Newton’s universal law of gravitation :
Every object in the Universe attracts every other object with a definite force. This force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them.
Mathematical form: Consider two objects of masses m1 and m2. We assume that the objects are very small spheres of uniform density and the distance r between their centers is very large compared to the radii of the spheres.
Gravitational force between two objects
The magnitude (F) of the gravitational force of attraction between the objects is directly proportional to m1m2 and inversely proportional to r2
∴ F ∝ \(\frac{m_1m_2}{r^2}\)
∴ F = \(G\frac{m_1m_2}{r^ 2}\)
where G is the constant of proportionality, called the universal gravitational constant.
[Note: In the textbook, the word object/body is used. Newton’s law of gravitation applies to particles.]
