Using Newton's universal law of gravitation & second law of motion,find the mathematical expression for acceleration due to gravity on the surface of earth..
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Dear Student,
Consider an object of mass m lying on or near the surface of the the planet.

According to Newton's law of gravitation, the force of attraction (F) between the planet and the object is

F=GMm/R^{2  ...............}1

According to Newton's second law of motion this force produces an acceleration (g) in the object.
F = ma (a = g)
F = mg

put value of F in equation 1

mg=GMm/R²

g=GM/R²

where

g=gravity on the planet in m/s²

G=gravitational constant

M=mass of the planet

R=radius of planet
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