Newton’s Law of Gravitation

Newton along with his three laws of motion, Newton published the law of gravitation in 1687. According to Sir Isaac Newton,

“every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.”

F ∝ m₁m₂/r²

Thus, the magnitude of the gravitational forces F₁ and F₂ between two particles m₁ and m₂ placed at a distance r is,

Image source: Wikimedia(Dna-Dennis)

Here, G is a universal constant called gravitational constant whose magnitude is,

G = 6.674×10-11 N.m²/Kg² = 6.674×10-11 dyne.cm²/g^-2

[G] = [M^-1L³T^-2]

The direction of forces ‘F₁ and F₂‘ are opposite in direction and along the line joining the two particles.

Following three points are important regarding the gravitational force:

1.      Unlike the electrostatic force, it is independent of the medium between the particles.

2.      It is conservative in nature.

3.      It expresses the force between two points masses (of negligible volume). However, for external points of spherical bodies the whole mass can be assumed to be concentrated at its center of mass.

Gravity:

In Newton’s law of gravitation, gravitation is the force of attraction between any two bodies. If one of the bodies is earth, then the gravitation is called ‘gravity’. Hence, gravity is the force by which earth attracts a body towards its centre. It is a special case of gravitation.