Beautiful illustration of this principle! Now I’d love to see a depiction of an intangible point falling through an object of constant density (so gravity smoothly goes to zero at the exact center)! (please) 😄
As in: no gravity inside the shell because that’s just how it works out. But that’s only for a spherical shell. Is that what’s modeled here, with the in-plane gravitational contributions from out-of-plane parts of the shell still modeled, just not shown on the screen?
@ I’m saying I’ve only cranked through the math in 3D and I don’t remember the exact forms, so I can’t tell from memory if there’s anything that would make in NOT work in 2D.
I think you'd need to slightly modify gravity's distance-dependence in 2D to keep the shell theorem for circles. Instead of an inverse-square law, 2D gravity would have a 1/r dependence.
Yes, just inside the hole provided perfect sphere with homogeneous mass distribution and assuming a (very) small hole, which is kind of odd to think about.
Beautiful illustration of this principle! Now I’d love to see a depiction of an intangible point falling through an object of constant density (so gravity smoothly goes to zero at the exact center)! (please) 😄
I just love your simulations! Thanks for posting.
I like how the ball jumps higher around the ball at the end and compensates energy-wise the higher amplitude with a slower speed
As in: no gravity inside the shell because that’s just how it works out. But that’s only for a spherical shell. Is that what’s modeled here, with the in-plane gravitational contributions from out-of-plane parts of the shell still modeled, just not shown on the screen?
Yes, good point. The 3D shell is here just modeled as a 2D circle.
Mmmm are you saying that Newton's shell theorem doesn't work in 2D?
@ I’m saying I’ve only cranked through the math in 3D and I don’t remember the exact forms, so I can’t tell from memory if there’s anything that would make in NOT work in 2D.
I think you'd need to slightly modify gravity's distance-dependence in 2D to keep the shell theorem for circles. Instead of an inverse-square law, 2D gravity would have a 1/r dependence.
@@tuckermatis1572 you're encouraging me to run an integral I haven't seen in 25 years, aren't you
One mindblowing consequence of the generalized Stokes' Theorem, one of my favorite theorems
Is the effect of the hole ignored?
Yes.
When I'm in a "Not reading the description" challenge and my opponent is a Type A TH-cam commenter.
Cool idea.
How far underground would you have to dig to be weightless? Just below the ellipsoid?
Yes, just inside the hole provided perfect sphere with homogeneous mass distribution and assuming a (very) small hole, which is kind of odd to think about.
Kinda fun
Does this work with electric charge, too?
It should work for anything with an inverse-square law
Simple, easy, basic.
Proof the earth is hollow.
Proof the black hole is hollow.