan's law we have the formula for the radiated thermal power is P = (sigma)(A)(e)(T^4) T^4 = P / [(sigma)(A)(e)] T = {P / [(sigma)(A)(e)]}^(1/4) = 387 K

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