Derive Universal Law of Gravitation

Once Sir Isaac Newton himself seated underneath a tree in 1665, an apple fell from such a tree onto the earth, he proposed the notion of gravity. This triggered the thought in his head that almost all objects are drawn towards the earth’s core, wherein the defined gravity as the attractive forces between any two components divided by a space. This notion was crucial in the creation of stars and directing the overall structure of the cosmos. This notion has important applications in the progress of science at the moment. The gravitational force is the weakest of all the fundamental forces of existence.

Gravitational Force 

There are many forces at work in the cosmos and many pushes and pulls. Even if it’s only the earth, we’re constantly pushing or pulling stuff. However, it ends out that there have been just four basic principles in science, out of which everything else is derived: the strong, weak, electromagnetic and gravitational forces.

The gravitational force is indeed a force that pulls all mass-bearing objects. The gravitational force is attractive since it constantly strives to bring masses together rather than pushing things far. In reality, everything in the cosmos, including us, is tugging on another object! Newton’s Universal Law of Gravitation is the name for this. We may not have a lot of mass. Thus you’re not tugging on other items that much. Things that are extremely far apart do not noticeably tug on each other. However, the force exists and can be calculated.

Gravitation

The phrases gravitation and gravity were frequently interchanged when referring to the attraction between all things that have power or mass. Although gravity is the force that pulls an item forward towards the earth, gravitation is a much more broad term for this elemental force. “Each item in the cosmos pulls every other item in the cosmos with force directly equal to the product of their masses & inversely proportional to the square of the distance between them,” according to Sir Isaac Newton’s 17th-century Law Gravitation.

Dimensional Formula of Gravitational Constant

The Universal dimensional formula of the Gravitational Constant is:

[M-¹ L³ T-²]

Here,

M stands for mass.

L stands for length.

T is for Time.

Derivation:

Force = G × m₁ × m₂ × [r²]-¹

Or, G = Force × r² × [m₁ × m₂]-¹ . . . . . (1)

Where G = Universal Gravitational Constant

Now, the dimensions of,

Mass = [M¹ L⁰ T⁰] . . . . (2)

Radius = [M⁰ L¹ T⁰] . . . . (3)

Force = [M¹ L¹ T-²] . . . . . (4)

On substituting equations (2), (3), and (4) in equation (1), we get,

Universal Gravitational Constant = Force × r² × [m₁ × m₂]^–2

Or, G = [M¹ L¹ T^–2] × [M⁰ L¹ T⁰]² × [M¹ L⁰ T⁰]-1 × [M¹ L⁰ T⁰]^–1 = M^–1 L³ T^–2.

Therefore, the Universal Gravitational Constant is dimensionally represented as [M^–1 L³ T^-2].

Gravitational Constant

The gravitational constant’s magnitude is exceedingly hard to calculate precisely. Henry Cavendish invented an ingenious method of determining the gravitational constant. The masses m & m’ are affixed to the beam’s opposite ends. With the aid of a string, the frame is fastened to a solid support. The thread is linked to the centre of the beam, which allows it to balance. Two huge masses, M’ & M, are now lowered beside them. The rope twists due to such gravitational force between both the two bodies, and the degree of bending is just controlled by that of the gravitational force. Suitable calibration may be used to determine the gravitational force.

Conclusion

The article’s point was to look at the Universal Law of Gravitation and how the equation for the Gravitational Force was derived from this. Newton’s Universal Law of Gravitation describes the attraction between any two particles. This force is 1. inversely proportional to the square of the distance between the items, and 2. directly proportional to the sum of the masses of the two objects, according to this rule. This gravitational force equation sums up the Universal Law of Gravitation: FG = (G.m₁ × m₂)/r², wherein G is a constant known as the Universal Gravitational Constant or Gravitational Constant. The gravitational force is expressed using this formula.