Newton’s Universal Law of Gravitation

Every one of us knows that ”Whatever goes up must come down”. Just like an apple falling from the tree or a pencil falling from the desk. But have you ever thought why do satellites don’t fall? The answer this is the universal law of gravitation. So whatever goes up must come down and might not come down too. Let us study this in detail.

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Newton’s Law of Gravitation

The questions like why did the apple fall on the ground and why didn’t the satellite fall on the ground fascinated the scientist Newton. He came up with the universal law of gravitation.

Statement

”Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them ”. That is if objects are very close to each other than the distance between them is less and so the force with which they attract each other will be more.

Suppose you have a ball and a box both lying on the floor. Do they actually start moving towards each other?  According to the universal law, the ball and the box should be moving towards each other. But in actual this does not happen. This is because the force with which they are attracting each other is very much small.

So here if the mass of the ball is m₁ and mass of the box is m₂ then, F ∝ m₁ m_2, and is inversely proportional to the distance between them.

F ∝  \( \frac{1}{r²} \)

As you move the objects far away from each other the force will be less and if the objects are brought close then the force will be much greater.

Browse more Topics under Gravitation

• Thrust, Pressure and Buoyancy
• Acceleration Due to Gravity
• Earth Satellites
• Escape Velocity
• Gravitational Potential Energy
• Kepler’s Law
• Weightlessness

You can download Gravitation Cheat Sheet by clicking on the download button below

The Mathematical Form of Law of Gravitation

We have two masses  m₁ and  m₂

We know that, F ∝ m₁ m₂ and F ∝  \( \frac{1}{r²} \)

From these two we can say that, F ∝  \( \frac{m_1 m_2}{r²}\)

Now we need to convert this proportionality into equality, So we introduce a gravitational constant,

F =  \(\frac{Gm_1 m_2}{r²}\)

• G = Gravitational constant.
• SI unit of G is Nm² kg-²
• Value of G is 6.673×10^-11 Nm² kg-²

Suppose you have kept two pens on the table and you want to know the force of attraction between them, you can find out easily if you know the masses of the two pens, we can calculate the force by the above universal formula.

Importance of  Newton’s Universal Law of Gravitation

• It has explained us the force that binds us to the earth i.e how every object is pulled from the earth.
• It explains the motion of the moon around the earth.
• Also, the motion of the planets around the earth is explained.

Suppose you are standing on the top of the building and you throw a stone from a great height. Have you noticed that the stone falls to the ground? That is a  free fall. The object is falling freely on the ground.The gravitational pull attracts the object and the object completely. During free fall the direction of the motion remains unchanged. The motion is in a downward direction towards the motion of the earth.

Solved Question For You

Q. The gravitational attraction between the two bodies increases when their masses are

1. reduced and distance reduces
2. increased and distance is reduced
3. reduced and distance is increased
4. increases and distance is increased

Ans: B. F = \( \frac{Gm_1 m_2}{r²} \) where F is the gravitational force of attraction, which increases when the masses are increased and distance is reduced.