Newton's Law of Gravity

In 1686 Sir Isaac Newton published his work on the law of gravity in his Mathematical Principles of Natural Philosophy.

Newton's law of gravity states that every particle in the universe attracts every other particle with the force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.If the particles have masses m1 and m2 and are separated by a distance r, the magnitude of this gravitational force is

Where G is a universal constant called the universal gravitational constant, which has been measured experimentally. Its value in SI units is

Measurement of the gravitational constant

The universal gravitational constant, G, was measured in an important experiment by Henry Cavendish in 1798.

The Cavendish apparatus consists of two small spheres each of mass m fixed to the ends of a light horizontal rod suspended by a fine fiber or thin metal wire.

Two large spheres each of mass M are then placed near the smaller spheres. The attractive force between the smaller and the larger spheres causes the rod to rotate and twist the wire suspension. If the system is oriented as shown, the rod rotates clockwise when viewed from above.

The angle through which it rotates is measured by the deflection of a light beam reflected from a mirror attached to the vertical suspensions. The deflected spot of light is an effective technique for amplifying the motion.

The experiment is carefully repeated with different masses at various separations. In addition to providing a value for G, the results show that the force is attractive, proportional to the product mM, and inversely proportional to the square of the distance r