When doing my calculations I mostly used a solar constant of 1361W/m^2. When I use the exact value of 1360.8W/m^2 given by NASA I realize that their measurements probably are very exact. 1360.8W is the mean value, total solar irradiance varies a bit during a year in orbit and the 11-year cycle. It was revised not so long ago due to some discovered problem in measurements, from about 1365.4W to the present value.
When taking a closer look at what the 4th power of temperature calculated with TSI is, I found that it isn´t a random number, it is
1360.8/0.0000000567=24 000 000 000
When transforming through the sphere it becomes 18 000 000 000
And 13 500 000 000 on the way to the surface.
The fourth power of surface temperature is 6 750 000 000
4/3g^2(tropopause mean emissive power) is 2 250 000 000
g^2 is 1 687 500 000.
From what I can see, that is not the case for Venus and Mars. But we might have similar problems in measurements of TSI there as well. It is surprising that we get such pure numbers from the power in watts which is with a decimal of .8 and a constant of 0.0000000567. I suspect the fourth power of Temperature is the ”real” value of power, and maybe it can be used to find solutions easier in physics. But lets get rid of all the zeros first, right?
And, well done NASA! Good work in measuring.