### Law of Gravitation

##### April 12, 2017

# Law of Gravitation

**Law of Gravitation or Law of Universal Gravitation by Newton**: Every object in this universe is attracting every other object towards it with a force called *gravitational force of attraction*.

*According to Newton’s law of gravitation*, this force of attraction is (i) **inversely proportional to the square of the distance** between the objects and (ii) **directly proportional to the product of the masses** of these two objects involved.

Hope you have heard the story about Sir Isaac Newton and a falling apple which was pulled toward earth by the force of gravity.

If it is true then we can say that an apparently unimportant event led to Newton’s formation of a fundamental law of nature which involves gravitational forces.

We’ll discuss on this law now and also **derive** the **equation of the Gravitational force.**

## Derivation of Gravitational Force formula from the Newton’s universal Law of Gravitation

Say F_{G} is the magnitude of 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 later in this post.

This equation gives us the **expression** of the **gravitational force**.

## Direction of the gravitational force

This force acts along the line joining the two objects.

The object with mass m1 will apply this force on m2 and the direction of the line of this force will be from m2 towards m1.

The object with mass m2 will apply a force of same magnitude on m1 and the direction of the line of this force will be just opposite i.e it would be from m1 towards m2.

**Universal Gravitational Constant **

**or Gravitational constant**

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

** Its unit is Nm ^{2}kg^{-2}**

**Its value 6.67408 × 10 ^{-11} Nm^{2}kg^{-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.)