Question

Derive the formula of gravitation

Answer 1

Heya !!

The Universal Law of Gravitation was stated by Newton and according to it, gravitational force exists between each and every two masses in this universe and, this force is directly proportional to the product of the two masses and is inversely proportional to the square of the distance between their centers.

Let's formulate this law mathematically. For this, we'll have to consider some things....

So, Let's consider two objects A and B, having masses m₁ and m₂ respectively. Let the distance between their centers be d, and the gravitational force between them be F. Then, according to the Universal Law of gravitation,

$F \propto m_{1} \times m_{2} \: \: and \: \: also, \: \: F \propto \dfrac{1}{(d)^{2}} \\ \\ \implies F \propto \dfrac{m_{1} \times m_{2}}{(d)^{2}} \\ \\ or, \: \: F = \dfrac{G \times m_1 \times m_2}{(d)^2} \\ \\ \text{Where, G is the universal gravitation}\\ \text{constant and its value was found to be}\\ 6.67 \times 10^{-11} Nm^{2} Kg^{-2}$

This was the Mathematical derivation of the Universal Law Of Gravitation.

Hope it Helps !!

Answer 2

Answer:

The Universal Law of Gravitation was stated by Newton and according to it, gravitational force exists between each and every two masses in this universe and, this force is directly proportional to the product of the two masses and is inversely proportional to the square of the distance between their centers.

Let's formulate this law mathematically. For this, we'll have to consider some things....

So, Let's consider two objects A and B, having masses m₁ and m₂ respectively. Let the distance between their centers be d, and the gravitational force between them be F. Then, according to the Universal Law of gravitation,

This was the Mathematical derivation of the Universal Law Of Gravitation.