9.1.1. UNIVERSAL LAW OF GRAVITATION

Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.

The gravitational force is a fundamental force of nature that acts between any two masses in the universe. This force depends on two factors: the masses of the objects and the distance between them. It is stronger when the masses are larger and weaker when the objects are farther apart. Mathematically, the gravitational force (F) is defined by the formula:

F = G * (M * m) / d^2,

where G is the universal gravitational constant, M and m are the masses of the two objects, and d is the distance between their centers. This formula illustrates how gravitation works universally—not just between large celestial bodies like planets and moons but also between everyday objects.

Think of gravitational force like a magnet attracting metal objects. The larger the magnet (mass), the stronger the pull (gravitational force), and if the objects (metal pieces) are further away, the pull weakens, similar to how a magnet loses its grip as you move it farther away.

The force of attraction between two objects is directly proportional to the product of their masses. That is, F ∝ M × m.

When we say the force is directly proportional to the product of the masses, it means that if one or both of the masses increase, the force of attraction also increases. For example, if two objects have a mass that is doubled, the gravitational force between them quadruples, given that the distance remains constant. This relationship highlights the importance of mass in gravitational interactions.

Imagine two people pushing a car. If one person is very strong (mass) and the other is not, the car will move more easily. Now, if a second strong person joins in, the force pushing the car increases significantly—similar to how increasing mass increases gravitational attraction!

The force between two objects is inversely proportional to the square of the distance between them. That is, F ∝ 1/d^2.

This aspect of the universal law indicates that as the distance (d) between two masses increases, the gravitational force (F) decreases dramatically. If you double the distance between two objects, the gravitational force is not halved; it becomes one-fourth of its original value because it decreases with the square of distance. Thus, distance plays a crucial role in how strong the gravitational attraction will be.

Think of it as throwing a ball. If you throw it directly to a friend who is close by, it reaches them quickly. But if your friend moves further away, the ball takes longer to reach them and may not even reach them at all. Similarly, being farther apart weakens the gravitational 'reach' between two objects.

According to the third law of motion, the apple does attract the earth. But we do not see the earth moving towards the apple due to its enormous mass compared to the apple.

In everyday life, we observe large forces acting. For instance, when you drop an apple, it falls to the ground due to Earth's gravity. The apple attracts the Earth with the same force, but because Earth’s mass is so massive compared to the apple, the effect on Earth is imperceptible. The concept explains the nature of gravitational attraction where every mass attracts every other mass, but the effect of smaller masses on larger masses is negligible.

Imagine a tiny puppy tugging on a huge dog’s leash. The tiny puppy can pull the leash, but it doesn’t affect the dog’s position significantly due to the dog’s much larger mass. Similarly, the apple's attraction to the Earth is there, but it’s overshadowed by the Earth’s massive pull on the apple.

The law is universal in the sense that it is applicable to all bodies, whether the bodies are big or small, whether they are celestial or terrestrial.

This law applies to all masses around the universe. It doesn't matter if we are talking about planets in our solar system or everyday objects like cars or humans; the gravitational force acts between all of them. This universality helps in understanding various motions and even orbits of celestial bodies based on the same fundamental principles.

Think of how gravity affects everything we do; from walking to running to jumping, we are constantly influenced by gravity. Likewise, planets orbiting the sun follow this law without exception, demonstrating that this principle holds true in all situations involving mass.

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