Universal law of Gravitation

Key Concepts

• Gravitational force
• The universal law of gravitation
• Importance of the universal law of gravitation

Recall: 

• All the bodies on the Earth, revolving around the Earth and falling towards the Earth, are under the action of the gravitational force exerted by the Earth’s gravity. 
• Gravitational force is an attractive force. 
• Newton’s second law motion: The acceleration produced by a particular force is inversely proportional to the mass of the body. 
• Newton’s third law of motion: Every action has an equal and opposite reaction. 

Introduction: 

We commonly see things falling towards the Earth. Such movements are caused due to the gravitational pull of the Earth on those objects. However, Newton’s 3rd law of motion says, “Every action has an equal and opposite reaction”. This means that the gravitational pull that the Earth exerts on the falling bodies must have a reaction force as well. This reaction force is said to be equal in magnitude and opposite in direction to the gravitational pull of the Earth. The reaction force is nothing but another gravitational force that the falling body exerts on the earth. Surprisingly, this reaction force is exactly equal in magnitude to the gravitational pull that the Earth exerts on the falling body and acts in the opposite direction to it. Having said that, a natural question that might pop up, i.e., why the Earth does not move towards the body despite being subjected to an equal gravitational pull by the object. 

Explanation: 

The answer to the above question lies in Newton’s 2nd law of motion. It says that the acceleration produced by a particular force is inversely proportional to the mass of the body. 

Mathematically,                            a α 1/m 

If a mango falls towards the Earth, it exerts a force equal in size and opposite in direction to that of the Earth’s gravitational pull, as shown in figure 2.1 below. The mango moves towards the Earth. However, the Earth does not seem to move towards the mango even though it is under the action of a force of the same size. This is because of the negligibly small mass of the mango as compared to the mass of the Earth. And, according to Newton’s 2nd law, the acceleration gained by a body on application of a particular force is inversely proportional to its mass. 

Mathematically,                            m_mango <<<  m_earth 

     a_mango >>>  a_earth 

The mango, being of a negligibly small mass, gains a considerable acceleration to move towards the Earth. However, the same sized force produces an extremely small acceleration for the Earth to move. Thus, the Earth also moves towards the mango because of the gravitational pull of the mango on the Earth. However, the acceleration of the Earth towards the mango is negligibly small and hence, not apparent. 

For the same reason, the Earth does not seem to move towards any falling object, including the Moon. 

Now, if there is a force that mango exerts on the Earth, there must be some attractive force between any two objects. In fact, it is true. A similar force of attraction exists between any two objects in this universe. This was put forth by Sir Issac Newton in the year 1687 as the universal law of gravitation. 

The Universal Law of Gravitation 

This law provides a way to measure the amount of gravitational force of attraction between any two objects in this universe by using the factors on which the force depends. 

It states, “Every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” 

This force is a non-contact and attractive gravitational force. The gravitational force is measured in the SI unit of ‘Newton’ abbreviated as ‘N.’ 

If A and B are two bodies with masses m₁ and m₂, separated by a distance r. The force F between two objects is given by, 

F α m₁

×

m₂ 

F α 1/r² 

On combining the above equations, we get, 

F α m₁

××

m₂/ r² 

F = G (m₁m₂/r²) 

where G (Universal gravitational constant) = 6.673

××

10^-11 Nm²/kg² 

The gravitational force of attraction between two uniform objects is directed along the line joining their centers. 

Even though an attractive gravitational force seems to exist between any two bodies in this universe, two bodies do not generally stick together because the magnitude of this force is negligible between two less massive bodies. 

Importance of the Universal Law of Gravitation 

The law is called ‘universal’ because it is applicable to any two bodies in this universe. No matter how small or large the bodies are, the value of the universal gravitational constant is the same everywhere and for everybody in this universe. 

The universal law of gravitation successfully explains many natural phenomena which were believed to have no connection at all, such as, 

1. The force that binds everything on the Earth to the Earth. 

2. The motion of the moon around the Earth. 

3. The motion of all the planets around the Sun. 

4. The high and low tides are due to the Moon and the Sun.