Area of gravity at the center of large, dense celestial bodies...

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

octoperson ,

If you had a planet that was hollow in the center*, the entire hollow region would have zero gravity. You could have a thin-skinned planet with the entire interior an empty weightless void. I doubt any planets like this actually exist.

  • Assuming radial symmetry. If you can represent the planet as concentric spherical shells then you’re good.
awwwyissss ,

A center of gravity is a single point and couldn’t be expanded to fill a planet’s interior, even if the space was only 1m^3

Rayleigh ,

You’re right but that was not the point. The comment just explained that at any point inside a hollow sphere gravity forces cancel out so that effectively there is no gravity.

Spzi ,

If you had a planet that was hollow in the center*, the entire hollow region would have zero gravity. You could have a thin-skinned planet with the entire interior an empty weightless void. I doubt any planets like this actually exist.

  • Assuming radial symmetry. If you can represent the planet as concentric spherical shells then you’re good.

I thought this was wrong, but it is true:

Brb fixing my other comments.

octoperson , (edited )

Yeah it’s a pretty counter intuitive result. I’d expect a greater pull of gravity towards the nearer side, but it turns out to be exactly cancelled out by the greater mass on the further side.

E: oops, looking at your edited comment, I should stress this is only for hollow bodies. Your comment pre-edit was correct for non-hollow bodies. If you’re part way to the middle of a planet, you can think of the planet as two sections, a small sphere for the part that’s below you, and a larger hollow shell for the rest. You experience no gravity from the outer shell, so only feel gravity of the smaller mass below. 10m from the earth’s center, you feel equivalent gravity to if you were on a 10m radius iron sphere.

Spzi , (edited )

There is no area or volume of zero gravity inside planets or stars. It exists as a point, but since it’s a point, it has zero size.

Go in any direction from that point, no matter how little. Now more mass is behind you than in front of you; you feel gravity pulling you back.

Edit: Seems I was wrong, sorry.

“If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object’s location within the shell.”

Jeredin OP ,
@Jeredin@lemm.ee avatar

So it’s not zero but low gravity and increases the more mass-I leave behind me as I move out from the center?

Spzi ,

That’s exactly what I meant, yes.

I’m not sure if it was correct though, edited my previous comment. Though maybe you did not ask about hollow bodies.

FlowVoid ,

Inside a sphere of constant density, gravity is linearly related to distance from the center.

So for example the Earth has a radius of ~4000 miles. Assuming it has constant density, you would experience 0 gravity at its center, 0.1% of surface gravity at 4 miles from the center, 1% of surface gravity at 40 miles from the center, half of surface gravity at halfway to the surface, and so on.

Jeredin OP ,
@Jeredin@lemm.ee avatar

So for the Sun, taking its density/pressure into account, will the same gravity gradient exist but on a much larger scale?

Thank you

FlowVoid , (edited )

A linear relationship would exist if the sun were uniform in density, but it isn’t.

Though there is still a nonlinear change in gravity as you approach the center of the sun.

Jeredin OP ,
@Jeredin@lemm.ee avatar

So the larger the star, given that most (or all) aren’t uniform, there will come a gradient of gravity at its center that one can’t even call it low gravity - it’s heavy material is simply churning too much for their to be a stable center of gravity?

FlowVoid ,

I think the best way to visualize it is that when you are inside a star, you are effectively “standing” on a smaller star. Everything behind you can theoretically be ignored. When you are very close to the center, you are standing on a very tiny star.

Jeredin OP ,
@Jeredin@lemm.ee avatar

So instead of the hole density from one side to the other, I only have the density from the center to its surface, am I understanding that correctly?

FlowVoid , (edited )

I’m not sure what you mean by “surface”.

Imagine you are standing on the surface of Earth, and you weighed 200 pounds.

Now imagine Earth were magically transported to the center of the sun, completely replacing an equal volume of solar core. Inside the very middle of the sun, standing on planet earth, you would still weigh 200 pounds. The gravity of all the solar mass surrounding the Earth would cancel out.

If you traveled upwards, to the surface of the sun, your weight would increase. At the sun’s surface, you would weigh 5400 pounds.

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