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April 19, 2023

December 27, 2021

Scientists have been always curious about the planets, stars, and their motion since ancient times. *Nicholas Copernicus* was the first to say that the sun is stationary and the earth revolves around the sun. Later, the German scientist *Johannes Kepler* discovered three elegant laws *(Known as ***Kepler's laws**) of planetary motion. By analyzing these formulas, the scientist *Sir Isaac Newton* determined the nature of the *force* of attraction between the sun and the planets.

The force of attraction is called *gravitation*, which is not only between the sun and the planets but also between any two objects or particles in the universe.

The force by which any two objects in this universe attract each other is called **gravitation**. Newton observed that all the objects in the universe attract each other with a certain amount of force, but in most cases, the force is too weak to observe due to the very large *distance* of separation.

The range of this force is infinite but the force becomes weaker as the objects move away. To measure this gravitational force, Newton introduced a law in 1680 called **Newton's Law of Gravitation** or the *Universal Law of Gravitation*.

According to Newton’s law of gravitation, any two particles in the universe attract each other along their connecting straight lines. The magnitude of this gravitational attraction is

1. Directly proportional to the product of the masses of the two particles and

2. Inversely proportional to the square of the distance between them.

Now let the distance between two particles of mass *m1* and *m2* be *r*. If the force of attraction between the two particles is *F*, then according to Newton's law of gravitation,

Now by combining these two formulas

This is the formula of this gravitational attraction between two objects. Here *G* is the universal gravitational constant.

For the earth and any object on the earth the gravitational attraction

Where *M = mass of the earth, m = mass of the object, and R = radius of the earth*.

When *m1 = m2 = 1* and *r = 1* then from equation no - (3) we can write *G = F*. It defines the gravitational constant.

So units of G in the different unit systems are

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