So, the manual David gave me when he made me an Author said that I was supposed to alternate frivolous and serious posts*.  CharlieMao was one of those; this is the other—it’s time for some physics.

One of the long-term goals of sending men to Mars has traditionally been to establish a permanent population on the planet.  If that population is to be much more than hideously expensive spam in a can, they’ll need to be able to breathe something other than canned air and live outside of a pressurized environment.  The process of turning Mars from its current status of a desert at the temperature of dry ice with a soft vacuum for an atmosphere to something vaguely tolerable is called terraforming.

The question of how one might go about terraforming the planet is an interesting one, but I’m not going to write about that.  8-) It’s been done, over, and over again.  Instead, I will assume the success of terraforming and take a look at one complication that will arise afterwards.

(I’m just going to assert most of the physics here; if you want more information, it’s pretty easy to find.)

Temperature is defined as a measure of the mean (broadly, what most people think of as “the average") kinetic energy of a particle.  Kinetic energy is proportional to the mass times the square of the velocity.  That means that temperature is a measure of average particle velocity, with higher velocities for lower mass particles.  (At any temperature, hydrogen will be moving much faster than oxygen at the same temperature, because the hydrogen is much less massive.)

Planetary escape velocity is proportional to the square root of (the planet’s mass divided by the planet’s radius).  For Earth, this is a bit over 11 km/s; for Mars this is a bit over 5 km/s.  Both of these are higher than the mean velocity of important components of the atmosphere at tolerable temperatures, but that turns out not to be enough.

Because temperature is only a measure of mean velocity, some particles are faster than the mean and some are slower.  For our purposes (and for nearly any purposes, for that matter), we can treat the distribution of velocities as “normal”, which is commonly graphed as the sort of bell curve you have probably seen used for grading.  Without going into the math, it turns out that if the escape velocity is greater than about 10 times the mean velocity, the particles will hang around for billions of years.  If the escape velocity is about the same as the mean velocity, the time is only a few days.

So lets take a look at a few important gases and make some assumptions about a post-terraformed Mars:

My definition of “terraformed” includes liquid water and breathable air, so I will assume an average temperature of about 0 degrees C (32 degrees F or approximately 273 Kelvin) and an atmosphere with lots of free oxygen.  It can’t be pure oxygen (which is quite dangerous), and most very heavy gases are either difficult to make or find or are toxic, so we’ll assume lots of free nitrogen as well.  (In other words, we’ll assume something like the atmosphere of earth.) That means we need to find out the mean velocities of water vapor, oxygen, and nitrogen at 273 Kelvin.

Given these assumptions, the results are as follows:

V_rms O₂ = 0.461 Km/s

V_rms N₂ = 0.493 Km/s

V_rms H₂O = 0.615 Km/s

Since the escape velocity for Mars is 5.03 Km/s, this means that the oxygen and nitrogen are close, but probably ok, but the water vapor is going to be bleeding off into space.  (Remember that we need a velocity below 10% of the escape velocity for safety.) Even after terraforming, you will have to provide a constant source of new water to maintain a civilization.

By the way, this is why the current atmospheres of both Venus and Mars are predominantly CO₂.  Its molecular mass is enough higher than that of lighter gases (like methane and nitrogen) to keep it from escaping the planet in the high temperatures of Venus and the shallow gravity well of Mars.

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