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
The Attempt at a Solution
I had completely forgotten binomial expansions, so I looked it up and found an equation that seemed to apply:
(Δr±rE) = rEn(1±Δr/rE)n
I plugged this into the equation for gravitational acceleration and got
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 :)