Newton’s law of gravitation governs the working of gravitational force. Gravitational force is the force that stays at play in the universe as a consequence of the mass carried by matter. Newtonâ€™s law of gravitation states that gravitational force between two objects is numerically equal to the ratio of the product of their masses and the square of the distance between them.

Before beginning to state and derive Newton’s law of gravitation, let us first begin by gaining some primary insight into the force that it governs. Gravitational force is essentially one of the most fundamental four forces in science. It is always attractive in nature and comes into play as a virtue of interaction between matter and its mass.

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It is the weakest of all the fundamental forces put there, but, on the contrary, has infinite range. This essentially means that any two objects existing in the universe are attracted by the said force.

There are many natural consequences of the force being at play, i.e., it explains many natural phenomena. We shall discuss the same in a certain following subtopic. For now, the following points should be kept in mind:

Gravitational force is a consequential attraction arising as a result of matterâ€“matter interaction.

It is the weakest of all the four fundamentals.

It works over an infinite range.

Newtonâ€™s Law of Gravitation
Now that the basic understanding of the force is developed, let us now let us focus on the governing universal law. The governing law was formulated by Issac Newton and is hence is known as Newtonâ€™s law of gravitation. Before diving a little deeper into the concept, let us first begin by stating a formal statement for the same. Therefore, the law can be worded as follows:

â€œNewtonâ€™s law of gravitation or the universal law of gravitation states that two bodies when kept at a distance from each other, exert an attractive force at each other as a consequence of the masses they contain. This force is indirectly proportional to the square of the distance between them.â€

Mathematically, the same law shall be represented in the following way. For the sake of representation, let us first begin by taking clues from the formal statements.

Firstly, the statement talks about the force (Fg) being inversely proportional to the square of the distance (r). It can be shown as

{F_g} \propto \frac{1} {r^2}F
g
â€‹
âˆ
r
2

1
â€‹

Secondly, the statement calls the force to be a consequence of the masses of the two objects. The masses will be incorporated in the formula as a product-

F_{g} \propto m_{1} m_{2}F
g
â€‹
âˆm
1
â€‹
m
2
â€‹

The final expression turns out to,

F_{g} \propto \frac{m_{1} m_{2}}{r^{2}}F
g
â€‹
âˆ
r
2

m
1
â€‹
m
2
â€‹

â€‹

The proportionality symbol here can be replaced by G, which is the universal gravitation constant. Its value is 6.673 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}6.673Ã—10
âˆ’11
Nm
2
/kg
2
The final equation turns out to be-

F_{g}=G \frac{m_{1} m_{2}}{r^{2}}F
g
â€‹
=G
r
2

m
1
â€‹
m
2
â€‹

â€‹

The Consequences
As the gravitational force is found to be present in every scientific phenomenon, it is safe to conclude that it does give way to certain consequential influence in all these scenarios. It is difficult to come up with a limited number of examples of this law, but for the sake of better understanding, two brief ones are considered here-

Planetary attractive forces

It is already discussed that anybody that contains mass is capable of exerting a gravitational field around it. The same is the case with the planets in our universe. They exert a force of gravity on each other, and on the Sun, and also mutually responded with the same. As a result of this interaction, the planets manage to stay in fixed orbits as they revolve around the Sun.