### Universal Law of Gravitation

##### April 12, 2017

# Universal Law of Gravitation

Have you heard of the story about Sir Isaac Newton and a falling apple which was pulled toward earth by the force of gravity? An apparently unimportant event led to Newton’s formation of a fundamental law of nature (**Law of universal gravitation** or **Law of Gravitation**) which involves gravitational forces. We’ll discuss on this law now and also **derive** the **equation of the Gravitational force.**

As said by this **law of universal gravitation** every object in this universe is attracting every other object towards it. This force of gravitational attraction between any two objects in the universe is **inversely proportional to the square of the distance** between the objects. This force is again **directly proportional to the product of the masses** of these two objects involved.

## Derivation of Gravitational Force formula from the Law of Gravitation

Say F_{G} is the force of gravitational attraction between any two objects,

m1 is the mass of one object,

m2 is the mass of a second object,

d is the distance between the centers of the two objects. (Objects are assumed to be spherical.)

Now as said in the **Law of Gravitation**:

**F _{G} ∞ m1.m2**

and

** F _{G} ∞ 1/d^{2}**

So, **F _{G} ∞ m1.m2/ d^{2}**

** F _{G} = (G.m1.m2)/ d^{2
}**

G is a constant which is discussed in the next section.

This equation gives us the

**expression**of the

**gravitational force**.

### **Universal Gravitational Constant or Gravitational constant**

In the equation above, G is a constant, called **Universal Gravitational Constant or Gravitational constant.**

**Its value is 6.67408 × 10 ^{-11} m^{3} kg^{-1} s^{-2}**

### Law of Gravitation-Notes

With the law of universal gravitation, it is important to notice that two equal but opposite forces are present between any 2 objects. Earth pulls on the Moon and the Moon pulls on Earth with a force of equal magnitude.

On the Earth’s surface, Earth pulls down on a 1 kg mass with a force of magnitude 9.8 N, and the 1 kg mass pulls upward on Earth with a force of magnitude 9.8 N. (Ref: Newton’s third law of motion.)

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