Gravity and volume

[Daymare17]

Assuming a spherical body, is the gravitational acceleration at a given distance from the sphere's center, independent of the body's volume?

 

For instance if you were orbiting the Earth, and the Earth suddenly shrunk to one tenth of its volume, would you continue to orbit?

[5614]

Volume:

 

No, volume doesn't really matter. The density and distance you are from it are the main 2 factors.

 

Obviously if increasing the volume means decreasing the density then this makes a difference, but volume by itself (ie. without altering any other factors) won't make a difference.

 

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Earth shrink:

 

There are other factors that come into this.

 

If the earth shrinks but in doing so becomes denser then it's gravitation field strength will become stronger, but you be further away from it, weakening its now stronger effect on you. I don't know what the end result would be.

 

[edit] the crossed out part is wrong (hence the crossing!) keep reading the thread, all the answers are here.

[swansont]

As long as the mass distribution in uniform, and you are outside of it, you will behave as if all the mass were concentrated at the center. Works the same as with charge distributions for electrostatics. (Gauss's law)

[Daymare17]

Thanks a lot!

[J.C.MacSwell]

Volume:

 

No' date=' volume doesn't really matter. The density and distance you are from it are the main 2 factors.

 

Obviously if increasing the volume means decreasing the density then this makes a difference, but volume by itself (ie. without altering any other factors) won't make a difference.

 

=====

 

Earth shrink:

 

There are other factors that come into this.

 

If the earth shrinks but in doing so becomes denser then it's gravitation field strength will become stronger, but you be further away from it, weakening its now stronger effect on you. I don't know what the end result would be.[/quote']

 

5614, I don't think you wrote what you meant to write.

[5614]

Which part are you referring to?

 

Was it the last para? Because that isn't, err, technically correct!

 

If the Earth shrinked but still retained it's mass (ie. it's volume decreased and density increases proportionally) then you would continue to orbit exactly how you were before.

 

That sounds better to me, what you think?

[timo]

As long as the mass distribution in uniform, and you are outside of it, you will behave as if all the mass were concentrated at the center. Works the same as with charge distributions for electrostatics. (Gauss's law)

I´d like to add that the mass/charge distribution doesn´t have to be uniform. It is sufficient if it´s spherical symmetric (each shell gives a contribution as if the mass was at the center of the sphere and so does the total force, then). Still, you have to be outside of the mass distribution (=the body).

 

For instance if you were orbiting the Earth, and the Earth suddenly shrunk to one tenth of its volume, would you continue to orbit?

Assuming the mass of earth remains unchanged, then "yes" (just added this remark because there seemed to be a bit of confusion).

[5614]

just added this remark because there seemed to be a bit of confusion

Yeah, I kinda screwed up the answer first time round! Sorry bout that.

[swansont]

I´d like to add that the mass/charge distribution doesn´t have to be uniform. It is sufficient if it´s spherical symmetric (each shell gives a contribution as if the mass was at the center of the sphere and so does the total force' date=' then). Still, you have to be outside of the mass distribution (=the body).

[/quote']

 

 

But if you aren't it still works if applied properly. The enclosed mass still acts like a point mass at the center. You ignore the mass outside, as it has no net contribution.