Thanks for taking the time – very interesting! I see the key is the idea of a field; I do vaguely remember that result for electric fields inside a hollow sphere from Physics many moons ago. It seems my intuitive idea of 2 hemispheres close together, & moving slightly off-centre making a big difference, is misleading.

So perhaps there really is a race of super-intelligent (heat- & pressure-resistant) beings at the centre of the Earth after all.. :)

No, it is a well-known effect in calculus that inside a hollow symmetrical sphere, the resulting gravitation cancels out to zero. Instead of getting splatted, you would be in free fall. You get similar resultant effects with other fields such as electric fields inside a hollow sphere. If you are a programmer without the necessary calculus, you can have some fun programming a finite-element simulation to demonstrate the effect; just regard the shell as a spherical (NOT circular!) cloud of particles, and use the formula for gravitational attraction as G*m1*m2/r/r. Remember to round off your results before making the comparison to allow for limited precision.

Piece of cake. Having done that, compare your results with the results for other shapes.

Good fun!

It also has a very important (or possibly very unimportant, cf  CHAPTER XII of Alice's Adventures in Wonderland: Alice's Evidence) implication: a solid, homogeneous, symmetrical sphere can be regarded as a nested set of hollow spheres, and at any level in the sphere, you only feel the gravity of the spheres below you. So at a depth of say 3000 km from the centre of the earth, you would be subjected to the same downward pull as if you were standing on a bare 3000 km-radius sphere.

And if you were at a distance of 0 km from the centre, your downward pull would be zero.

Got it?

Cheers,

Jon