# Gravitation | The Universal Law of Gravitation

Gravitation ~ The  earth exerts  some  invisible  force  on  the  object,  which  is known  as  the  Gravitational  Force.  When  the  object is  thrown  up  an  external  force  is  applied  by  the person  throwing  it  up.  At  that  time  also  earth’s gravitational  force  is  working  on  it  and  hence  its velocity  gradually  decreases  down  to  zero.  Then after  it  again  starts  falling  down  towards  the  earth surface.  This  also  is  an  example  of  earth’s gravitational  force. Another  example  of  this  force  is the  movement  of  water  drops  from  the  clouds  to  the earth  surface.

Contents

## ✍️ Gravitation

It  is  said  that  once  Newton  was  sitting beneath  an  apple  tree  and  an  apple  fell  on  him. Newton  was  inspired  to  find  the  reason  underlying this  episode.  He  thought  as  to  why  the  apple  fell towards  earth?  Why  was  it  not  attracted  towards  the moon.  Thus  on  the  daily  life  observations  Newton proposed the theory of Gravitation. In  this  chapter  we  will  study  about  the Gravitation  and  the  Universal  Laws  of  Gravitation. We  will  also  consider  the  movement  of  object  under the  influence  of  the  gravitational  force,  the  change in  weight  of  objects  and  why  do  objects  fly  in  the space.

Activity

• Tie  a  small  stone  to  a  piece  of  a  thread.
• Move  the  stone  on  a  circular  path  by catching  hold  of  the  other  end  of  the thread,  as  shown in  fig.
• Observe the direction of the movement of  the  stone.
• Now  leave  the  thread  and  observe  the direction  of  movement of the stone.

Before  we  left  the  thread  the  stone  was moving in a  circular  path. At  that  time  it  experienced a  force  towards  its  center  which  is  known  as  the Centripetal  Force.  This  force  is  responsible  for  the circular  motion of  the  objects. On  leaving  the  thread  the  stone  proceeds  in  a simple  line  and  then  moves  in  a  free  manner  i.e.  the circular  motion  ends  on  removing  the  Centripetal Force.

The movement of moon around the earth is due  to  the  presence  of  centripetal  force.  This centripetal force is derived from the earth’s gravitational force.  Gravitational Force occurs naturally between all the objects of the world, but we are unable to experience the gravitational force working between the normal objects. Since the mass of celestial bodies is more this force becomes effective and controls their motion.

It was in fifth century that the Bhartiya astronomer Aryabhatt propounded the geocentric model to understand the movement of planets. Nearly 500 years before Newton and Kepler, Bhaskaracharya in the grah-ganit section of his famous work Siddhantsiromani had discussed the gravitational power of earth and the planetary movements, in detail. Bhaskaracharya calculated the radius (R) and circumference (2pr) of the earth.

The western scientist Copernicus (1473-1543) propounded the model of the movement of celestial bodies on the basis of Aryabhatt’s vision. Even Kepler and Galileo also worked out some laws to clarify the understanding about the movement of the planets.

The famous seventeenth century scientist Isaac Newton (1642-1727) gave the Laws of Motion and the Universal Law of Gravitation. These were based on substantial scientific logic and were proved mathematically. The contributions of these scientists in the sphere of physics were very important.

## ✍️ Universal Law of Gravitation

Each particle (body) of the universe exerts a force of attraction towards itself on every other particle (body) which is known as the Gravitational Force.  According to the Law of Gravitation “the force of attraction between two particles of matter or bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.

The direction of this force is the same as the direction of the line joining the two particles”.  Suppose two bodies of mass M and m are placed at a distance d from each other. Then the gravitational force F working between will be Here G is the proportional constant known as the Universal Gravitational constant.

The value of G has been worked out to be – 6.67×10-11 Newton–meter2–Kilogram2, from various experiments. Its value does not depend on the nature of the particles, medium, time, temperature etc., i.e. it remains the same at every place.

Hence it is known as the Universal Constant. The earth also attracts things towards itself. This, earth’s force of attraction is known as the Force of Gravitation.

Many phenomenon can be easily interpreted by the Law of Gravitation. Some of the important ones includes :

(1) The force that binds us to the earth

(2) Movement of planets around the sun

(3) Movement of the moon around the earth

(4) Occurrence of tides in the sea.

## ✍️ Gravitational Acceleration

When the change in an object’s velocity i.e. acceleration, is due to the earth’s force of gravitation, it is known as the Gravitational Acceleration. It is denoted by g and its unit is ms-2.

From the second law of motion

Force = mass × acceleration  or F = mg

The gravitational acceleration of any planet depends upon its mass and radius. In other words, heavier a planet comparatively more will be its gravitational acceleration.

## ✍️ Movement of objects under the influence of the earth’s force of gravitation

It is clear from the equations 10.4 and 10.5 that the Gravitational Acceleration experienced by various objects does not depend upon the mass and shape of the objects. This means that different objects should fall down with the same rate when dropped from the same height. But is it so? Again we will perform an activity to get an answer.

The initial velocity of the free falling objects is zero.

The value of gravitational acceleration ‘g’ remains constant for a height of some kilometers from the earth’s surface. Therefore to study the motion of objects near the earth’s surface, the equation for uniform acceleration motion described in the last chapter is made use of.

## ✍️ Mass

Mass is the measure of the inertia of an object. In other words, greater the mass of a body more will be its inertia. The mass of a body remains the same every where; whether it is on earth or in space.

## ✍️ Weight

On earth the weight of an object is a type of a force that takes it towards the earth. As per definition the weight of a substance is the force by which it is attracted towards the earth.

Mathematically  F = mg

the weight of the body w = mg.

Since the value of g at a given point is constant, therefore, the weight of an object is proportional to it’s mass. The mass remains the same with the change in the value of g but the weight changes.

## ✍️ Weight of an object on the Moon

Weight  of  a  body  on  Moon  is  the  force  with which the moon attracts it towards itself.  The mass of  moon  is  less  as  compared  to  that  of  the  earth therefore  even  the  force  of  attraction  will  be  less. We can  say  that  the  weight  of  an  object  on  moon  is relatively  less  than  that  on  earth. Since  we  have  seen  that  the  gravitational  acceleration  on  moon  is  1.61  m/s2   which  is  1/6  of that  present  on  the  earth’s  surface,  whose  gravitational  acceleration  is  9.8  m/s2 ,  therefore  the weight  of  the  object  on  moon  will  be  1/6  of  its weight on earth.

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