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Gravitation and Binomial Expansion

  1. Oct 28, 2014 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations

    g=GM/r2

    3. 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 :)
     
  2. jcsd
  3. Oct 28, 2014 #2
    Never mind, I figured it out!
     
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