Gravitation and Binomial Expansion

  • #1

Homework Statement


Use the binomial expansion (1± x)n = 1± nx + (n(n-1)/2) x2 ±....
to show that the value of g is altered by approximately Δg ≈ -2g(Δr/rE) at a height Δr above the Earth's surface, where rE is the radius of the Earth, as long as Δr<<rE

Homework Equations



g=GM/r2

The Attempt at a Solution


I had completely forgotten binomial expansions, so I looked it up and found an equation that seemed to apply:
x=Δr/rE
and then
(Δr±rE) = rEn(1±Δr/rE)n
I plugged this into the equation for gravitational acceleration and got
g=GM/[rEn(1±Δr/rE)n]2
I'm not sure if I should substitute 2 for the n? Honestly I'm not sure where to go from here at all. Hopefully I did something correctly? (Note: this is my first time on Physics Forums, so I hope I formatted this correctly and everything)

Any help would be appreciated, thank you :)
 

Answers and Replies

  • #2
Never mind, I figured it out!
 

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