Does Gravity Increase with Depth Inside the Earth?

[Dadface]

How about an oblate spheroid cavity at the centre of a sphere? All mass from the maximum radius of the spheroid and above cancels, but there are still two masses above and below you, so your head experiences slight attraction upwards and your feet slightly downward.

Or have I got this all wrong?

Have you got it all wrong?Don't know I am trying to visualise the set up you describe.As I understand it there is zero force at all points within a concentric spherical shell in an idealised spherical world .How do we know this to be the case since we can't enter such a space to do the measurements?We can use theoretical predictions by summing the contributions of all points from the surrounding shell but when we come to other shaped cavities the integration can become more complex.To make it even more complicated we are dealing with extended objects the various parts of which attract each other gravitationally.

 

[rossphysics]

Doesn't anyone like Einstein any more? General Relativity says that space/time is pushing from the out, in. The center of the Earth would be at maximum pressure.

 

[DaveC426913]

Doesn't anyone like Einstein any more? General Relativity says that space/time is pushing from the out, in. The center of the Earth would be at maximum pressure.

Space-time does not push. Space-time simply curves.
Einstein has nothing to say about pressure.

 

[rossphysics]

I thought that the Earth displaced space/time and made it more dense . . . you're right, if it were hollow, it would displace the same as if it were solid.

 

[DaveC426913]

I thought that the Earth displaced space/time and made it more dense . . . you're right, if it were hollow, it would displace the same as if it were solid.

Made what more dense? Earth?