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
I will throw out 2 hypothesises to answer the why of the question. Not saying it is true, just saying that it may be valid hypothesises. And both hypothesises don't discount the internal properties of greenhouse gasses.

Somehow positive and negative feedback forces level each other out in the 1 bar thick atmosphere sytems on all 3 planets

There is another overruling equilibrium mechanism, as proposed by Dr. Ronan Connolly &amp; Dr. Michael Connolly, who studied all the weather balloon data.


https://youtu.be/XfRBr7PEawY?t=2506