A rocket moving around the earth at height “H”, If the gravitational acceleration “g1” at height His of gravitational acceleration ‘g

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

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  1. Answer:

    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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