How the size of a planet determines its atmosphere

People have asked me to write something about terraforming Mars, a subject that is of great interest to SF buffs. I think Kim Stanley Robinson in his Mars series does a pretty good summary of all the currently-held scientific opinions on techniques of how we could achieve this. Yes, it would involve some form of artificial warming, it would involve melting the polar ice and finding underground water. It would involve long-term (think hundreds of years) and large-scale engineering, but most importantly, two things: it would involve the introduction of large quantities of nitrogen, and it would be a constant and ongoing process, since there is nothing we can do about the main reason why Mars lost nitrogen and oxygen from its atmosphere in the first place: the planet is simply too small.

The mass of a planet defines its gravity. To understand this, we need to go back to physics. According to Newton’s law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses, and inversely proportional to the square of the distance between them:
If one of the masses were really small, say a human body compared to a planet, the force described by this law would be what we experience every day as gravity. The law says: more mass, more gravity. Hence, gravity on the Moon is smaller than that on Earth, which in turn is smaller than that on Jupiter (presuming there was a surface on Jupiter you could stand on).

Another term: escape velocity, which is the speed needed to break free from a gravitational field. Speed itself is attained as function of an object’s mass and the forces holding it in place versus the forces applied to it in the other direction (OK, I’m confuddling speed with acceleration here, but you get the gist). Since the force that holds all objects on a planet is gravity, which is the same for objects of all sizes, it becomes easy to see that if you are planning to propel something off a planet, the best tool available to you to make it easier is to reduce the object’s mass.

In simple terms: your highest jumps on Earth would be mega-leaps on the Moon, while on an asteroid, your best effort at jumping might well hurtle you into space. Try jumping on Jupiter, however, and you might not even get off the ground. Say you wanted to get off the ground on Jupiter, you might train your muscles, but assuming you are reasonably fit, it’s probably more effective to go on a strict diet.

Now imagine you were a particle in the atmosphere. Our atmosphere is made up of gas. The gas state indicates atoms or molecules moving about freely without any attachment to each other. In a gas, particles are constantly bouncing off against each other. In doing so, they acquire speed, helped along by the heat of the Sun’s rays. For a proportion of these particles, that will mean gaining a speed greater than the escape velocity of the planet.

Following the above, the heavier a particle is, the less easy it will gain that speed. Earth’s gravity, for example, is too weak to hold onto its hydrogen or helium. Jupiter’s gravity is not. This is why the large planets are all gas giants. A planet starts retaining helium at about 6 Earth masses, and when it is bigger, about 10 Earth masses, it will retain hydrogen.

Move down the periodic table and see that of the next of the most common elements in the universe that exist in gas form at relatively low temperatures, Earth’s gravity is strong enough to retain atomic nitrogen. Nitrogen (atomic weight 14 grams per mol) is an element that doesn’t tend to form bonds easily. Simply said, it likes being a gas. The next element down, oxygen (atomic weight 16 grams per mol), loves attaching itself to other things, and bonds readily with carbon, another element common in the universe, but not a gas at any temperatures below 4000C. Carbon dioxide, nitrogen dioxide water and methane are all simple combinations of these common elements that we find in Earth’s atmosphere. Add up their atomic weights (44, 46, 18 and 16 grams per mol respectively) and you will see that as planet size becomes smaller, the atmosphere will lose its methane at approximately the same size as it loses its oxygen, then water, then carbon dioxide and then nitrogen dioxide.

Where is Mars on this scale? Well, it’s just big enough to retain carbon dioxide and nitrogen dioxide. There is plenty of the former, but since nitrogen in atomic state is lost from Mars, and since nitrogen doesn’t easily react with anything much, there is not much nitrogen dioxide to be had. Thus the atmosphere of Mars contains mainly carbon dioxide. If we were to artificially establish an atmosphere on Mars, any oxygen wouldn’t immediately evaporate into space, but the atmosphere would require constant and probably expensive maintenance.

