[Physics] Force inversely proportional to the squared distance

Question

Newton's law of universal 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."

Coulomb's law:
"The magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them."

How did Sir Isaac Newton and Sir Charles Augustine De Coulomb come to know that the force, gravitational or coulomb's, is inversely proportional to the square of the distance between two point masses or charges, why didn't they just say that the force is inversely proportional to the distance of two bodies from each other or two charges? There must have been something that made them formulate these inverse-square laws.

Answer 1

The short answer is "observations".

In the case of the gravitational law, the orbits of the planets around the sun, the moon around the earth fit mathematically a force with an inverse square law for the distance. An inverse law does not.

In the case of electricity this article points out the observational history:

Early investigators who suspected that the electrical force diminished with distance as the gravitational force did (i.e., as the inverse square of the distance) included Daniel Bernoulli 1 and Alessandro Volta, both of whom measured the force between plates of a capacitor, and Aepinus who supposed the inverse-square law in 1758.

and then others took it from there to end up with the comprehensive publications of Coulomb, based on measurements.

Finally, in 1785, the French physicist Charles Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law. This publication was essential to the development of the theory of electromagnetism.[8] He used a torsion balance to study the repulsion and attraction forces of charged particles and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.