Will a Terraformed Mars Leak?

Yes, but ...

I'm in favor of colonizing the Solar System. Mars. The Moon. Mar's moons. The asteroids — Ceres, Vesta, Pallas, and the earth-crossing asteroids. Venus. Yes, Venus. It's a topic for another time, but it's not as crazy as it sounds. Well, close, maybe. But basically anything big enough to have resources to be mined or provide a convenient anchor for colonization.

Probably Mars first, because we have a prodigiously rich man who is crazy enough to do it. The Moon, I suspect, at the same time, because water — and consequently hydrogen and oxygen — and thorium and engineering metals can be obtained there without needing to lift them out of an 11 km/s bucket.

So let's focus on Mars for the moment. If we are going to colonize Mars, we have two major decisions to make: terraform, or not?

My intuition is that we'll choose not to terraform, because I think by the time it's feasible to terraform Mars, the Martians will like their planet the way it is, thank you very much. But who knows?

Certainly there's been a lot of thought applied to terraforming Mars. The key problems all center around somehow delivering or obtaining enough oxygen and nitrogen, and water, to provide an atmosphere that will be livable.

That's the point at which an objection you'll hear over and over again is "but Mars doesn't have a magnetic field! The atmosphere will just be stripped away by the solar wind!!"

Now, this is an objection that seems intuitively — at least to me — not very plausible. If we can deliver that much material to Mars to start with, surely we can continue to top it up if necessary.

I am, however, one of those annoying people who thinks it's better to work the numbers instead of depending on intuition. I know it annoys other people regularly, and honestly, it kind of annoys me, although I also like the puzzle-solving aspects. In the engineering world, this is often spoken of as a "back of the envelope" estimate, and has a real advantage: if you do a BOE estimate and it says your idea is completely infeasible, you probably need to think again. (I've written about these in the context of software architecture here and here.)

Terraforming Mars: An Atmosphere

For the moment, we'll ignore the question of how we're going to provide an atmosphere — which has some interesting problems of its own — and just assume it's done. Mars' atmosphere will have approximately the same oxygen-nitrogen composition as Earth's, with a surface pressure of about 0.8 bar or 80,000 Pascal. (I’m trying to stick with metric throughout, and the proper metric is Pascal or Gods help us hectoPascal. But bar and millibar are most common.)

Why that? Because that's the average pressure in my home town of Alamosa, Colorado (altitude 2300 meters or 7543 feet) and people live there comfortably. Of course, people live comfortably at higher altitudes but this is my estimate.

We also will assume that there is no artificial magnetosphere. For the moment we're addressing the objection that the Sun would strip away the atmosphere without one. There are some cool proposals to provide one, which I'll write about another time, but that's another topic. (See, however, Bamford et al. 2002.) It's also worth noting that an artificial magnetosphere would address the problem of the radiation level at Mars' surface, another problem which, you guessed it, we'll address another time.

One more thing that will come into these calculations is that Mars is much smaller than Earth, with a surface gravity of about 3.7 m/s^2 compared to Earth's 9.8 m/s^2.

How Would a Terraformed Mars Lose Its Atmosphere

So, here we are in Marsopolis. Pretty town, third largest on Mars, with a lot of old-fashioned pre-terraforming architecture — airlock doors and most of the living space below ground level. You look up and think "but when will this nice air go away? There's no roof on the city any more."

There are basically two ways Mars can lose atmosphere.

Thermal Escape

Gas molecules in an atmosphere have an average velocity from heat — the warmer something is, the faster the molecules go, on average, and the lighter the molecules go the faster they go. If the molecules of the atmosphere are warm enough, they can exceed the escape velocity of their planet. This is called "Jeans Escape" and I'll leave it up to the reader to make an off-color remark on the name, but it's actually named for British astrophysicist Sir James Jeans, who first developed the theory in the early 20th century.

This explains, among other things, why the cold gas giants in the outer Solar System have retained atmospheres containing lots of light gases, like hydrogen and helium.

Mars' escape velocity is about 5 km/s. It turns out that at 250K — a little chilly but it's still winter — the most probable speed for N2 molecules is about 385.3 m/s, and for O2 about 360.4 m/s. Now, that's a statistical value — you might think "but there will be some fast molecules, won't there?" and you'd be right. I won't go through the whole calculation, because that's what AI is for, but my research assistant Grok has the full calculation here. The outcome of this is that yes, you will lose a few molecules:

At 250 K, N₂ molecules move at ~385–472 m/s and O₂ at ~360–441 m/s, peaking far below Mars’ 5,000 m/s escape velocity. The Maxwell-Boltzmann distribution’s tail is so tiny (less than 1 in 10^70 molecules) that thermal escape of these gases would take millions to billions of years, ensuring a stable atmosphere on human timescales.

So we can discount thermal escape.

Solar Wind "Sputtering"

So now we're down to the real question. "Won't solar wind, unimpeded by Mars having no magnetosphere, strip off the new atmosphere, making terraforming infeasible?"

The mechanism here is called "sputtering". The solar wind ionizes the upper atmosphere and accelerates those ions, stripping them away.

An interesting point here is that the current rate of loss has actually been measured by the NASA MAVEN Mission.

Mars' current atmospheric pressure is about 6 millibar, and according to MAVEN it's losing between 100 and 300 grams/sec.

If Mars got a 0.8 bar atmosphere (remember, Alamosa Colorado) it would require about approximately 3x10^15 metric tonnes of additional atmosphere. So, scaled to that pleasant and comfortable Earth atmosphere, you could expect to lose as much as around 3000 tonnes a year.

We're in that area where the numbers make a whistling noise as they rush past, but this is an easy division: 3x10^15 tonnes / 3x10^6 kg/yr gives us around 10^12 years. So yeah, in about a trillion years, Mars will lose its terraformed atmosphere.

That loss rate is a back-of-envelope estimate, and it wouldn't be too surprising if it's off by a factor of 10. So maybe it's only good for around 100 billion years.

Except...

In around 5 billion years, the sun will exit its normal lifetime and move on to a red giant. But well before that, the Sun's luminosity will increase dramatically. So after only a couple billion more years, the Sun will have made Mars uninhabitable.

In the meantime, my intuition is confirmed. And you know, if we can provide 10 quadrillion metric tonnes of new atmosphere to Mars, I don't think providing 3000 metric tonnes a year additionally is going to be a problem.