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Calculating the surface temperature of a regular tetrahedron using Mr. Hansen’s formula from NASA

Author: kegasaExecutions: 32

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Assuming the Earth’s thermal conductivity is infinite and its thermal resistance is zero,
based on solar radiation and blackbody radiation, the equation explained by Hansen shows that
without greenhouse gases, the Earth’s surface temperature would drop to -18°C.
Science, August 23, 1981 issue
Te = [So(1 - A)/4σ]^(1/4)
TeZero = (So*(1-A)/(4*σ))^(1/4);
TeSun = ((So*(1-A)/(1*σ))^(1/4));
TeInfinite = (TeSun + 0 + 0 + 0)/4;
print(TeZero);
print(TeZero - 273.15);
print(TeInfinite);
print(TeInfinite - 273.15);
print(TeSun);
print(TeSun - 273.15);
Solar radiation So = 1367 W/m^2
Earth's albedo A = 0.3
Stefan-Boltzmann constant σ = 5.67*10^(-8) W/m^2/K^4
Solar radiation So
W/m²
Earth's Albedo A
Stefan-Boltzmann constant σ
W/m²/K⁴
Temperature Te of a regular tetrahedron with infinite thermal conductivity K
Temperature Te of a regular tetrahedron with infinite thermal conductivity ℃
Temperature Te of a regular tetrahedron with zero thermal conductivity K
Temperature Te of a regular tetrahedron with zero thermal conductivity ℃
Surface temperature facing the sun Te K
Surface temperature facing the sun Te ℃
SCIENCE August 28, 1981
Climate Impact of Increasing
Atmospheric Carbon Dioxide

J. Hansen

πR^2(1 - A)So = 4πR^2σTe^4
Te = [So(1-A)/4σ]^(1/4) (2)
Te = 255 K
The mean surface temperature is
Te = 288 K
https://pubs.giss.nasa.gov/docs/1981/1981_Hansen_ha04600x.pdf

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