# Why is the average 1 Bar temperature on planets with a thick atmosphere proportional to the distance of the sun?

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
• Have you checked the wikipedia page on en.wikipedia.org/wiki/Planetary_equilibrium_temperature? Feb 16, 2021 at 17:13
• @ AtmosphericPrisonEscape . Looked at it but in the calculation on that page there is a correction for albedo. In this case there is no need to adjust for albedo, and for the amount of greenhouse gasses. The temperature at 1 bar is proportinal to the distance of the sun alone.
– MP1
Feb 16, 2021 at 17:18
• You need the high Albedo correction at Venus and at Earth, together with green-house gases to get the right temperature. Your statement " The temperature at 1 bar is proportional to the distance of the sun alone" is wrong. What your scaling formula is computing, is the equivalent Temperature of solar radiation at a distance. Check this paper arxiv.org/pdf/1312.6859.pdf for a solar-system wide comparison taking into account all the available data. Feb 16, 2021 at 17:32
• @ AtmosphericPrisonEscape. So the temperature at 1 Bar of planets with a thick atmosphere is proportional to the equivalent Temperature of solar radiation at a distance?
– MP1
Feb 16, 2021 at 19:28
• The total solar irradiation at the top of the atmosphere is proportional to the distance of the sun. So it doesn't matter if it is related to the distance of the sun or the TSI at the TOA, principle is the same. And the question remains unanswered ...why?, or how is that possible?
– MP1
Feb 16, 2021 at 20:47