Integrating Mass of a Hollow Sphere: Multivariable Calculus Explained

[cwill53]

Homework Statement

I'm just trying to prove that gravitational force on an object within a hollow sphere is zero when these are the only two objects under consideration within the system.

Relevant Equations

$$F_g=G\frac{mM}{r^2}$$

I know some multivariable calculus, I just want someone to walk me through the integration deriving the mass element dM and the integration of thin rings composing the hollow sphere. It would also be nice if you could show me doing it one way using the solid angle and one way without using the solid angle. Thanks.

 

[jedishrfu]

This reference may help:

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell2.html