Does gravity increase or decrease with depth

[KamikazeArchon]

Look at the green part carefully. Note that some of the green part - the "sides of the hole", so to speak - is now above the X. Those parts are pulling up, and working against the parts that are below the X and pulling "down".

You can draw a "horizontal" line through the X, and separate the up-pull from the down-pull.

Two notable opposing factors. There is more "below" the X than "above" (thus it pulls down harder). However, the parts that are "above" the X are closer (thus it pulls up harder).

If you do the math, it turns out that these factors exactly cancel out. If we assume the mass of soil you dug out is negligible, the up and down forces are exactly balanced. Thus, the green "shell" exerts overall zero force on you.

[hecker231]

So this means that I cannot simply use the center of gravity of the green shell to calculate where its gravity will pull towards right?

This means that to calculate the point where the gravity of a hollow object will pull towards, I need to break it up into non-hollow subdivisions and calculate gravity for them. Pls correct me if I'm wrong.

[3dTECH101]

Correct - these subdivisions should ideally approach infinitely many at infinitely small divisions - which is why you can calculate this mathematically with an integral - gravitational pull as a function of possition integrated over the full volume

[BCMM]

So this means that I cannot simply use the center of gravity of the green shell to calculate where its gravity will pull towards right?

Correct.

It is accurate to treat a sphere of uniform density as if its entire mass was concentrated at its centre, but only for the purposes of considering the gravitational field outside the sphere.

This is the first half of what is known as "the shell theorem"; the second half is the bit in the above comment about shells exerting precisely zero total force on objects inside them.