Flat Earth Follies: vacuum of space would suck the atmosphere off the Earth

Flat Earth Claim

The vacuum of space would suck the atmosphere off the Earth!

Figure 1 - Flat Earth Meme

Facts

The vacuum of space (or any other vacuum) does not 'suck' things into it. It has no energy or force with which to do so. What we need to be concerned about are the forces contained in the mass that is adjacent to the vacuum to see if they are sufficient to hold the matter together against their own kinetic energy.  First, you need to understand that air pressure decreases with altitude -- this is a hard fact.  Why doesn't the high-pressure air at sea-level equalize with the lower-pressure air above it?  Gosh, a mystery.  I guess there must be some force proportional to mass and inversely proportional to distance...  Since pressure drops dramatically with altitude there is no boundary at which high-pressure air is against the vacuum.  It just slowly drops to near-zero.

With that out of the way let's work through a simpler example of a marble in a near-vacuum. There are intermolecular forces within the glass of the marble that are holding the atoms bound together, these forces are sufficient to prevent the silicon dioxide (SiO₂) molecules in the glass from flying off the marble and into space due to their thermodynamic forces under normal circumstances (hopefully we can agree on that). However, if we heat that marble up eventually some of those silicon dioxide molecules will have enough energy to break those bonds and separate into the vacuum. This is the same as water evaporating into the air. Once that one water molecule has enough enough to break the weak bonds with other water it can shoot off into the air. And we know a lot about this process.

If we put that marble in a pressure chamber and apply pressure to the marble then we would have to heat the marble up more before the thermodynamic energy would be suffice to liberate the molecules. The same thing happens when you put a lid on the water pot, the greater pressure means the water has to get hotter to boil - that increased heat in the water is also available to cook your food faster.

The near-vacuum just represents near-zero pressure pressing back on the marble, or our water, or the Earth's upper atmosphere.

Now let's consider the gaseous atmosphere of the Earth.

In a gas the average molecular speed is given by √(3RT/M)

where

R = molar gas constant = 8.31447 J mol⁻¹ K⁻¹
T = temperature in kelvin = 190K (at 100km altitude) to 290K (at 0km altitude) [chart]

M = molar mass (g/mole) =

• hydrogen (H) = 1.00794
• oxygen (O) = 15.9994
• oxygen gas (O₂) = 31.9988 (just 2 × oxygen)

Lighter molecules go faster since M is a divisor and higher temperature goes faster since T is on top.

So let's compute some velocities and since this is an average, we will double this value so we're looking at much faster than average molecules. We will also use the hotter temperature of 290K even though by the time it's 100km up in the atmosphere it would have necessarily cooled down to ~190K.

hydrogen (H) = √(3RT/1.00794) = 2678.9 m/s -- WOAH, that's pretty fast... 2× = 5357.8 m/s
oxygen (O) = √(3RT/15.9994) = 672.4 m/s -- and 2× = 1344.8 m/s
oxygen gas (O₂) = √(3RT/31.9988) = 475.46 m/s -- and 2× = 950.92 m/s

Now we can compare this speed against the Escape Velocity required for an object to leave the influence of Earth's gravity.

At 0km altitude Escape Velocity is ~11180 m/s
At 100km altitude Escape Velocity is ~11100 m/s

To escape the pull of Earth's gravity our particle would need to be going in excess of 11100 m/s** but as we've shown, even with the fastest hydrogen (H) molecules they are MOSTLY going maybe half that. Now if you add in some extra solar radiation hitting a high speed molecule (exospheric H can reach 1800K/6674.2m/s average with MUCH higher peaks, perhaps up to 18000m/s) -- so sure, some gas particles are going to escape, the lightest ones are most likely to do so. One estimate is that we loose about 95,000 tonnes of Hydrogen every year (3kg/sec). Other gases do not escape at a very significant rate -- these calculations show why.

For more details see Atmospheric Escape

** they also need to not hit other molecules before they escape, this is called the 'mean free path', and there are a few other considerations, but this is a good first approximation.

Conclusion

Earth's gravity is what holds our atmosphere to the planet and we see here that the force of gravity, which necessitates the 'Escape Velocity', far exceeds the molecular speeds for most cases. So the force of Gravity works exactly like the intermolecular bonds in our marble, which holds the molecules with sufficient force to prevent them from escaping even through there is nothing in space pushing them down.

See Also:

David C. Catling and Kevin J. Zahnle, The Planetary Air Leak, Scientific American, May 2009, p. 26