This sounds really dumb, so forgive me. But one thing that's always felt weird to me about gravity is how we consider things to be one body.
Like yes, when we look at earth from incredibly far away, it's a pale blue dot. But all those oceans on it are flowing and separate from the solid ground underneath. Those large boulders on earth that would have their own (tiny) gravitational pull on their own in space are just part of earth's single gravitational force. All the airplanes in the sky are subject to the pull of the earth, but they're also a part of the gravitational pull that pulls other things to earth.
When shaking cereal, the big flakes rise to the top, but tiny bits of dust from each flake also separates and settle at the bottom. But earth, as a whole, has big bits and little bits everywhere all flowing freely. And gravity seemingly treats all those bits as a single object. But with sufficient distance between objects (e.g. different planets), it treats them separately. And with greater distance (e.g. galactic scale), it treats them as one again.
> And gravity seemingly treats all those bits as a single object.
It does not; but when you learned about gravity in school or wherever, you were only presented with scenarios in which it was valid to do so. Specifically, for Newtonian gravity, an object whose density is spherically symmetrical may be treated as a point mass at its center (w/r/t other point masses farther from the center than any point in the first object); this can be seen by integrating Newton's equation.
There's no reason to attribute this to special behavior by gravity with respect to "objects" which you identify. You could decompose a (spherically symmetrical) mass into several different spherically symmetrical "objects" and sum up their influence on a test mass, and the result is the same as if you had treated the original mass as a point mass. The hypothesis that gravity is "treating" the object one way or another now fails to distinguish all these possibilities; it's no longer physically meaningful.
At sufficiently large distances, or for sufficiently large ratio of large to small mass, the difference between, say, a planet and a spherically symmetrical mass is so small with respect to the main effect that it can simply be ignored.
> gravity seemingly treats all those bits as a single object
Understanding the tides depends very much on disabusing oneself of this scaffolding.
There’s a bit of math you can do where you calculate the gravitational effect of standing on a sphere. You can redistribute the mass within the sphere and it won’t affect the gravitational pull, assuming it’s radially symmetrical.
One of those unintuitive results.
It probably only works in classical gravity but it’s still neat.
The bit of math is the Shell Theorem <https://en.wikipedia.org/wiki/Shell_theorem>.
That actually sounds really intuitive to me. If you start with a uniform mass and then redistribute mass symmetrically it makes sense that the change in the two sides would cancel out.
It works for some types of symmetry but not others!
Interesting! Now, that sounds like a more unintuitive result to me. Can you give examples of symmetries for which it doesn't work?
The (Newtonian) Shell Theorem is fairly sensitive to spherical symmetry. In General Relativity one can write down a metric wherein inside any boundary surface there is flat spacetime. It's easiest to do this for a spherical boundary, but one can work out a metric which is axisymmetric (e.g. oblate and spinning or prolate and tidally deformed) and probably all sorts of other weird shapes following ideas from Gauss's Law for Gravitation. Writing down a metric for that is hard though -- really hard if the idea is to make it time-independent, and really really hard if the idea is to make it time-dependent but static (as in a complex Gaussian surface doesn't relax into a more spherical shell). For example, bumps raised on each other by binary black holes will vanish after merger (or if they fly away on hyperbolic trajectories, having "grazed" each other), leaving you with a spherical horizon (if nonspinnning) or an oblate one (if spinning).
Essentially to break spherical symmetry (or axisymmetry where there's spin) and keep it broken you have to introduce something like a dark energy. One can do that outside (retaining flat space inside) or inside (leading to the equivalent direction-dependent attraction of outside objects).