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Taylor series expansion for gravitational force 
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#1
Feb712, 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 "nontrivial" 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
Feb712, 08:35 PM

P: 1,376

(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
Feb712, 09:06 PM

P: 8

Thanks for the help



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