I What's the proof that R2 /(R+h) = (1 – 2h/R)

[Karagoz]

TL;DR Summary

When proving formula for acceleration due to gravity at height h – with derivation, there are some steps I don't understand.

Hi,

On this link: https://physicsteacher.in/2020/07/1...n-due-to-gravity-at-height-h-with-derivation/

They prove the formula for acceleration due to gravity at height h, which is: g1 = g (1 – 2h/R).

There are similar articles online.

When they go through the last steps, it shows something like this:

g1/g = R2 /(R+h)2

= 1/(1 + h/R)2 = (1 + h/R)-2 = (1 – 2h/R)

But I don't understand, how does one move from R^2 /(R+h)^2 to 1/(1 + h/R)^2 = (1 + h/R)^-2 and then to (1 – 2h/R)

Could someone explain what's happening there?

 

[phyzguy]

The first step is simply to divide both numerator and denominator by R^2. In the second step, they have assumed that h<<R, so h/R <<1. You can then do a Taylor series expansion and keep only the first term in h/R.