# Taylor series expansion for gravitational force

1. Feb 7, 2012

### physics1311

1. The problem statement, all variables and given/known data
The magnitude of the gravitational force exerted by the Earth on an object of mass m at the Earth's surface is
Fg = G*M*m/ R^2
where M and R are the mass and radius of the Earth.
Let's say the object is instead a height y << R above the surface of the Earth. Using a Taylor series or binomial expansion, find a polynomial expression in y for the force of gravity acting on this object, correct to first order (i.e., in this case, the lowest "non-trivial" order of the Taylor series).

2. Relevant equations
taylor series equation

3. The attempt at a solution
I set up the equation as Fg=G*M*m/(R+y)^2 centered around y=0

I'm just lost on how to set this up, what is the right equation and point to center around?

2. Feb 7, 2012

### Spinnor

(R+y)^-2 = R^-2(1 + y/R)^-2 Expand this about y = 0

Using as input "R^-2(1 + y/R)^-2"

In the following link, you may need a free plugin,

http://www.wolframalpha.com/input/?i=R^-2%281+%2B+y%2FR%29^-2&cdf=1

See series expansion in the above link.

3. Feb 7, 2012

### physics1311

Thanks for the help