<p>If we assume that energy transport in atmospheres happens purely via radiation, then we can estimate a simple adjustment time to an exchange of exterior forcing factors (change in mean solar angle, orbital distance, aliens building giant shades, etc ...) of the atmosphere by using the internal energy equation of thermodynamics, coupled with the radiation transport equation.<br />
I will omit the details here and merely state the result of the timescale as<br />
<span class="math-container">$$\rm t_{adjustment} \approx \frac{c_v M_{atmo} \tau_{IR}}{R_p^2 \sigma_{SB} T^3},$$</span>
where we have the mean specific heat capacity of the atmospheric gas <span class="math-container">$\rm c_v$</span>, the total atmospheric mass <span class="math-container">$\rm M_{atmo}$</span>, the infrared optical depth of the atmosphere <span class="math-container">$\rm \tau_{IR}$</span>, the planetary radius <span class="math-container">$\rm R_p$</span>, the Stefan-Boltzmann constant <span class="math-container">$\rm \sigma_{SB}$</span> and the temperature <span class="math-container">$T$</span> at which the atmosphere is cooling (NOT the surface temperature).
For Earth, I get about 23 days (the number quoted in my comment above was apparently the same number but for the stratosphere, i.e. not the entire atmospheric mass), and for Venus about 60 Earth years.</p>
<p>Those numbers are however only the 'slowest' estimates, as in effect, convection acts to equilibrate the lower atmosphere much faster with the stratosphere on both planets.
Still, with this caveat we can state that both planets follow any perturbations, be it solar or man-made much faster than millions-of-years timescales.
Hence, the temperature state we currently see Venus at is a result of current atmospheric optical depth and forcing.
<strong>Venus will therefore always be as hot as current geological and astrophysical conditions dictate.</strong></p>

CC BY-SA 4.0
2023-09-19T23:08:40.960Z
2023-09-19T23:08:40.960Z
AtmosphericPrisonEscape
<p>I have <a href="https://www.astronomy.com/science/does-or-will-the-planet-venus-get-hotter-as-years-and-centuries-pass-or-will-it-stay-at-the-same-temperature/" rel="nofollow noreferrer">read</a> that Venus is roughly at radiation equilibrium - that is, heat out is approximately equal to heat in. I have also <a href="https://www.cnn.com/2019/09/20/world/venus-habitability-scn/index.html" rel="nofollow noreferrer">read</a> that Venus began its heating-up around 700-750 million years ago.</p>
<p>My question is, around when did Venus reach approximate radiation equilibrium, where it stopped getting appreciably hotter in the Venusian atmosphere?</p>

CC BY-SA 4.0
2023-09-19T18:41:59.840Z
The approximate radiative timescale to reach equilibrium is a few hours on Venus - on Earth it is minutes due to the lower infrared optical depth. Hence the equilibrium state always follows other perturbations which move that state around on millions on years timescales.
AtmosphericPrisonEscape
CC BY-SA 4.0
2023-09-19T19:04:15.403Z
This definitely answers the question as asked. I guess I should have asked a question more in line with "at what point did the Venusian atmosphere get roughly as hot as it is now".
Michael Bonnet
CC BY-SA 4.0
2023-09-19T21:14:48.357Z
Both is an interesting question. Maybe @AtmosphericPrisonEscape should write his comment as answer - and you ask a new question where you ask what you really meant to ask :)
planetmaker
<planet><planetary-atmosphere><temperature><venus><radiation>
When did Venus reach approximate radiation equilibrium?
Michael Bonnet
# When did Venus reach approximate radiation equilibrium?

(Asked by: username_0 on 2023-09-19)

I have [read](https://www.astronomy.com/science/does-or-will-the-planet-venus-get-hotter-as-years-and-centuries-pass-or-will-it-stay-at-the-same-temperature/) that Venus is roughly at radiation equilibrium - that is, heat out is approximately equal to heat in. I have also [read](https://www.cnn.com/2019/09/20/world/venus-habitability-scn/index.html) that Venus began its heating-up around 700-750 million years ago.

My question is, around when did Venus reach approximate radiation equilibrium, where it stopped getting appreciably hotter in the Venusian atmosphere?

**Tags:** planet, planetary-atmosphere, temperature, venus, radiation
> **Comments:**
> **username_1**: The approximate radiative timescale to reach equilibrium is a few hours on Venus - on Earth it is minutes due to the lower infrared optical depth. Hence the equilibrium state always follows other perturbations which move that state around on millions on years timescales.  
> **username_0**: This definitely answers the question as asked. I guess I should have asked a question more in line with "at what point did the Venusian atmosphere get roughly as hot as it is now".  
> **username_2**: Both is an interesting question. Maybe @AtmosphericPrisonEscape should write his comment as answer - and you ask a new question where you ask what you really meant to ask :)  

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## 1 answers

### Answer by username_1 on 2023-09-19. Score: 5 | Accepted answer

If we assume that energy transport in atmospheres happens purely via radiation, then we can estimate a simple adjustment time to an exchange of exterior forcing factors (change in mean solar angle, orbital distance, aliens building giant shades, etc ...) of the atmosphere by using the internal energy equation of thermodynamics, coupled with the radiation transport equation.  
I will omit the details here and merely state the result of the timescale as  
$$\rm t\_{adjustment} \approx \frac{c\_v M\_{atmo} \tau\_{IR}}{R\_p^2 \sigma\_{SB} T^3},$$
where we have the mean specific heat capacity of the atmospheric gas $\rm c\_v$, the total atmospheric mass $\rm M\_{atmo}$, the infrared optical depth of the atmosphere $\rm \tau\_{IR}$, the planetary radius $\rm R\_p$, the Stefan-Boltzmann constant $\rm \sigma\_{SB}$ and the temperature $T$ at which the atmosphere is cooling (NOT the surface temperature).
For Earth, I get about 23 days (the number quoted in my comment above was apparently the same number but for the stratosphere, i.e. not the entire atmospheric mass), and for Venus about 60 Earth years.

Those numbers are however only the 'slowest' estimates, as in effect, convection acts to equilibrate the lower atmosphere much faster with the stratosphere on both planets.
Still, with this caveat we can state that both planets follow any perturbations, be it solar or man-made much faster than millions-of-years timescales.
Hence, the temperature state we currently see Venus at is a result of current atmospheric optical depth and forcing.
**Venus will therefore always be as hot as current geological and astrophysical conditions dictate.**


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