# Newton's Shell theorem- Gravity inside spherical shell

1. Dec 19, 2015

### ovais

Hello all,

Guys in my text book they state that on a point mass at point outside spherical shell of uniform density, the gravitational force is just as if the entire mass of the shell is concentrated at the Centre of shell.

The text also states, the force of attraction due to a hollow spherical shell of uniform density on a point mass situated inside it, is zero.

The text also tries to make us believe it by saying some qualitative arguments and end its message by saying, this works out be as stated.

I searched the Internet get some proofs. And I also come across what is called as shell theorem. The shell theorem as given by Newton seems to be the real thing. In shell theorem Newton actually proof what the text claims.

I am here not to know the maths of shell theorem nor for the easiest version of shell theorem or anything that contains the proof of book's claim. What I want, is to know, would I be correct, if I tell those of my students who know calculus but yet are not very comfortable with a bit harder calculus and who questioned me how can I state this things(appearing too simple) to tell them without proof; the below statement-

"Dear students your are asking me why I state it without proof but let me tell you one of the reasons why Sir Issac Newton invented Calculus is to prove this very thing and it took him 20 years. "

Thanks a bunch.

2. Dec 19, 2015

### mathman

The calculation is a two dimensional integration. Once calculus was invented, the theorem wasn't that hard.

3. Dec 20, 2015

### ovais

Thanks mathsman, I actually want to know in historical the historical context that how big this was a deal for Newton to prove the two statements in my first post as taken from the text book.

I am not after how easy or difficult the prove NOW! I want to know if this is ONE OF THE THINGS that has something to do with the intention of Claculas by Newton.

I heard from my favorite Walter lewin that it took Newton 20 years to prove this(what the book claims).

Regards

4. Dec 20, 2015

### mathman

I am not a historian, so I don't know the details of the history of Newton's work. Just on the basis of the difficulties involved, I suspect inventing calculus took a lot more time than proving this theorem. He also needed to have the basic law of gravity. $F=G\frac{m_1m_2}{r^2}$.