# Why gravity decreases as we go under ground? [duplicate]

We all know that gravity decreases as we go upward, we also know that gravity decreases as we go inside the earth? I don't know why gravity decreases as we go downward or inside the Earth? Please explain?

## marked as duplicate by ManishearthOct 21 '13 at 7:09

In a sphere with uniform mass distribution your assumption is correct - gravity decreases as you go beneath the surface.

The explanation is Gauss's law.

If you consider a sphere centered at the center of the earth with radius $r$. The force exerted by the mass outside the sphere would cancell perfectly. This means that only the mass enclosed by the surface contributes to the gravitational field.

The mass contained in the sphere would be: $M=\rho V_{sphere}=\frac{4}{3}\pi r^2\rho$. If you substitute in Newton's gravitation law: $g=G\frac{M}{r^2}=G\frac{4\pi}{3}\rho$ or in terms of force, $F=mg=G\frac{4\pi}{3}\rho m$.

So the deeper you go, less gravity you feel, assuming the Earth's mass density is constant.

Since the mass is not uniformly distributed (the Earth mantle consists of lighter elements on average), gravity actually does increase for approximately the first 2000km you go below the earth's surface.

Jinawee's answer is correct, but here's a simpler explanation without any math. At the center of the earth, the gravitational field is zero by symmetry. Therefore as you go from the surface to the center, the field must decrease in strength.

And perhaps even simpler, when you go underground some of the earth's mass is above you. Even though it is above you, it still creates a gravitational force, but now it's lifting you up instead of pulling you down. This upward force counteracts a small part of the downward force due to the rest of the earth that's below you. As Ben notes, once you get to the center you're pulled equally in all directions, so the net force is zero.

• I don't think this argument quite works, because you're also closer to the mass that's below you, so that could make its force stronger. – Ben Crowell Oct 19 '13 at 18:00