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submitted 2 years ago by [email protected] to c/[email protected]

I've read that at the center of large celestial bodies there's zero gravity (or close to). While confirmation would be nice, if true, I'm wondering how large that area can actually be and moreover, does it scale up with more mass and/or even size - that is, does the sun have a larger center area of low (zero?) gravity than the earth and so on with evermore mass. Or is that area the same regardless of mass' size?

Thank you

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[-] [email protected] 7 points 2 years ago* (last edited 2 years ago)

It's basic math. You can do the gravitational calculations yourself. Basically any sphere of uniform density is going to exert gravity uniformly. So if you're in the center the pull from the mass on any direction will be counteracted by the pull in the opposite direction. It's one of the basic introduction to physics calculus examples.

Example:

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell.html

So to your question about what the zone of negligible gravity would be, you can define negligible gravity, and then figure out how large that zone would be based on the material on the outside of the shell.

Basically the further you get from the exact center of the sphere, you're going to have more gravity from the closer edge pulling you, and less gravity from the further edge offsetting that. So there'll be a gradient of increasing gravity as you get further away from the center

[-] [email protected] 3 points 2 years ago* (last edited 2 years ago)

Not quite. If by "edge" you mean the surface of the earth, then the force of gravity from the closer edge will always exactly offset the gravity from the farther edge. So if the earth were hollow, then you would experience zero gravity at any point in the hollow portion.

Of course, the earth is not hollow. And any mass under you (i.e. closer to the center than you are) will not be offset, and all of it will pull you towards the center. As you move further away from the center, more of the earth's mass will be closer to the center than you and therefore the force of gravity will increase.

[-] [email protected] -4 points 2 years ago

Nah, there's only one exact center of gravity for a given body of mass. You can't just make a vacuum and have gravity equalizer throughout it.

[-] [email protected] 3 points 2 years ago* (last edited 2 years ago)

Yes you can, as long as you are inside a perfectly spherical shell.

The net gravitational force on a point mass inside a spherical shell of mass is identically zero! Physically, this is a very important result because any spherically symmetric mass distribution outside the position of the test mass m can be build up as a series of such shells. This proves that the force from any spherically symmetric mass distribution on a mass inside its radius is zero.

From: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell2.html#wtls

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this post was submitted on 13 Aug 2023
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