derive the variation of gravity with altitude and depth
Answers
Force of gravity acting on a body of mass m on the earth surface = F = GMm/R^2 ____________ (1)
Where R is the radius of the earth (considering it a homogenous sphere)
and M here is the total mass of earth concentrated at its centre. G is the gravitational constant.
Now, from Newton’s 2nd Law of Motion,
F = mg.___________________(2)
Just to recapitulate, as a body falls downwards it is continuously acted upon by a force of gravity. The body thus possesses an acceleration, called Acceleration Due to gravity(g).
From equation 1 and 2 we can write
mg = (GMm) / R^2
=> g = GM / R^2 _______________ (3)
Another expression of g here:
If mean density of earth is p then mass of the earth = M = volume X density = (4/3) Pi R^3 p
(Pi = 22/7)
g = G.( (4/3) Pi R^3 p) / R^2
g = (4/3) Pi R p G ________________ (4)