Variation of ‘g’ with Altitude

by • 04/07/2012 • 1st Year PhysicsComments (0)183

Variation of ‘g’ with Altitude

Suppose earth is perfectly spherical in shape with uniform density ρ. We know that at the surface of earth

g = G Me / Re2

where

G = Gravitational constant

Me = Mass of earth

Re = Radius of earth

At a height ‘h’ above the surface of earth, gravitational acceleration is

g = G Me / (Re + h)2

Dividing (1) by (2)

g / g = [G Me / Re2] x [(Re + h)2 / G Me)

g / g = (Re + h)2 / Re2

g / g = [Re + h) / Re]2

g / g = [1 + h/Re]2

g / g = [1 + h/Re]-2

We expand R.H.S using Binomial Formula,

(1 + x)n = 1 + nx + n(n-1) x2 / 1.2 + n(n + 1)(n-2)x3 / 1.2.3 + …

If h / Re < 1, then we can neglect higher powers of h / Re.

Therefore

g / g = 1 – 2 h / Re

g = g (1 – 2h / Re) …………………………… (3)

Equation (3) gives the value of acceleration due to gravity at a height ‘h’ above the surface of earth.

From (3), we can conclude that as the value of ‘h’ increases, the value of ‘g’ decreases.

Pin It

Related Posts

Leave a Reply