From what I understand, air gets thinner the further up you go. This I assume is because Earth’s gravity pulls all the heaviest particles down to its centre. I’m wondering about gravity itself though, is there a gradual shift in the strength of gravity as there is in the consistency of the air, or does gravity apply to the whole field surrounding the Earth up to the very perimeter and then quickly fall off?
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The force of gravity follows the inverse square law. That is, the strength of gravity falls off with the square of the distance to the mass. Double your distance from a source of mass and the force isn’t halved, it’s divided by X^2. That means it falls off pretty quickly.
However, it never actually gets to zero. The force of gravity is infinite. No matter how far away from the Earth you go, you will still feel the pull of the Earth. Local sources of gravity will almost certainly overwhelm it, though. Like, if you’re right next to Jupiter, the force of gravity from the Earth isn’t zero, but you’re *very* far away and the force is pretty tiny, while the force from Jupiter is much *much* stronger, so you will fall towards Jupiter.
The Earth doesn’t have a smooth transition from “not space” to “space.” There are various definitions used for convenience, but there’s never a line where if you’re coming to Earth from space suddenly you *are* in the atmosphere but you weren’t before. The International Space Station, for example, has to periodically boost itself back up because it does experience just a teeny tiny bit of drag from the very very thin wisps of atmosphere at that altitude above the Earth. The atmosphere sticks to Earth because, mostly, the force of gravity is stronger than other forces that would push or pull it away. But some atmosphere is lost to solar winds, or just wanders off into deep space. But other particles come in from space and get captured by Earth’s gravity. So, overall, the atmosphere stays *more or less* the same.
Some other things to consider: The Earth is not a *point*, it’s a big ball with volume. You’re already pretty far away from the center of Earth’s gravity. But you’re also right next to *part* of the Earth – the ground underneath you. But you’re also quite far away from the opposite side of the Earth. The point is that although gravity falls off very quickly with distances, you’re already at a distance, not right next to *all* of the mass. [This graph](https://upload.wikimedia.org/wikipedia/commons/thumb/b/be/Grav_field_sphere.svg/524px-Grav_field_sphere.svg.png) shows how the force changes over the distance. Notice that at first the line goes up: if you’re at the center of a sphere of mass – at the center of the Earth – there’s no mass below you, only mass above you. And, there’s mass in all directions canceling it all out so that the *overall* force of gravity is zero. As you move away from the center of the Earth, there is more mass below you and more mass above you, so the force increases until you reach the surface. After that, all of the mass is below you (except for the atmosphere, which is negligible) and the force will decrease as you move away.
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