However, it might not be easy to see why : a uniform shell of matter exerts no gravitational force on a particle located inside it.

The following applet was designed to help you understand it.

There are 2D view and 3D view in the applet.

The green surfaces (curves) represent mass distributed on a uniform shell.

The blue dot represent the particle inside the shell (with mass M).

The gravitation force is propotional to mass and r

^{-2}: .

Let's consider mass distributed on those two green shell (m

_{1}and m

_{2}).

The solid angles for both sirface related to particle are the same (solid angle=),

and the distance to both those two surface are r

_{1}and r

_{2}.

Assume the surface density is

The surface area for two surface are and

So , and

, and .

But those two force are in the oppositive direction so all the gravitational force cencel each other.

You can drag the particle with your mouse to watch how the surface area changed at the same time.

Another question for you: what happened to the rest of the mass on the surface (upper and lower parts)?

Does the gravitational force due to those mass also cancel each other? Why?

**Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.**This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

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