Derive the relationship between #"g"# and #"G"#?
1 Answer
r is the distance between object and the center of earth
h is height of object from the surface and R is the radius of earth.
and
Explanation:
Suppose Earth is a sphere of radius
Gravitational Force on the object of mass
If the object is free falling from the height h from the surface of earth (or at a distance
According to Newton's second law
Force on the object due to acceleration
Comparing Equation [A] and [B]
Where
If
then we can write
or
(When the object is near the surface of earth so we can neglect the height of object comparing with Radius of Earth)
If average density of earth is
then mass of earth
In equation [c]