State Newton's Universal law of gravitation?

Newton 's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (Separately it was shown that large spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers.) This is a general physical law derived from empirical observations by what Newton called induction. ^[2] It is a part of classical mechanics and was formulated in Newton 's work Philosophi� Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. (When Newton 's book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him – see History section below.) In modern language, the law states the following:

Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them: [3]
, where: F is the force between the masses, G is the gravitational constant, m 1 is the first mass, m 2 is the second mass, and r is the distance between the centers of the masses.

Assuming SI units, F is measured in newtons (N), m ₁ and m ₂ in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674�10⁻¹¹ N m² kg⁻² . ^[4] The value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G. ^[5] This experiment was also the first test of Newton 's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton 's Principia and 71 years after Newton 's death, so none of Newton 's calculations could use the value of G; instead he could only calculate a force relative to another force.

Newton 's law of gravitation resembles Coulomb 's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies. Both are inverse-square laws, in which force is inversely proportional to the square of the distance between the bodies. Coulomb 's Law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant.

Newton 's law has since been superseded by Einstein 's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity. Relativity is required only when there is a need for extreme precision, or when dealing with gravitation for extremely massive and dense objects.

Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

This force of gravitational attraction between the two bodies acts along the line joining their centres. This force is hence mutual.

Consider two bodies of masses m 1 & m 2 with their centers separated by r. let F be the force of gravitational attraction between two bodies. According to newton 's law of gravitation,

combining both the factors , we get

Or

Value of G is constant everywhere and hence called as universal constant of gravitation.

Value of G

In si units, G = 6.67 x 10^-11 newton m² kg^-2

In cgs , G = 6.67 x 10^-8 dyne cm² g^-2 .