# Q & A: gravity in earth

Q:
i have heard people say that gravity of the earth increases when we near the centre of the earth. my books say that gravity is related to distance from the surface of the earth.
- Nimish (age 15)
India
A:
Sure, the baic principle is that the gravitational field falls off as the square of the distance from any little bit of stuff. When you add up the fields from all the parts of the spherical Earth, it turns out that outside the Earth the field falls off as the square of the distance from the center of the Earth. Newton invented integral calculus largely to show that. Inside the Earth, using similar calculus techniques, you can show that only the part of the Earth closer to the center than you are contributes to the field on you. As a result the total field varies linearly from zero at the center up to the usual value at the surface. (That's assuming fixed mass density, the real distribution is a little different.)
As for what people say, people often say wrong things.
Mike W.

(published on 10/22/2007)

## Follow-Up #1: Newton's shell theorem

Q:
Can you please point me to Newton's calculation, preferably on a web page?
- Peter Fry (age 81)
Winchester, England
A:

Here's one on Wikipedia: https://en.wikipedia.org/wiki/Shell_theorem https://en.wikipedia.org/wiki/Shell_theorem. I'm not sure if it exactly follows the argument in Newton's Principia but the key ideas are the same.

Mike W.

(published on 03/30/2018)