Newton's law of universal gravitation

Lore & Background

Newton also found a proof that the Earth's gravity acts as if all its mass were concentrated at its center, a conjecture that took him twenty years to prove. The law was later condensed into the inverse-square formula F = G m₁m₂/r². Newton did not use the constant G or the formula explicitly; he only discussed proportionality. Newton was uncomfortable with the notion of 'action at a distance' implied by his equations.

Reader's Guide

Newton's law of universal gravitation marked a pivotal moment in science, unifying celestial and terrestrial mechanics under a single mathematical framework. It provided a quantitative explanation for planetary orbits, tides, and falling objects, and became a cornerstone of classical mechanics. The law resembles Coulomb's law of electrical forces, both being inverse-square laws. Although later superseded by Albert Einstein's theory of general relativity for extreme accuracy or strong gravitational fields, Newton's law remains an excellent approximation for most applications. The universality of the gravitational constant G is intact. Newton's work also sparked philosophical debate about action at a distance, which he himself found troubling. The law's legacy endures as a foundational principle of physics, taught worldwide and used in countless practical calculations.

Did You Know?

• Newton's law of universal gravitation is known as the 'first great unification' because it unified gravity on Earth with astronomical behaviors.
• Newton did not use the gravitational constant G or the formula F = G m₁m₂/r²; he only discussed proportionality.