State Newton's universal law of gravitation. Express it in mathematical form.

Explanation

Newton's universal law of gravitation :
Every object in the Universe attracts every other ohject with a definite force is directly proportional to the product of the masses of the two objects and invesely proportional to the square of the distance between them.
Mathematical form : Consider two objects of masses `m_(1) and m_(2),` We assume that the objects are very small spheres of uniform density and the distance r between their centres is very large compared to the radii of the spheres.

The magnitude (F) of the gravitational force of attraction between objects is directly proportional to `m_(1)m_(2)` and inversely proportional to `r^(2)`.
`therefore F prop (m_(1)m_(2))/(r^(2)) therefore F=G(m_(1)m_(2))/(r^(2))`,
where G is the constant of proportionality, called the universal gravitational constant.
Note : In the textbood, the word object/body is used. Newton's law of gravitation applies to particles.