Law of Gravitation with Example

The law of gravitation is also known as the “first great unification.” It previously described methods related to gravity on earth with known physics or astronomy behaviour. The law of gravitation was derived from empirical observations by the scientist Issac Newton, who called it inductive reasoning. Love gravitation states that every point mass attracts every object of point mass by force acting along its line while intersecting those two points. This article will tell you about the universal gravitational law, gravitational force and its examples.

Gravitation

Isaac Newton didn’t just conceive his three laws of motion. In addition to that, he also discovered the law of gravity, also known as Newton’s law of gravitation or universal gravitational law. The Newton law of gravitation states that every object present in this universe or nature attracts every object towards each other, and the object can be of point mass or have very less pull. Still, the gravitational pull is present between the two bodies. The range of gravity is infinite, but due to the large separation, it becomes weak, and objects move away. This universal gravitation law was presented by Sir Isaac Newton in 1680.

The gravitational can exhibit only in two certain conditions, namely:

• The attraction between the objects due to Earth.

Let us consider this point with the help of an example:

When you throw a ball upwards in the sky, the ball reaches a certain height or to its maximum height, then it comes downwards to the surface of the Earth. This is all due to gravitation as Earth has a larger area and has greater pulling force.

• The presence of gravitation can be in the cosmos, or outer space between the objects present there.

Let’s take a look at this condition with the help of an example:

The attraction of forces presents between the sun and the planets around it.

The law of gravitation is inversely proportional to the distance between the masses(r) and directly proportional to the product of masses(m1,m2) in which out of the two masses(m1,m2) present, the dense one is known as the source mass, and the low-density one is known as the test mass.

The central force or the gravitational force solely depends on the line of work of a test mass measured from its source mass.

Law of Gravitation

Newton’s law of gravitation states that everybody present in this nature or universe pulls or attracts other bodies present with the gravitational force. The study about the action between two masses is also known as gravitation. Gravitational force is directly proportional to the product of masses (m1,m2) and inversely proportional to the distance between them.

It can be represented as:

F is directly proportional to (m1m2)…….eq(1)

F is inversely proportional to the square of the distance from their centres, F is inversely proportional to 1/r² ……eq(2)    

On combining both the questions (1) and (2);

F is directly proportional to m1m2/r²

F = G[m1m2]/r²

F can also be defined as f(r) as it is an uncertain force and conservative.

The dimensional formula for the gravitational force can be represented as [M-¹L³T-²] and the SI value of the G is 6.67 x 10-11 Nm² kg-².

The Formula for Gravitational Force 

Harmonising to the law of gravitation by Newton, each and every particle in this universe attract other particles with force in it known as the gravitational pull of gravitational force, which is directly proportional to the masses(m1,m2)  and inversely proportional to the square of the distance between the centre of the masses.

The mathematical representation for the formula of gravitational force can be depicted as:

F = Gm1m2/r²

Where, 

F is the gravitational pull of gravitational force between two objects, calculated in Newton.

G is known as the universal gravitational constant, having a value of 6.674 x 10-11 Nm² kg-².

m1 is the mass of the heavier mass, calculated in kg

m2 is the mass of the lighter mass, calculated in kg

r is the distance or the separation between the centre of masses calculated in Km

Let’s take another look at the Law of Gravity Force by solving some Examples

• The force was acting on an object having a mass of 3000 kg at the Earth’s surface. What is the force of gravity on it?
  Given

m1 = 6.00 x 1024 kg

m2 = 3000 kg

r = 6.38 x 106 m

g = 9.8 m/s²

G = 6.67 x 10-11 N-m² / kg²

Solution

F = G[m1m2]/r²

F = (6.67 x 10-11) (6.00 x 1024)(3000) /  6.38 x 106

F = 21 N (approx)

Conclusion

The law of gravitation or Newton’s law of gravitation depicts that if there are any two bodies present in this nature or in-universe, they both attract each other with the force of a pull known as the gravitational pull of gravitational force, which is directly proportional to the product of the masses and inversely proportional to the square of the distance between the centre of the masses. The universal gravitational law justifies the procedure of the revolution of celestial bodies and shapes the downward force existing on the Earth’s surface.