**Newton’s Law of Gravitation Formula**

** Statement:- **According to Newton’s, “every object in the universe attracts every other object with a force. This force is directly proportional to the product of mass and inertly proportional to the square of the distance between them”.

Consider the two objects of masses m_{1} and m_{2} and these two objects separated by distance d.

From the statement, mathematically, the gravitational force of attraction between two object can be written as,

F ∝ m_{1}m_{2} —- (1)

F ∝ 1/d^{2} ——- (2)

Combine equation (1) & (2)

F ∝ m_{1}m_{2}/d^{2}

F = G m_{1}m_{2}/d^{2} —— (3)

Where, G is the constant of proportional and called the Universal gravitational constant. The SI unit of G is N m^{2}/kg^{2}

From formula (3) the value of G becomes,

G = Fd^{2}/m_{1}m^{2}

From this formula we can calculate the gravitation constant as well as force. The experimentally measured value G is 6.673 × 10^{-11} Nm^{2}/kg^{2}

**Numericals on Newton’s Law of Gravitation Formula:**

**Consider a two objects of mass 25 kg and 30 kg respectively. These two objects are separated by distance 1 m. What is gravitational force between them?**

__Given: __d = 1m

m_{1} = 25 kg

m_{2} = 80 kg

and G = 6.67 × 10^{-11} Nm^{2}/kg^{2}

F = Gm_{1}m_{2}/d^{2}

F = 6.67×10^{-11}×25×30/1^{2}

F = 5, 002.5×10^{-11}

F = 5.0025×10^{-7} N

The gravitational force between these two objects is 5.0025×10^{-7} N.