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Taylor series expansion for gravitational force

by physics1311
Tags: gravitational force, kinetics
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physics1311
#1
Feb7-12, 06:56 PM
P: 8
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?
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Spinnor
#2
Feb7-12, 08:35 PM
P: 1,369
(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.
physics1311
#3
Feb7-12, 09:06 PM
P: 8
Thanks for the help


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