It's helpful to visualize Earth's gravity well as a literal well--a corridor that things fall down to impact Earth. If you start outside of it, you have to traverse the whole tube in order to hit the planet. "Falling" that far imparts a certain amount of energy, regardless of what you were doing before you "jumped in" to the well. If you fell straight through the well and then "up" the other side, you'd come out at the other end with the same velocity you had before you entered, since the energy is conserved. Since you started outside the well, you have to have enough velocity to exit the well again. That's escape velocity. Therefore, anything captured by Earth's gravity well has to (more or less) be moving at at least escape velocity when it gets to the planet itself.
Remember that gravity is (among other things) a way of accelerating. In Earth's case, something "in our well" is having its velocity increased by 9.8 meters/second every second. Until you hit atmosphere, there's basically nothing else counteracting that acceleration, so you can pick up quite a bit of velocity with respect to the ground. There's no such thing as a terminal velocity in space, so you can get going good and fast. Once you hit atmosphere, all that kinetic energy has to go somewhere as other forces start decelerating you toward your terminal velocity. Heat is among the places that kinetic energy goes.
Your explanation is way better than my rambling answer I think. But just to nitpick a bit, 9.8 meters/second every second is the surface level acceleration, but since gravity weakens with distance and the edge of the gravity well is the furthest point from earth you could conceivably "drop" something and have it ever landing on earth, the initial acceleration would be incredibly slow. If we imagine a meteor that starts off static relative to earth and at the very limit of our gravity well it might be accelerated by a cm/year every year for the first few thousand years, and might take a million of years to actually hit. But when it hit it would do so at pretty much perfect escape velocity, and if it could pass through Earth it would just barely not escape our gravity well and would eventually fall back after another 2 million years.
Yeah, there's a lot of weird details here that can complicate things; I was going for a very basic answer. Even in the kind of case you're talking about, it's unlikely that the object would stay in a stable equilibrium--if it's really that close, perturbations from other objects' gravity would almost certainly kick it out of that cycle. The solar system is chaotic, and orbital dynamics get messy. Thanks for the elaboration, though!
Of course! Moon fuckery alone messes up orbits enough that you quickly realize this is impossible even without bringing the gravity of the fucking sun or Jupiter into it. It was just meant as an example of how gravity works and what escape velocity is. So this is what orbital mechanics says would happen if there were only two bodies of matter in the entire universe.
It's helpful to visualize Earth's gravity well as a literal well--a corridor that things fall down to impact Earth. If you start outside of it, you have to traverse the whole tube in order to hit the planet. "Falling" that far imparts a certain amount of energy, regardless of what you were doing before you "jumped in" to the well. If you fell straight through the well and then "up" the other side, you'd come out at the other end with the same velocity you had before you entered, since the energy is conserved. Since you started outside the well, you have to have enough velocity to exit the well again. That's escape velocity. Therefore, anything captured by Earth's gravity well has to (more or less) be moving at at least escape velocity when it gets to the planet itself.
Remember that gravity is (among other things) a way of accelerating. In Earth's case, something "in our well" is having its velocity increased by 9.8 meters/second every second. Until you hit atmosphere, there's basically nothing else counteracting that acceleration, so you can pick up quite a bit of velocity with respect to the ground. There's no such thing as a terminal velocity in space, so you can get going good and fast. Once you hit atmosphere, all that kinetic energy has to go somewhere as other forces start decelerating you toward your terminal velocity. Heat is among the places that kinetic energy goes.
Your explanation is way better than my rambling answer I think. But just to nitpick a bit, 9.8 meters/second every second is the surface level acceleration, but since gravity weakens with distance and the edge of the gravity well is the furthest point from earth you could conceivably "drop" something and have it ever landing on earth, the initial acceleration would be incredibly slow. If we imagine a meteor that starts off static relative to earth and at the very limit of our gravity well it might be accelerated by a cm/year every year for the first few thousand years, and might take a million of years to actually hit. But when it hit it would do so at pretty much perfect escape velocity, and if it could pass through Earth it would just barely not escape our gravity well and would eventually fall back after another 2 million years.
Yeah, there's a lot of weird details here that can complicate things; I was going for a very basic answer. Even in the kind of case you're talking about, it's unlikely that the object would stay in a stable equilibrium--if it's really that close, perturbations from other objects' gravity would almost certainly kick it out of that cycle. The solar system is chaotic, and orbital dynamics get messy. Thanks for the elaboration, though!
Of course! Moon fuckery alone messes up orbits enough that you quickly realize this is impossible even without bringing the gravity of the fucking sun or Jupiter into it. It was just meant as an example of how gravity works and what escape velocity is. So this is what orbital mechanics says would happen if there were only two bodies of matter in the entire universe.