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Firstly I’m genuinely interesting in a working explanation for this question. It is for this reason that I am editing the question to fine tune the question. In essense the question has remained the same.

In order for me to check mark the best answer I’m going to ask for citations for the claims made in the answers because I’m getting lots of theory and responders are not in agreement, as far as I can tell. Also I cannot accept circular reasoning i.e. if we assume x then y, since y therefore x. That’s fallacious logical reasoning because x was never proven it was assumed and y might be independent of x.

The vacuum of space is incredibly powerful, 1 x 10^-17 torr, and the vacuum between the Earth and the Moon is 1 x 10^-11 torr.

How can such a vacuum (very low pressure) in close proximity to the Earth’s atmosphere (high pressure) that goes to 8.5km elevation, coexist with the open system of the Earth’s atmosphere? How does this not defy the second law of thermodynamics and still remain true?

Space is low pressure and the earth’s atmosphere is high pressure. In order to have any pressure the gas requires (demands) that it press upon something.

Pressure is a force exerted by the substance per unit area on another substance. The pressure of a gas is the force that the gas exerts on the walls of its container. When you blow air into a balloon, the balloon expands because the pressure of air molecules is greater on the inside of the balloon than the outside. Pressure is a property which determines the direction in which mass flows. If the balloon is released, the air moves from a region of high pressure to a region of low pressure and the balloon deflates. 1

Earth is an open system that presses against the vacuum of space, why therefore is the second law of thermodynamics suspended if indeed it is a law.
Space is low pressure, therefore the atmosphere which is not in a container should disperse into the low pressure space.

• VACUUM (There’s nothing to it…)




• Vacuum Technology PHY451 October 22, 2014

Your assertion that our atmosphere doesn't escape is wrong.

Helium and Hydrogen atoms have a low enough mass that they do have an escape velocity at the temperatures on the edge of our atmosphere. This means that when those gasses are released, if they fail to react on their way out, then they will be lost forever to the planet. This is why when you look at our atmosphere we just don't have any.

You also seem to assert that there's a "line" where it's the high pressure of our atmosphere on one side, and a low pressure of space on the other; that line doesn't exist. The pressure is a gradient, in the same way as you swim down in a pool, at the top the pressure is low; at the bottom it's high; and it changes steadily as you traverse between the two. Hence why climbers of Everest need to carry oxygen.

The heavier gasses don't escape for the same reason that a rock you throw doesn't escape. It requires energy to escape the gravitational well of Earth; and they don't have it; currently. Of course, as the atmosphere heats up from global warming, heavier and heavier particles will gain the energy to leave our atmosphere...

The underlying reason that the molecules of Earth's atmosphere do not fly away into the surrounding vacuum is that they are slower than the escape velocity, which would be 11200 m/s. The typical molecule speed at ground level and room temperature appears to be 500 m/s. If it had a free path such a molecule could fly vertically for $t = v/a = frac500m/s9.81m/s^2 approx 50s$ before starting to fall back, with an average velocity of 250 m/s, thus reaching an altitude of 12 or 13 km. (In reality it would collide with other molecules on the way, transferring some kinetic energy to them, so that they could in turn rise higher. Obviously, molecules at the outer fringes of the atmosphere are the real escape candidates.)

Molecules which are fast enough surely do escape Earth's gravity well. Some may have been accelerated by particles of the solar wind, some may just have been on the long tail of the standard distribution. The latter is more likely for light atoms and molecules which are faster, like Helium and Hydrogen. Hydrogen's average speed at room temperature is perhaps 2000 m/s. These gases have indeed mostly left Earth for good long ago.

(By the way, the solar wind would likely "blow away" our atmosphere in the long run — as it did on Mars — if it weren't deflected by the Earth's magnetic field.)

update: This answer was written before the question was modified. I've tried to explain where a value like 10^-17 Torr for deep space might come from, but it's since been dropped in lieu of 10^-11 Torr at the Moon, which is probably a better way to formulate the question.

I think the answer is the same, two points very far away can have very different pressures. They can coexist in the same solar system, just not right next to each other. I think "Why doesn't the Moon have at least a small atmosphere?" could also be an excellent, but very different question.

In a comment the OP links to the presentation VACUUM (There’s nothing to it… ) written from the perspective of an engineer in the semiconductor manufacturing industry.

Slide 6 gives examples of vacuum levels in different situations:

Going down:

• Low vacuum: 760 Torr to 1 x 10^-3 Torr
  
  
  • Vacuum cleaner: to 600 Torr
  
  
  • Thermos bottle 10^-3 Torr
  
  


• High vacuum: 10^-3 to 10^-9 Torr
  
  
  • Electron microscope
  
  
  • Ion Implanter
    – Evaporator
    – Sputterer
  
  


• Ultra high vacuum: 10^-9 to 10^-12 Torr
  
  
  • CERN LHC: 1 x 10^-10 Torr
  
  
  • Moon’s surface: 1 x 10^-11 Torr
  
  
  • Deep Space 1 x 10-¹⁷ Torr = 0.000,000,000,000,000,01 Torr
  
  

So we can see that the value of 1 x 10-¹⁷ Torr is associated with a place in "Deep Space" which is (probably) beyond that of the Moon.

