Universal Law of Gravitation

State the Universal Law of Gravitation

Law of Gravitation or Law of Universal Gravitation by Newton states that “Every object in this universe is attracting every other object towards it with a force called the gravitational force of attraction. This force of attraction is (i) inversely proportional to the square of the distance between the objects and (ii) directly proportional to the product of the masses of these two objects involved.

I hope you have heard the story about Sir Isaac Newton and a falling apple that was pulled toward the earth by the force of gravity. If the story is true then we can say that an apparently unimportant event led to Newton’s formation of a fundamental law of nature which involves gravitational forces.
We’ll discuss this law now and also derive the equation of the Gravitational force. This post is apt for students who are looking for the universal law of gravitation derivation for class 9 and class 11/12 courses. [CBSE, ICSE, Other International boards for science]

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Derivation of Gravitational Force formula

Say FG is the magnitude of the force of gravitational attraction between any two objects, m1 is the mass of one object, m2 is the mass of a second object, d is the distance between the centers of the two objects. (Objects are assumed to be spherical.)

Law of Gravitation

Now as said in the Law of Gravitation:

FG ∞ m1.m2

and

        FG ∞  1/d2

So,   FG ∞ m1.m2/ d2

Derivation of Universal Law of Gravitation

The Universal law of gravitation can be summed by this formula   
FG = (G.m1.m2)/ d2

G is a constant which is discussed later in this post.
This equation gives us the expression of the gravitational force.

State the direction of the gravitational force

This force acts along the line joining the two objects. The object with mass m1 will apply this force on m2 and the direction of the line of this force will be from m2 towards m1.
The object with mass m2 will apply a force of the same magnitude on m1 and the direction of the line of this force will be just opposite i.e it would be from m1 towards m2.

Define Universal Gravitational Constant or Gravitational constant

In the equation of gravitational force, G is a constant, called Universal Gravitational Constant or Gravitational constant.

Its unit is Nm2kg-2

Value of G:
Its value 6.67408 × 10-11 Nm2kg-2

Law of Gravitation-Notes

With the law of universal gravitation, it is important to notice that two equal but opposite forces are present between any 2 objects. Earth pulls on the Moon and the Moon pulls on Earth with a force of equal magnitude.

On the Earth’s surface, Earth pulls down on a 1 kg mass with a force of magnitude 9.8 N, and the 1 kg mass pulls upward on Earth with a force of magnitude 9.8 N. (Ref: Newton’s third law of motion.)

Importance of  Newton’s Universal Law of Gravitation

It has explained how every object on earth is bound to the earth’s surface in spite of it rotating continuously.

It explains the motion of the Satellites (e.g. moon) around planets (like earth).

The motion of the planets around the Sun is also explained by this Universal law.

It helps us to find out the value of g (acceleration due to gravity) for earth.

It helps us to understand why g on earth is different from g on the moon.

Now why does a stone fall towards the earth but the earth doesn’t seem to run upwards towards it ? Read here.

Universal Law of Gravitation
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