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
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
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