Let's see if we can figure out where the author is getting that number.

According to the Wikipedia article on the interstellar medium (space between stars, far away from solar systems and other things):

In all phases, the interstellar medium is extremely tenuous by terrestrial standards. In cool, dense regions of the ISM, matter is primarily in molecular form, and reaches number densities of 106 molecules per cm³ (1 million molecules per cm³). In hot, diffuse regions of the ISM, matter is primarily ionized, and the density may be as low as 10⁻⁴ ions per cm³. Compare this with a number density of roughly 10¹⁹ molecules per cm³ for air at sea level, and 10¹⁰ molecules per cm³ (10 billion molecules per cm³) for a laboratory high-vacuum chamber.

It is harder to talk about pressure than density because pressure is related to both number density and temperature. The atmosphere is more than 10x hotter than interstellar medium, so let's look for a number density ratio of 1/10 of 1000 Torr versus 10^-17 Torr, or a ratio of 10¹⁹.

If (according to Wikipedia) Earth's atmosphere has a density of 10¹⁹ per cm³, we're looking for a density of 1 per cm³. Checking Wikipedia we can see that there are components of the interstellar medium with number densities between 10⁶ and 10^-4.

It looks like the value in the presentation a rough ballpark estimate, but isn't off by more than a handful of orders of magnitude ;-)

How can such a vacuum coexist with the open system of earth’s atmosphere whereby debris from space can enter in?

While these two pressures can coexist in the same universe, they don't coexist in proximity at all. The interstellar medium is very, very far away from Earth's atmosphere, on the order of a lightyear.

Gravity keeps Earth's atmosphere nearby Earth, the solar system has gas produced by (and attracted by) the Sun's gravity. In interstellar space, there just isn't any source of gas, and what might have been there at one time has moved away, towards sources of gravity, over billions of years.

Space is low pressure and the earth’s atmosphere is high pressure. In order to have any pressure the gas requires (demands) that it press upon something.

Yes, and that 'something' is Earth's gravity. Gas molecules are pulled down toward the surface just like all other matter.

So there's an equilibrium between gravity and gas pressure. At the upper end of the atmosphere, some gas escapes (molecules reach escape velocity), this is predominantly the light gases.

I think uhoh covered proximity but just to induce equilibrium to further elaborate:

First of all, positive pressure and negative pressure are just terminology based on where we started i.e. 1 atm and above/below, we just went along. There is zero pressure and gradually moving up from that. Say, perfect vacuum starts at zero pressure and move up as comes across high pressure open system. Things are always at equilibrium and if you want to move something from low pressure to high, you do some work as you have mentioned second law of thermodynamics. Gravity does that work in this case till some point. Ignore everything, lets say there is one good looking blue dot aka earth, and as you move close, gravity starts to get stronger. So, it will invite more molecule to be cuddly and at same time pressure gradient will move gas the other way. Eventually they will reach at equilibrium i.e. same transference. This is true for any height from earth. In absence of such equilibrium earth would loose its atmosphere or gain more (may be case at astronomical time scale). We start at one (gravity rules) to continuously (important) merge to space vacuum with equilibrium all along the line. Once gas truly escape earth gravity (i.e. temperature movement is way stronger than earth gravity), it has no reason to hang around. Same way we can gain by unsuspecting wandering gas molecules. Earth atmosphere looks at equilibrium at human timescale. But earth loose and gain as these forces continuously change with distance.

Edit: let's try to come up based on fundamental property of universe:

Let's take two points A and B sealed in perfect vacuum by a long tube.

1 insert some gas at point A. You would expect, given enough time, gas will diffuse uniformly between point A and B. That is one property of universe: entropy always maximize. (Remember pressure is not a force). There is no answer why but it does and give rise to interesting open physics problem: arrow of time. Wikipedia has nice article on it.

2. Now second property: fundamental force gravity which attracts everything. Say gas is diffused and you switch on gravity at point A. You expect gas to move towards point A.
   And it will.




3. Now both at play. At any cross section , gas would cross to go to A due to gravity and B to maximize the entropy. Given enough time there will be equilibrium. Equal transference at any length between A and B. But you would expect A to be more concentrated since gravity wants all gas at A where entropy wants all uniformly distributed between A and B. So there will be gradient between A and B.




4. Now think of tube between earth and space and make it disappear. Now B at low concentration, there can be escape but is it significant at human scale. In short atmosphere gradually thins out.

Answer based on escape velocity are fine but couple of things:

1. Escape velocity is consequence of fundamental force gravity.




2. You don't need escape velocity to leave earth. Only true for projectile thrown from ground.




3. Gas velocity is function of temperature. Earth atomposhere temperate decreases and then increases and then again decreases and guess -increases again. (With height).See Wikipedia. So will Gas velocity. Where escape velocity will decrease with height.




4. Gas in space is hot because of high kinetic energy and lack of collision to transfer heat. Speed is not due to lack of gravity. You can argue lack of gravity explains lack of concentration but that feels like going in circles.

All of this is in Wikipedia and basic science
Hope it is more clear..