# Why is it useful

1. Feb 16, 2008

### scott_alexsk

...to do a Taylor series expansion of an expression for the gravitational field? My physics teacher did a it few times on the board, but I do not understand how it gives me more information about the asymptotic behavior than substituting some scaled factor in for r, and then solving the limit as that dimensionless number goes to 0 or infinity. (i.e. finding the field of a uniform ring w/ radius d and distance r away from something, approaches the field of a point mass as r goes to infinity or d goes to zero). Maybe it is useful for something else?

Thanks,
-Scott

Last edited: Feb 16, 2008
2. Feb 16, 2008

### olgranpappy

can you be a little more specific?

3. Feb 16, 2008

### scott_alexsk

Sorry in advance for not using latex...

So if I have the equation for the gravitational field of a ring, g=G*m*z/(z^2+r^2)^1.5 (where z is the distance to some point along a line perpindicular to the center of the ring, and r is the radius of the ring), what useful thing can I get out of making a Taylor series for this equation?

I was saying before that I can already find information about the asymptotic behavior by setting v=r/z, and then plugging it into the equation and solving for the limit as v goes to zero (to show that the gravitational field of the ring approaches a point mass as the distance from it goes to infinity, or r goes to zero etc.) So I conclude from this that I don't need a Taylor expansion to determine the asymptotic behavior.

So just to rephrase, is there any reason why I would want to make a Taylor series expansion for the field function? My teacher certainly knows what he is doing, but I missed the point for doing the expansion.

Thanks,
-Scott

4. Feb 16, 2008