Question

How did Newton discover the law of universal gravitation?

Answer 1

It was an afternoon while Isaac Newton was sitting or somewhere it is said that he was taking a nap that an apple fell on his head or nearby him. This simple incident made him pushed to research further and eventually he discovered the gravitation.

Complete answer:
An afternoon while Newton was taking a nap or sitting under an apple tree, an apple fell on him. By first law of motion, he knew that a force must have acted upon that apple to make it fall on earth. This simple event made him think that perhaps everybody in the Universe attracts every other body. So, in order to find answers he started studying the motion of moon around the earth and concluded that the force responsible for the motion of moon is same as that which made that apple fall on earth and after rigorous study he postulated the law of universal gravitation in 1867 which state that “Every particle in the universe attracts every particle by a force which is directly proportional to the product of their masses and inversely proportional to the square of distance in between them.”
Mathematically, ${\text{F}} \propto \dfrac{{{m_1}{m_2}}}{{{R^2}}}$
where F be the force of attraction between two bodies of mass m1 and m2 separated by a distance R

Note:
It is to be noted that this formula also indicates inverse square law as force is inversely proportional to the square if distance in between two bodies. This law was derived from the third law of Kepler’s law of planetary motion after assuming that the orbits of planets are circular instead of elliptical (as stated in first law of Kepler’s planetary motion).