Gravity of hollow sphere vs. solid sphere of same mass

[Andy SV]

Would a hollow sphere measure the same gravitationally as a solid sphere if it was the same mass?

Just sharing an interesting question

 

[PeterDonis]

Just sharing an interesting question

Which belongs in a separate thread, so I have spun it off into one.

 

[PeterDonis]

Would a hollow sphere measure the same gravitationally as a solid sphere if it was the same mass?

As far as its external gravity, yes (assuming it also had the same radius). Internally, the stresses and spacetime curvature would be different, but these differences would not show up in the external field.

 

[Andy SV]

Oh yes sorry bout that and thanks

 

[Arkalius]

I've also heard that if you are inside a hollow sphere that has uniform density and thickness, you will experience no net gravitational force from the sphere from anywhere within it. I've never bothered to check if this was true though...

 

[PeterDonis]

if you are inside a hollow sphere that has uniform density and thickness, you will experience no net gravitational force from the sphere from anywhere within it

That is correct. More precisely, spacetime inside a hollow sphere is flat. (Note that this is true even if the density of the sphere varies, as long as the variation is purely radial, i.e., as long as everything remains spherically symmetric.)