I'm trying to calculate the steady-state temperature of a body in space, but my numbers are coming up much too small. For example, for a 1-meter cube, I'm getting a temperature of 194 K (or -81 C). I'm hoping someone can spot where I'm going wrong.
I'm working from the equations here, which are based on energy intensity (W/m^2) at the surface. The example given assumes that solar radiation the spacecraft is uniform over its entire surface area. I can't make that assumption, so I'm assuming the sun illuminates only one face of the cube, i.e. 1m^2 of area. I'm also using the more accurate figure of 1361 W/m^2 for solar intensity, so this gives 1361 W insolation. As in the example, I'm assuming an absorptivity of 0.3, so we multiply that by 13.61 MW to get 408.3 W absorbed energy.
Now here's where I may be stepping in something: to use the formula given, I need energy input per unit surface area. So I'm just dividing this absorbed solar energy by the total surface area of the cube, 6 m^2, to get Q_in = 68.05 W/m^2. This is quite a lot less than the 300 W/m^2 in the example. But it doesn't seem reasonable to expect the sun to be shining on the craft from all directions, does it?
Anyway, once I have Q_in, I just plug it into the formula (using an epsilon of 0.85), and 194 K pops out, which seems too cold.
So, where have I gone wrong?