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Gravity

Aug 20, 2022
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Topic: Gravity of Earth and Sun 

Recall: 

  • Forces cause motion. 
  • The states of rest and uniform motion are caused by a set of balanced forces acting on a body. 
  • A non-uniform motion, such as accelerated or decelerated motions, is caused by a set of unbalanced forces acting on a body. 
  • Uniform circular motion is an accelerated motion. 

Introduction: 

All motions happening in this universe are caused by one or the other kind of force. However, in this session, we will be looking at a particular group of motions caused by a particular force called gravitational force. We see many things falling in our daily life. For example, when dropped, a stone falls, and a fruit when ripens falls towards the Earth. Such falling bodies move towards the Earth when released or loosened because they are subjected to the Earth’s gravitational pull. 

Moreover, the motions made by celestial bodies, such as the motion of the Moon around Earth and the motion of the Earth around the Sun, are also caused by gravitational forces. However, these celestial bodies do not seem to move toward each other. Instead, a massive object seems to be revolving around a further massive object. In this session, we shall first understand the gravitational force and its nature and then justify the role of gravitational forces in the motion of the celestial bodies. 

Explanation: 

Gravitational Force 

parallel

Gravitational force is an attractive force that pulls an object towards another. It is always attractive in nature. Some of the examples of the motions caused by gravitational forces are: 

  1. A mango falling from the tree 
  1. A stone dropped from the top of a building, falling down 
  1. Water in a waterfall falling from a higher point 
  1. Revolution of the Moon around the Earth 
  1. Revolution of all the planets around the Sun in the solar system 

The gravitational force is responsible for holding everything, including the atmosphere and the water on the Earth. If it disappears someday, all the objects are going to fall apart, including the Earth itself. 

The first three examples directly show the Earth’s gravitational pull on the objects in the examples mentioned above. However, in examples 4 and 5, a massive object revolves around another massive object. As an object does not seem to move towards another object, it gets difficult to understand that gravitational force causes such movements. Therefore, to understand such movements let us look at a simple illustration. 

Illustration: 

When a stone tied to a string is swirled around, the stone starts moving in a circular path. To maintain this motion at the same pace and the same horizontal plane, one must constantly apply an inward pulling force on the stone through the string, as shown below in figure 1.1(a). This force that is necessary to keep the stone moving in a circular path is called the centripetal force. It produces an acceleration that is directed towards the center of the circular path and is called the centripetal acceleration. The velocity of the body at every point is along the tangential direction, as shown below in figure 1.1(b). Thus, we can define the centripetal force as under: 

parallel

The force that produces the acceleration directed towards the center and keeps the object moving in a circular path is called the centripetal force.” 

In the above case of the motion made by the stone tied to a string, the centripetal force is supplied by the tension on the string. 

Revolution of the Moon around Earth and Earth around the sun 1
   (a)
Revolution of the Moon around Earth and Earth around the sun 2
(b)
Revolution of the Moon around Earth and Earth around the sun 3
(c) 

 

The gravity of the earth and the sun 

The motion of the Moon around the Earth and the Earth around the Sun shown in figure 1.2 is similar to the motion of the stone illustrated above. Thus, a centripetal force should be holding them in their orbits. In this case, the required centripetal force is supplied by the gravitational pull of the Earth and the Sun, respectively.  

Revolution of the moon around earth and earth around the sun 

The gravitational force is supposed to pull a body towards another. However, that does not seem to be the case for the revolution of the Moon and the Earth as they do not move towards the Earth and the Sun, respectively.  

Actually, the gravitational force of the Earth pulls the Moon towards its center at every point in its motion in orbit. As a result, the Moon falls towards the Earth at every point of its motion. However, it is never able to land on the Earth because of its spherically curved surface and continues to revolve around the Earth in an attempt to land on it. Thus, the Moon keeps revolving around the Earth in circular orbits because of the gravitational pull of the Earth. 

Similarly, the gravitational force exerted by the Sun on the Earth is directed from the Earth towards the center of the Sun. This gravitational force exerted by the Sun on the Earth supplies the necessary centripetal force to keep the Earth moving in its orbit. 

Question 1 

What would happen if the gravitational force between the Moon and the Earth disappears someday? 

Answer: 

The Moon flies away in the tangential direction in a straight line undergoing a uniform motion. 

This is like the case of breakage of the string tied to the stone wherein the stone flies away in a straight line tangentially in a uniform motion. 

Question 2 

What will happen to everything on planet Earth if its gravity disappears? 

Answer: 

If Earth’s gravity is lost, all items held to the Earth’s surface by gravity, such as atmosphere, water, people, cars, and animals, would float away. 

Objects strongly secured to the Earth, such as a tree with deep penetrated roots, might remain attached to it. 

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