Universal Law of Gravitation

Introduction

We see that objects fall towards the Earth, planets move around the Sun, and the Moon moves around the Earth. All these motions are possible because of gravitational force. The law that explains this force is called the Universal Law of Gravitation.

Universal Law of Gravitation

The Universal Law of Gravitation states that every object in the universe attracts every other object with a force.

The magnitude of this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

|F⃗| ∝ m1m2

|F⃗| ∝ 1 / r2

Therefore,

|F⃗| ∝ m1m2 / r2

Removing proportionality, we get:

|F⃗| = Gm1m2 / r2

Here, F⃗ is the gravitational force, m1 and m2 are the masses of the two objects, r is the distance between their centers, and G is the universal gravitational constant.

Vector Form

If r̂ is the unit vector from mass m1 towards mass m2, then the gravitational force on m1 is:

F⃗12 = (Gm1m2 / r2) r̂

The gravitational force on m2 is in the opposite direction:

F⃗21 = − (Gm1m2 / r2) r̂

Thus, the two forces are equal in magnitude and opposite in direction.

Explanation

According to this law, the gravitational force increases when the masses of the objects increase. If the distance between the objects increases, the gravitational force decreases.

  • Greater the masses, greater is the gravitational force.
  • Greater the distance, smaller is the gravitational force.
  • This force always acts along the line joining the centers of the two objects.

This law is called universal because it applies to all objects in the universe.

Formula

|F⃗| = Gm1m2 / r2

Vector form:

F⃗12 = (Gm1m2 / r2) r̂

F⃗21 = − (Gm1m2 / r2) r̂

Where:

  • F⃗ = gravitational force
  • G = universal gravitational constant
  • m1 = mass of first object
  • m2 = mass of second object
  • r = distance between their centers
  • r̂ = unit vector along the line joining the two masses

Examples from Daily Life

  • Fruits fall from a tree towards the Earth.
  • The Moon revolves around the Earth.
  • Planets revolve around the Sun.
  • Rain falls towards the ground due to gravitational force.

Illustration

m1 m2 r F⃗21 F⃗12

In the figure, two objects of masses m1 and m2 attract each other. The distance between their centers is r. The forces F⃗12 and F⃗21 are equal in magnitude and opposite in direction.

Important Points

  • Every object attracts every other object in the universe.
  • Gravitational force depends on masses of the objects.
  • Gravitational force depends on the distance between the objects.
  • The magnitude of force is directly proportional to the product of masses.
  • The magnitude of force is inversely proportional to the square of distance.
  • The force acts along the line joining the centers of the two bodies.
  • This law is universal in nature.

Conclusion

The Universal Law of Gravitation explains the force of attraction between any two objects in the universe. In vector form, it also shows the direction of the force clearly. This law helps us understand falling bodies, motion of planets, and many other natural phenomena.

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