Gravitation

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About the lesson

Previous Knowledge required : Kinematical equations and Newton's laws of motion
Time duration : 45 minutes
Level : IX Std.

Reference: IX Std NCERT textbook

After the lesson the students will be able to:

  1. use Newton's law of gravitation to explain various phenomena and apply in various situations
  2. explain the concepts of gravitational acceleration and weight

Introduction

People have always wondered why doesn't the Moon fall to the Earth? Let us explore this question using a simulation given by Michael Fowler of Department of Physics, University of Virginia . You may change the speed with which the object is thrown from a mountain and see whether it will always hit the ground. Click on the image below to interact use the simulation.

Newtonsmountain.png

Now that you have seen how an object can revolve around earth , let us know the history of this interesting exploration of gravity.


There have been numerous theories of gravitation since ancient times. Greek philosopher Aristotle (f. 4th century BC) believed that objects tend toward a point due to their inner gravitas (heaviness). Vitruvius (f. 1st century BC) understood that objects fall based on their specific gravity. In the 7th century, Brahmagupta spoke of gravity as an attractive force.

In the early 17th century, Galileo Galilei found that all objects tend to accelerate equally in free fall. In 1632, he put forth the basic principle of relativity. The existence of the gravitational constant was explored by various researchers from the mid-17th century, helping Isaac Newton formulate his law of universal gravitation. Newton's classical mechanics were superseded in the early 20th century, when Albert Einstein developed the special and general theory of relativity. Let us watch a youtube video by John Bernad Moylan, which explains Galileo's ideason gravitation. Click on the image below to watch the video.

Galileoandgravitation.png

Newton's law of Gravitation

Sir Isaac Newton was able to prove that the there is a force of attraction between the objects and this force called gravitational force depends on the masses and the distance between them. This law is also called as universal law of gravitation and can be stated as under.

Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.

Newtons law of gravitation.png

where:

F is the force between the masses; G is the gravitational constant (6.674×10−11 N · (m/kg)2); m1 is the first mass; m2 is the second mass; r is the distance between the centers of the masses.

Saying that F is inversely proportional to the square of distance means, for example, that if d gets bigger by a factor of 6, F becomes 1/36 times smaller.


The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:

  1. the force that binds us to the earth;
  2. the motion of the moon around the earth;
  3. the motion of planets around the Sun; and
  4. the tides due to the moon and the Sun.

You may have some questions like the ones given below:

Questions to Ponder
  1. How did Newton guess the inverse-square rule?
  2. Do I weigh less on the equator than at the North Pole?
Isaac Newton and gravitational law :
Newton2.png Isaac Newton was born in Woolsthorpe near Grantham, England.He was born in a poor farming family. He was sent to study at Cambridge University in 1661. In 1665 a plague broke out in Cambridge and so Newton took a year off.

It was during this year that the incident of the apple falling on him is said to have occurred. This incident prompted Newton to explore the possibility of connecting gravity with the force that kept the moon in its orbit. This led him to the universal law of gravitation. It is remarkable that many great scientists before him knew of gravity but failed to realise it.

Newton’s work combined the contributions of Copernicus, Kepler, Galileo, and others into a new powerful synthesis. It is remarkable that though the gravitational theory could not be verified at that time, there was hardly any doubt about its correctness. This is because Newton based his theory on sound scientific reasoning and backed it with mathematics. This made the theory simple and elegant. These qualities are now recognised as essential requirements of a good scientific theory.


  "I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me....... If I have seen further than others, it is by standing upon the shoulders of giants."-Sir Isaac NewtonBold text


There has always been a great interest in the motion of planets. By the 16th century, a lot of data on the motion of planets had been collected by many astronomers. Based on these data Johannes Kepler derived three laws, which govern the motion of planets. These are called Kepler’s laws.


These are: 
1. The orbit of a planet is an ellipse with the Sun at one of the foci, as shown in the figure given below.


Newton.png

In this figure O is the position of the Sun. 
2. The line joining the planet and the Sun sweep equal areas in equal intervals of time. Thus, if the time of travel from A to B is the same as that from C to D, then the areas OAB and OCD are equal.
3. The cube of the mean distance of a planet from the Sun is proportional to the square of its orbital period T. Or, r3 /T2 = constant.

It is important to note that Kepler could not give a theory to explain the motion of planets. It was Newton who showed that the cause of the planetary motion is the gravitational force that the Sun exerts on them. Newton used the third law of Kepler to calculate the gravitational force of attraction. The gravitational force of the earth is weakened by distance.

Let us now understand how Newton discovered law of gravitation. Click on the image below to watch the video.

Newtonandgravitation.png


Further Reading

 1) Lecture Notes: Michael Fowler, UVa. :  http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravityIndex.htm
 2) NASA Archives : https://www-spof.gsfc.nasa.gov/stargaze/Sgravity.htm