This a very simplistic summary of an interesting subject. Yes, things are not quite as straightforward as this (you may stop yelling ‘Titan’ in the background, you over there), but these are the simple, physical processes involved. If you want to read more, I recommend the book Terraforming by Martin Beech.

7 comments on “How the size of a planet determines its atmosphere

  1. Because I’m about to start teaching this to first years… technically escape velocity is the velocity required to get a kinetic energy equal to the gravitational potential energy that’s holding things down. It’s not quite directly related to force.

    You got me thinking though. The density of the atmosphere would also depend on temperature. If you had some way of only heating the layer immediately adjacent to the ground (ie where the people are) while keeping the top layers relatively cold, you could make yourself a thicker atmosphere… Hmm…

    • agree about the fuddling, but I was trying to say things without having to resort to formulae, which tend to scare people. There is probably a better way of saying it, but I’d be the first to admit that I’m not a physicist.
      Temperature of course is the big white elephant, as is surface composition. And while I was writing that I was wondering just how did Titan fetch up with an atmosphere? I’m presuming there is some sort of outgassing going on, maybe in combination with temperaure effects that create some sort of atmospheric cell circulation that prevents air being shot into space. But I’m still thinking there has to be replenishment from the bottom, too. Do you know any more about this? Can’t recall the book I have about Titan giving an explanation.

  2. I think part of the reason is that Titan has a lot if organic molecules floating around. I’m going to look into this further (also because the part I’m up to in current WiP edit requires a heavily populated Mars). I do remember reading about Titan having an unusual amount of hydrogen in it’s upper atmosphere and hence that some (bio?) chemical processes on the surface had to be to blame. I don’t know the full atmospheric composition, though. Naively, I might suspect that temperature on Titan also played a part (being much further from the sun etc) but I don’t know enough about the tidal heating happening (or not happening).

    I will get back to you when I know more.

    • Geoffrey Landis wrote this on my facebook page:

      “Titan is very cold; the kinetic energy of a gas molecule is proportional to temperature, and hence Jeans’ escape is exponential in the temperature. Titan also spends much of its orbit inside Saturn’s magnetosphere.”

      I suppose magnetic radiation has to do with it. A quick check on Titan’s atmosphere confirms that it’s mostly N2. Why hasn’t that gone sproinging off into space? Very good question. Could you theoretically reproduce those conditions?

      • OK, so I did some googling/research and found a paper/conference proceedings ( which explains the mysteries of Titan’s atmosphere, more or less.

        I get the impression that without the sun, the methane on titan would happily hang about there (and methane is lighter than nitrogen molecules, for reference). However, the sun dissociates/reacts the methane into other, lighter molecules which either escape the planet or rain down on it. So a possible theory to explain the persistent methane in the atmosphere (apparently it’d only take 10-20 million years to deplete if it wasn’t being replenished) is that it’s seeping out from inside the planet somehow.

        On the matter of nitrogen, the main dilemma seems to be where it came from, more so than why it’s still there. According to that article, atmospheric nitrogen has deleted over time (particularly the lighter isotope) and probably came from cometary collisions, although there are some problems with that too.

        But basically, Titan’s atmosphere IS depleting, but other things are adding to it (notably the methane). Also, the fact that it has a thick upperish layer that prevents the sun from reaching lower layers and photodissociating them helps keep it in a kind of semi-equilibrium.

        Now I’m going to have to go read about Venus’s atmosphere and find out what it’s excuse for being so thick is 😉 (except not literally now, because now is sleep time).

        Oh, also, the magnetosphere would only affect charged particles, which most molecules aren’t, so I’m not sure how much of an effect that would have.

        And as for modelling Titan’s atmospheric conditions… they’re working on it, but it doesn’t look like there’s anything definitive.

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  4. Thanks for the great article. Clearest explanation I’ve found so far for determining alien atmospheres. Also hurray, Mars trilogy!

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