Equilibrium Temperature of a Spherical Black Body Satellite

[CaptainJames]

b) Real satellites are complicated objects (see photo above). To simplify the problem, suppose the satellite is a spherical black body with a 0.3 m radius. Suppose the satellite's electronics generated 3900 Watts. What would be the equilibrium temperature, Teq, of the satellite?

Okeedoke, so I started with the equation T=oT^4. So...

3900 J=(5.67x10^-8 W/m^2K^4)T^4

T=(3900 J/(5.67x10^-8 W/m^2 K^4))^(1/4)

Which gives me an incorrect answer... any hints in the right direction?

 

[Andrew Mason]

b) Real satellites are complicated objects (see photo above). To simplify the problem, suppose the satellite is a spherical black body with a 0.3 m radius. Suppose the satellite's electronics generated 3900 Watts. What would be the equilibrium temperature, Teq, of the satellite?

Okeedoke, so I started with the equation T=oT^4. So...

3900 J=(5.67x10^-8 W/m^2K^4)T^4

T=(3900 J/(5.67x10^-8 W/m^2 K^4))^(1/4)

Which gives me an incorrect answer... any hints in the right direction?

You are given the total power but you need the power/unit area. On the Left side, divide the power by the surface area and equate that to the right side.

AM

 

[CaptainJames]

Ah! Thanks a bunch, I got it.