Newton’s law of gravitation states that “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.”
We can write newton’s law of gravitation as:
F ∝ m1m2/r2
Magnitude of the gravitational forces F1 and F2 between two particles m1 and m2 placed at a distance r is can be written as:
F1= F2 = Gm1m2/r2
G = 6.674×10-11 N.m2/Kg2 = 6.674×10-11 dyne.cm2/g-2
The direction of these two forces ‘F1 and F2‘ are opposite in direction and along the line joining the two particles.
Derivation of Newton’s law of Gravitation from Kepler’s law
Let us consider a test mass is revolving around a source mass in a nearly circular orbit of radius ‘r’, with a consistent angular speed (ω). The centripetal force applied on the test mass for its circular motion is given by,
F = mrω2 = mr × (2π/T)2
As per Kepler’s third law, T2 ∝ r3
Utilizing this in force equation we will get,
F = 4π2mr/Kr3 [Where, K = 4π2/GM]
⇒ F = GMm/r2,
This is the equation of Newton’s law of gravitation.