The universal law of gravitational force

The universal law of gravitational force between two objects is proportional to the product of the masses of the objects and inversely proportional to the square of the distance between the objects. All the heavenly bodies are bounded by the same type of force that is why it is known as the universal law of gravitational force. The smaller celestial bodies revolve around a bigger celestial body due to the universal law of the gravitational force, the orbital of the smaller bodies are fixed because of fixed mass.

The universal law of gravitational force

You will study here:

• Type of Natural forces in the universe
• Observation of gravitational force
• Verification of the universal law of gravitational force
• Verification of unit of the universal constant of gravitational force
• The relationship between g and G
• Difference between gravity and the universal law of gravitational force

Type of Natural forces in the universe:

Do you know why are all of the things are arranged in a matrix of the universe? Why does the moon revolve around the earth, and the same the earth and other planets do around the sun. The whole of the universe from the microscopic level to the macroscopic level is bounded by different kinds of natural forces. The microscopic level involves the forces between the particles of the matter like nuclear forces, intermolecular forces, electrostatic forces, etc whereas in the macroscopic level the forces between two objects are studied like a magnetic force, gravitational force. The discovery of gravitational force is said to be discovered by a great Indian astronomer and mathematician Bhaskaracharya in the eleventh century although it is self-examined, explored and deeply explained by Sir Issac Newton in 16 th century. The most popular discovery of Newton was the universal law of gravitational force. The whole of the universe is governed by this universal law of gravitational force.

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Observations of gravitational force:

Initially,  Newton observed an apple fell on him while he was sitting under an apple tree on a beach, a thought created in his brain why did it pour down. He concluded to the fact that the earth attracts everything towards its side by its gravitational force, then his brain clicked towards the moon and observed that the same kind of force might be applied by the earth on the moon, that causes the moon to revolve around the earth, and sequentially one by one he discovered three equation of motion and laws of motion, etc.

Verification of universal law of gravitational force:

If there are two objects of the masses m and M in the universe, the gravitational force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F      ∝     m×M ……….(i)

F  ∝    1/d²………………(ii)

From (i) and (ii) we have

F      ∝     m×M/d²

F     =  G.mM/d²

This equation is known as the universal law of gravitational force, in this equation, F is called the universal gravitational force due to which all the heavenly bodies suspended and moving with respect to each other in the space and are under the control of a balanced force.

Where G is constant of proportionality is known as the universal constant of gravitational force and its value is

6.67×10^-11Nm²kg^-2

Verification of the unit of the universal constant of gravitational force:

The unit of the universal constant of the gravitational force is determined as follows.

F     =  G.mM/d²

G = Fd²/mM

Unit of G = unit of F×(unit of d)²/(unit of m×unit of M)

Unit of G = Nm²/kg² = Nm²kg^-2

Hence unit of the universal constant of  gravitational force is Nm²kg^-2

The relationship between the universal constant of the gravitational force(G )and gravitational acceleration(g):

Let the mass of an object on the earth is m.

The force is (F) = product of mass and acceleration

According to the second law of motion

∴ F = mg……(i)

Here the acceleration on the object by the earth gravity is = g

F     =  G.mM/d²……(ii)

From (i) and (ii) we have

mg =  G.mM/d²

Since the object is on the surface of the earth, the distance must be substituted by the radius of the earth because the mass of the earth is centered at the center of the earth.

Therefore the above equation will become

g = G.M/r²

This is the relationship from which we can determine g,r, M or G if 3 physical quantities are given, then we can determine the unknown value whether it is g, M,r or G.

Difference between gravity and the universal law of gravitational force

The universal law of gravitational force exists between two bigger objects like the moon and the earth, the sun, and its planets while gravity exists between smaller objects and bigger objects like objects on the surface of the earth. In evaluating the universal law of gravitational force capital G is involved while computing gravity small g is involved.

We know the equation F = ma, where m is the mass of an object, a is the acceleration and F is the force applied on an object.

Any object with a mass m falling on the surface of the earth accelerates by the amount of g

Therefore gravity on the object by the earth is

W = mg, where g is the gravitational acceleration by the earth to the object

The gravity of the object is known as the weight of the object.

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