Why doesn't Earth's atmosphere escape into space?
Short answer:
Because gravity holds it in place.
Long answer:
There are two main forces to consider here:
- Gas pressure. As particles of gas bounce off each other, they create an outward pressure and the gas will expand unless it is constrained by an outside container or force. Earth's atmosphere creates such a pressure (we call it atmospheric pressure), and it wants to push all atoms in the atmosphere apart from each other, and therefore into space.
- Gravity. Created by the mass of Earth, gravity wants to pull all atoms in the atmosphere towards the centre of the Earth. This force opposes the atmospheric pressure(1).
Important: There is no "sucking" force coming from space. It's a "pushing" force from gas pressure (see example further below).
The two opposing forces of gas pressure and gravity will find a balance some distance from Earth's surface. All celestial bodies with an atmosphere work the same way. The stronger the body's gravity, the more the atmosphere will be pulled and compressed towards the surface. The stronger the gas pressure of the atmosphere, the more it will push away from the surface. If the gas pressure is high enough, the atmosphere will indeed be lost to space. Otherwise, it will find a balance with gravity that results in a relatively stable atmosphere up to a certain distance from the surface.
On Earth, the combined forces of atmospheric pressure and the planet's gravity results in an atmosphere up to about 100 km from the surface(2). Other planets vary wildly, depending on their gravity and atmospheric composition.
Example of sucking vs blowing:
Imagine being in a spaceship's pressurized airlock when the outside door is suddenly opened. You'd be sucked out into space, right? Not quite. As Commander Data explained in an episode of Star Trek, the air gets blown out of the airlock, not sucked(3). The physics is the same as on Earth, but the difference is gravity. On Earth, the pushing force into space is countered by the pulling force of gravity. In an airlock, the spaceship's gravity is nowhere near strong enough to hold the air back, so the pushing force wins (very quickly).
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Footnotes
1. Don't get hung up on whether we refer to gravity as a force or as space-time curvature. For the sake of this discussion, it doesn't matter, and thinking of it as a force is simpler. The end result is the same.
2. It's not actually a sudden drop-off. The atmosphere gets very thin much lower than 100 km, and continues extremely thinly out much farther. 100 km is simply a widely-accepted practical approximation of where space begins.
3. Some people argue that the word "sucked" can be correct in certain circumstances, depending on your relative perspective in the scenario. However, that discussion is really about semantics, not physics. The fact remains that the force is coming from the gas pushing, not space sucking.