The temperature of a planetary body in space varies with the fourth-root of the power incident upon it, this is derived from the Stefan-Boltzmann Law.
This is understandable when applied to a black body in space. However, when applied to certain pressure levels (like 1 bar) at planets with a thick atmosphere the outcome is the same
Meaning that the temperature of Venus at 1atm (Tv) should be the fourth-root of 1.91 times the temperature on Earth at 1atm (Te). Venus receives 1.91 times the solar insolation of Earth.
Venus Tv=∜1.91 x Te
Tv = 1.176 x 288
Tv = 339 Kelvin
For Titan, the temperature of a planetary body in space varies with the fourth-root of the power incident upon it, meaning that the temperature of Titan at 1atm (Tt) should be the fourth-root of 0.01089 times the temperature on Earth at 1atm (Te). Titan receives 0.01089 times the solar insolation of Earth.
Titan Tt=∜0.01089 x Te
Tt = 0.323 x 288
Tt = 93 Kelvin
Planet | Measured Temp 1atm | Relative Solar Insolation | 4th Root | Calculated Temp |
---|---|---|---|---|
Earth | ~288 Kelvin | 1.00 | 1.000 | 288 Kelvin |
Venus | ~340 Kelvin | 1.91 | 1.176 | 339 Kelvin |
Titan | ~90 Kelvin | 0.01089 | 0.316 | 93 Kelvin |