[Space] Getting Mars to 1% hydrographic coverage

[Michael Thayne]

Terraforming Mars is unlikely to be easy. This got me thinking: what's the minimal amount of Mars terraforming that would be interesting in GURPS terms? Looking at the habitability rules in GURPS Space, I notice that any hydrographic coverage, even 1%, is good for +1 to habitability. So what would it take to get Mars there?

My understanding of the physics is that in order to have liquid water of the long haul, you first need to add lots of water vapor so that the water vapor and liquid water can be in equilibrium. Average surface temperatures of a newly-terraformed mars are likely to be just above freezing, so we can probably use the vapor pressure of water at 0 C for these estimates, which happens to be just over 0.006 atm, coincidentally roughly equal to Mars' current atmospheric pressure. So we're talking about getting Mars' atmospheric pressure to at least 0.012 atm, which is technically no longer "trace" atmosphere according to GURPS but instead "very thin", not that that will do much for Mars' habitability by itself.

At first I thought this would also mean doubling the mass of Mars' atmosphere, but given that Mars' atmosphere is mostly CO2 and IIUC gas pressure is a function of number of molecules rather than mass, we might only be talking about a 40% increase in the mass of Mars' atmosphere. Since Mars' atmosphere is about 25 trillion tons, that means we need about 10 trillion tons of water. My big question is: how much of that could you get by melting Mars' polar ice caps with big solar mirrors? That, I think would represent less than 1% of the ice found in Mars' polar caps, though I really don't know how much of those you're going to melt even with solar mirrors that get the average surface temperature above freezing.

So, people who have more expertise on this sort of thing than I do, what say ye?

[Anthony]

You only actually need equilibrium where the bodies of open water are; most parts of earth's surface have less than 100% relative humidity. Unfortunately, you also need to account for all the water which condenses out of the atmosphere in places other than your bodies of open water and does not immediately return to them (i.e. it freezes or seeps into the ground and stays there).

Also, atmospheric pressure at the surface is equal to the weight of the atmosphere above that same area of surface, though the lower molar mass does mean the scale height of the atmosphere will increase.

[Michael Thayne]

Originally Posted by Anthony

Also, atmospheric pressure at the surface is equal to the weight of the atmosphere above that same area of surface, though the lower molar mass does mean the scale height of the atmosphere will increase.

D'oh. I was thinking of the ideal gas law, but that's for pressure due to heat (or at a more micro level, the momentum of individual gas molecules), not pressure due to gravity.

[Agemegos]

Originally Posted by Michael Thayne

D'oh. I was thinking of the ideal gas law, but that's for pressure due to heat (or at a more micro level, the momentum of individual gas molecules), not pressure due to gravity.

You're thinking of Gay-Lussac's law. The Universal Gas Law

PV = nRT

combines Boyle's, Charles', and Gay-Lussac's laws into a single relationship among four variables. Note that only R is a constant in that equation. The atmospheric gasses conform to that law (and to the hydrostatic condition giving pressure as a d.e. of altitude (give or take local weather), so therefore to the barometric formula), but they accommodate changes in temperature and molar quantity by changes in volume (a.k.a. by expanding upwards, a.k.a. altering the atmospheric scale height).

[Prince Charon]

Given that the temperature of Mars at the equator can actually get fairly high - up to 70 degrees F (20 degrees C) on a summer day, it would probably be easier to create hydrographic coverage there. The main difficulty would be getting enough liquid water that it doesn't just freeze over the night (temperatures even in summer on Mars can get down to -100 F/-73 C) and stay frozen; also needs to not freeze completely during the Martian winter, or only so much that it can still melt in the spring.

Of course, adding water and water vapor could prevent temperatures from plummeting as far as they do, now.

[AlexanderHowl]

You need enough atmosphere to prevent water from boiling off, which would realistically be around 5% Earth at the equatorial region. Given the area and gravity of Mars roughly balances out for this purpose, that would require around 250 trillion metric tons of gases (preferably carbon dioxide because of its greenhouse properties). The ice caps of Mars possess insufficient carbon dioxide, as their dry ice reserves are just frozen portions of the atmosphere that melt every summer. At the very least, you would likely need to transport ~68 trillion tons of carbon from the Main Belt (you can liberate oxygen for cheaper from the rocks of Mars).