# Universal Gravitation Formula

The law of universal gravitation states that any two objects in the universe attract each other with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Itâ€™s a general Physics law derived from the observations by Isaac Newton. In modern language, the law states: every point mass attracts another single point mass by a force pointing along the line intersecting both the ends.

The universal gravitation forceÂ  formula is given by

$F = \frac{Gm_{1}m_{2}}{r^{2}}$

Where,

F = Force of attraction between two objects (N)

G = universal gravitational constant =Â 6.67259 x 1011Â N m2/kg2.Â

m1,m1 = two different masses (Kg)

r = is the distance between them

## Solved Numericals

Example 1

Determine the gravitational force if two masses are 30kg and 50kg separated by a distance 4m.

G =Â 6.67259 x 1011Â N m2/kg2.Â

Solution:

Given:

m1 = 30 kg, m2 = 50 kg

r = 4m and

G =Â 6.67259 x 1011Â N m2/kg2.Â

Universal gravitation formula is given by,

$F = \frac{Gm_{1}m_{2}}{r^{2}}$

Â Â = [6.673Ã—1011Â Ã—30Ã—50] / 16

F = 62.55 x 1011N

Example 2

Determine the gravitational force if the mass of two bodies are 80 kg and 200 kg and they are separated by a distance of 6m.

Solution:

Given:

m1 = 80 kg, m2 = 100 kg,

r = 6m and

G =Â 6.67259 x 1011Â N m2/kg2.

Universal gravitation formula is given by,

F=Gm1m2 / r2

Â =6.673Ã—1011Ã— 80Ã—100 / 36

F =148.28Ã—1011N