A rocket moving around the earth at height "H", If the gravitational acceleration "g1" at height His of gravitational acceleration 'g at earth surface. If Earth radius is "R", find "H"
using R

At the earth's surface  g = G M / R^2        where G is the gravitational constant

at H       g1 = G M / (R + H)^2         using Gauss' theorem for enclosed mass

g1 = G M / (R^2 + 2 R H)    ignoring H^2 as it is small compared to R^2

g / g1 = (R^2 + 2 R H) / R^2 = 1 + 2 R H

g = g1 + 2 R H g1

g1 - g = - 2 R H     or H = (g1 - g) / 2 R

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