If it works exactly like a ball that is placed on top of a cloth, doesn’t the celestial bodies that is rotating around the ball will eventually get sucked into the center?
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That analogy is OK for getting a very general idea of how gravity can be viewed geometrically, but it’s a very oversimplified picture. The biggest flaw is that it makes it seem as if the “warping” is all in space, but that’s simply not the case. See, in general relativity, (Einstein’s model of gravity, which is the best model of gravity we currently have), space and time aren’t independent entities, but rather different components of one thing, which we uncreatively call “spacetime”. So, in the simple fabric analogy, the fabric represents not *space* but *spacetime*. And, here’s the key point, except in very extreme cases like with black hopes, almost all the “warping” of spacetime from massive objects happens not to the space components of spacetime, but to the time component. So, objects even as massive as planets have very little affect on the *space* surrounding them — instead, the gravitational affect they have on nearby objects is mostly an effect on those objects’ *time* trajectories.
This video does a really good job of breaking this all down and giving an intuitive and *visual* understanding. It’s one of the best ELI5-type explanations I’ve seen on any topic precisely because of how visual it makes things. In actually specifically starts with the simple ball on fabric picture, explains the problems with it, and then, piece-by-piece, fixes the problems and ultimately ends up with something much more accurate and yet still as intuitive as possible. I came across it a couple years ago and it really stuck with me. https://youtu.be/wrwgIjBUYVc
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