State and prove Newton’s law of gravitation

"The mutual force of attraction between two bodies in the universe is directly proportional to their masses and inversely proportional to the square of the distance measured from their centers."

Proving Newton's law of gravitation

Let us consider, two bodies A and B having mass m₁ and m₂ respectively. The distance between their center is "d" and gravitational force with which they attract each other is F. 

According to Newton's Law, 

\(F\propto m_1m_2\)   .................(i)

\(F=\frac{Gm_1m_2}{d^2}\)..........(ii)

Combining the two equation (i) and (ii) we get, 

\(F\propto\frac{m_1m_2}{d^2}\)

OR   /(F=\frac{Gm_1m_2}{d^2}\), where 'G' is the universal constant. 

the value of 'G' is \(  6.67\times10^{-11}\) Nm² /kg² . 

Hence, the equation (iii) gives the measure of the gravitational force between two masses. 

Proving newtons law of gravitation shows that all the matter in the universe attract each other through the force of gravity.