What are the calculations for the time it would take to create a minus 50⁰ C liquid CO2 ocean on Venus by shielding it totally from the Sun?

Question

Cooling down Venus will probably be by far the most efficient method to start terraforming the planet because then you wouldn't have to deal with the high temperatures and pressures at its surface.

I've chosen the final temperature of -50⁰ C since that is just above the triple point temperature of CO₂ where this gas could change into a liquid ocean and because at the same time the lowest possible atmospheric pressure could be reached at the surface of Maxwell Montes, with about 10 km elevation the highest area on Venus. (light-brown on the image below)

Credits and author: Zamonin. Screenshot of a part of the File:VenusLanderTopo.jpg, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Taking into account the total liquid mass of CO₂ in Venus' atmosphere at -50⁰ C, the total surface area of the planet and the liquid carbon density of 1155 kg/m³, a 835 m deep liquid CO₂ ocean could span the planet if its surface had the same elevation everywhere. So the surface of that ocean would then be at +835 m elevation, but since 80 % of the topography is within 1 km of the median radius the actual elevation would be somewhat lower.

With this peace software tool it can be calculated that at -50⁰ C CO₂ becomes liquid at about 7 bar, while the scale height for Venus' atmosphere at -50⁰ C can be found out to be 4751 m.

So from the ocean's surface at 7 bar air pressure to the Maxwell Montes plateau there's a difference of at least 1.93 scale heights, meaning the pressure on the plateau would be 6.89 less or 1.02 bar (1.01 atm.) !

By comparison, at -40⁰ C CO₂ would become liquid at 11 bar, and the scaleheight at that temperature 4964 m, while the CO₂ ocean surface would then be at a max. +821 m elevation.

Then from the ocean's surface to the Maxwell Montes plateau a difference of 1.85 scale heights turns out to be, meaning the pressure on the plateau would become 1.73 bar (1.71 atm.),
With such low temperatures the CO2 ocean could be covered by about a 1 cm thick layer of water ice from all the water in the present atmosphere since during the cooling period probably most of the precipitated water would have flown to the lowest regions.

But can it be calculated how long it would take for Venus to cool down to a -50⁰ C surface temperature when it would receive no sunlight anymore ?

Answer 1

I found a YouTube video that talks about terraforming Venus. It just happens to include information about the temperature of Venus dropping when all sunlight is blocked.

If you skip to a certain part (4 minutes 30 seconds) you will see that it will show the temperature based on year.

It will take around 164 years for the temperature to get to -50 Celsius. The video has sources in the description.

Answer 2

At the target temperature of -50⁰ C, a black body radiates 140 W/m². The real emissions is more complicated, but that should be the order of magnitude we are working with.

$$P = \sigma T^4$$

It's enough to conclude that for instance the geothermal power from the deep of Venus (~30mW/m²) is too small to be relevant to the calculation.

So for each square metre of Venus, we have to cool down 1040 tons of atmosphere, and some quantity of surface rock.

Basalt has a thermal conductivity of 2 W m^-1 K^-1, so at the final temperature, an equilibrium heat flow of 140 W/m² from the ground is at a thermal gradient of 7.2 K/m, meaning the original surface temperature is only 70 metres down. Conclusion: The mass of rock we need to cool is much lower than the mass of atmosphere we need to cool

---

$$Time \approx \frac{\Delta T \cdot R_{gas} \cdot n_{gas}}{P}$$

As a very pessimistic estimate, cooling down ~1000 tons of $CO_2$ takes 25 years at 140W/m².
That's of course assuming the radiation power at the end of the process, which is obviously way too low, as radiative heat loss scales with temperature to the fourth power, meaning the start of the process goes much faster.

In conclusion: A handful of years

Answer 3

Since the only guess we have is 30,000 years, perhaps we can get a little closer by observing seasonal temperature change on Earth. Some idea could be gained from data taken from the poles$^1$, which have no sunlight for many months in winter.

Although Venus has a CO2 atmosphere, data may be available to determine the amount of heat radiated from the planet as detected by an orbiter on the night side.

If the surface materials are known, a heat decay curve could be built based on the energy radiated vs heat holding capacity. This could actually be modeled in a laboratory by heating x amount of stone to 450C and determining its cooling rate. Atmospheric insulation would have to be accounted for.

If the entire planet were shrouded and 0 solar energy was able to get through, perhaps less than a century, maybe a decade or two, as a starting estimation for cooling time. Certainly worth investigating if one needed a spare planet in the future.

$^1$ Earth North pole average high: summer 0C, winter -40C