Gravitational Force Formula

Why are we able to walk on earth and not on any other planet? It is because of the gravitational force exerted by the surface of earth that attracts a body towards it and allows us to stand. Let us try to know more about it.

There are many forces, a lot of pushes and pulls, throughout the universe. In physics, there are four fundamental forces from which everything else is derived, these are the weak forces, the strong forces, the gravitational force, and the electromagnetic force.

Furthermore, the gravitational force is something that attracts any two objects with a mass. In other words, we can say that it is the tendency of gravitational force to attract two masses towards each other rather than pushing them apart. Moreover, every object including you pulls every other object in the entire universe, and this is called Newton’s Universal Law of Gravitation. It is denoted as F and the gravitational constant is denoted as G.

Gravitational Force Formula

Gravitational Force=Gm₁m₂/r×r

F = (Gm₁m₂)/r²

Where, m₁, m₂ are the mass of two objects

r is the distance between two objects 

and G stands for  the gravitational constant with a value of G = 6.67×10^-11 Nm²/kg²

Unit of Gravitational Force is Newtons.

Solved Examples

Below are some easy examples for the viewers to understand.

Ex. 1. Assume two satellites that circle the earth pass near one another. For a moment they are 150m apart from each other. Moreover, the masses of the satellites are 200kg and 40 kg. What is the Gravitational force between these two satellites?

Solution: 

Given: m₁ = 200kg,    m₂ = 40kg,    r = 150m

We know that,G = 6.67×10^-11 Nm²/kg²

So, applying the values in the formula, we get

F = (Gm₁m₂)/r²

F =6.67 × 10^-11× 200× 40/150 × 150

F = 6.67 × 10^-11×8000/22500

F = 6.67 × 10^-11 ×0.35

F = 2.33 × 10^-11N

Ex. 2. What will be the force of gravity on a body that is 10,000 meters over the Earth’s surface?

Solution: 

Given: r = 10000m

And we know that,

Earth’s mass = 5.98 ×10²⁴kg

Earth’s radius = 6.38× 10⁶m

G = 6.67 ×10^-11

Now,
F=Gm₁m₂/(r+h)²

F =6.67 × 10-11 × 5.98 ×10²⁴ × 10³/(6.38× 10⁶+10⁴)²

F= 6.67 × 10-11×5.97×10²⁷/40.8×10¹²

So, F=39.8 ×10¹⁶/40.8 ×10¹²

F = 9.755 N