Gravitation Law

Sir Issac Newton gave a mathematical relation to calculate the force of gravitation and this relation is known as the universal law of gravitation.
According to this law “Every particle in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, the direction of the force being along the line joining the masses”.
Consider two objects of masses m₁ and m₂ separated by a distance d. According to the law of gravitation, the force of gravitation F is proportional to the product of the masses,

and inversely proportional to the square of the distance between the masses,

Two objects of masses m₁ and m₂ separated by a distance d.
Combining eq (1) and eq (2), we get


Where G is a constant of proportionality called the universal gravitational constant. G is called universal constant because its value remains the same throughout the universe and is independent of masses of the objects.

Universal Gravitational Constant

The mathematical form of Newton's Law of Gravitation is
if m₁=m₂=1, d=1, then
or F = G. Hence universal gravitational constant may be defined as the force of gravitation existing between two unit masses separated by unit distance.
SI unit of gravitational constant
SI unit of force F is N, SI unit of distance is metres and that of mass is kg.
SI unit of G=Nm²/kg² or Nm² kg^-2 The experimental value of G equal to 6.6734x10¹¹ Nm²/kg² was measured by Sir Henry Cavendish in 1798.