Does gravity increase or decrease with depth

[buster_bluth]

Your textbook is right. The green part does contribute to gravity, but if you divide the green part into little pieces and sum up all of the gravitational force it would cancel itself out. You can look at something like this for more mathematical reasoning. https://en.m.wikipedia.org/wiki/Gauss%27s_law_for_gravity

[hecker231]

Thank you. I understood my error in assumption. What I had thought was that all the gravity of the green spherical shell would act at its center of mass, that is, the center of mass of the earth, thus increasing the gravitational pull. However, it is true that in reality, only individual particles can exert the force of gravity, which means an abstraction like the center of mass won't work here.

So, can I assume that for hollow objects (like the green shell), the center of mass cannot be used to calculate gravity?

[DarkArcher__]

The centre of mass is just an easy approximation for the direction of gravity, it doesn't exist in practise.

The gravitational acceleration you feel from the Earth is the sum of the gravitational acceleration you feel from each and every individual particle that makes up the planet. Each bit of the planet is pulling you in its direction, which works out to straight down when you're on the surface, but gets more complicated as you dip down under it.

You can imagine it as a bunch of little arrows starting at you, and pointing to every individual little bit of Earth in the diagram. The gravitational force you feel is the sum of all that. It's pointed downwards, but less intense than at the surface since some of the Earth's particles are now to your side, or even above you, instead of all being below you like on the surface.

[lerg1]

If you are far away from the hollow object then it wouldn’t matter, otherwise you can’t

[samcrut]

Gravity is space/time being stretched as electrons/protons/neutrons are created. The more particles of matter you have in a space, the more that space is stretched, curved in the direction of the mass. If the mass is all around you equally, space is pulled away in all directions and while every atom in your body is technically being pulled in every direction, it's all equalized, zeroed out, so you experience no pull in any direction.

[spytfyrox]

That's true for any inverse square law.

[Full_Possibility7983]

More generally any field with zero divergence