1. What is the Universal Law of Gravitation?
The Universal Law of Gravitation, proposed by Sir Isaac Newton, states that every object in the universe attracts every other object with a force. This force depends on their masses and the distance between them. It explains both why objects fall to the ground and how planets move around the Sun.
Newton realised that the same force that pulls an apple down also keeps the Moon in its orbit. This discovery connected everyday physics with astronomy for the first time.
1.1. Why is it Called 'Universal'?
The law is called universal because it applies to:
- Objects on Earth (falling bodies, tides, weight)
- Celestial bodies (planets, moons, stars)
- Large and small objects alike
It acts everywhere and on all masses, no exceptions.
2. Newton’s Mathematical Formulation
The universal law of gravitation states that the gravitational force between two bodies is:
\( F = G \dfrac{m_1 m_2}{r^2} \)
Where:
- \( F \) is the gravitational force
- \( m_1 \) and \( m_2 \) are the masses of the two bodies
- \( r \) is the distance between their centres
- \( G \) is the gravitational constant
2.1. Understanding the Equation
The equation tells us:
- The force increases if the masses are larger.
- The force decreases if the distance between bodies increases.
- The relationship with distance is an inverse square law—doubling the distance makes the force one-fourth.
2.2. Direction of the Force
The gravitational force acts along the line joining the centres of the two bodies. It is always attractive—never repulsive.
3. Inverse Square Law
A key feature of Newton’s law is that the force varies inversely with the square of the distance between two bodies. This is known as the inverse square law.
If the distance becomes \( 2r \), then the force becomes:
\( F' = \dfrac{F}{4} \)
3.1. Why the Inverse Square Law Makes Sense
As distance increases, the gravitational influence spreads out. This geometric spreading leads naturally to the inverse square behaviour. Many physical laws such as light intensity and electric force follow similar patterns.
4. Testing the Universal Law
Although Newton proposed the law in the 1600s, it was later verified with careful experiments. Henry Cavendish measured the gravitational constant and confirmed that the law accurately predicts forces between masses, even in small laboratory setups.
4.1. Evidence from Astronomy
The orbits of planets, moons, and comets closely follow predictions made using Newton’s law. This agreement is one of the strongest proofs of its correctness.
4.2. Evidence from Earth
Falling bodies, tides, and the behaviour of pendulums all match the predictions of gravitational force.
5. Importance of the Universal Law of Gravitation
Newton’s law is one of the most important discoveries in physics. It helps explain:
- The motion of planets and satellites
- The behaviour of tides due to the Moon's pull
- The weight of objects on Earth
- The stability of galaxies and star systems
5.1. Foundation for Future Physics
Newton’s law paved the way for later theories such as Einstein’s General Theory of Relativity, which refined our understanding of gravity.
6. Moving Forward
The next topic explores the gravitational constant (G), the fundamental quantity that allows us to calculate gravitational force using Newton’s formula.