2.16.2 Law of Universal Gravitation
Newton’s law of universal gravitation states that a particle with mass
attracts every other particle in the universe, with mass
, via a force
that is directly proportional to the product of their masses, and inversely proportional to the square of the straight-line distance
between their centers. Mathematically, this translates into the following equation:
Typically, the force
is measured in newtons, the masses
and
are measured in kilograms, while the distance
is measured in meters. The constant
is the universal gravitational constant. The first experimental test of this law was conducted by Henry Cavendish in 1798, between small masses in the laboratory, 111 years after the publication of Principia.
Newton derived this general physical law from empirical observations that he called: inductive reasoning. When Newton’s book was presented in 1686 to the Royal Society, Robert Hooke (1635-1703 AD) made a claim that Newton had obtained the inverse square law from him. It can also be noted that the law of gravitation resembles Coulomb’s law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies, since both are inverse-square laws.
Newton’s law of gravitation is now superseded by Einstein’s theory of General Relativity, but it continues to be used as an excellent approximation in most practical applications, when there is no need for extreme precision, or when the gravitational fields are not very strong.


