Formula of Acceleration due to Gravity

We know that the force on anybody is given by,

F = mg

where F is the force acting, g is the acceleration due to gravity, m is the mass of the body.

And according to the universal law of gravitation, 

F = GMm/(r+h)²

where F is the force between two bodies, G is the universal gravitational constant, m is the mass of the object, M is the mass of the earth, r is the radius of the earth, and h is the height above the surface of the earth.

Since the height is negligibly small compared to the radius of the earth, rearrange the above expression as,

F = GMm / r²

Now equating both the expressions,

mg = GMm / r²

⇒ g = GM / r²

The value of gravity’s attraction or potential is governed by the distribution of mass within Earth or another celestial body. As noted previously, the distribution of matter affects the geometry of the surface where the potential is constant. Gravity and potential measurements are thus critical to both geodesy, which studies the form of the Earth, and geophysics, which studies its interior structure. The orbits of artificial satellites are the greatest way to assess the potential for play an intermediary role and global geophysics. Surface gravity measurements are ideal for local geophysics, which studies the structure of mountains and seas as well as the hunt for minerals. In order to understand how the value of acceleration due to gravity affected lets first under its basics as: