1. What is the Gravitational Constant (G)?
The gravitational constant, represented by G, is a fundamental constant that appears in Newton’s universal law of gravitation. It determines the strength of the gravitational force between two objects. Without this constant, we would not be able to calculate how strongly objects attract each other.
Although gravity is familiar in daily life, its actual force between small objects is extremely weak. This weakness is reflected in the small numerical value of \( G \).
1.1. Value of G
The accepted value of the gravitational constant is:
\( G = 6.674 \times 10^{-11} \; \text{N m}^2 \text{kg}^{-2} \)
This value is universal—it is the same everywhere in the universe, whether on Earth, Mars, or in distant galaxies.
1.1.1. Units of G
The SI unit of \( G \) is:
- Newton metre squared per kilogram squared (N·m²/kg²)
2. Role of G in Newton’s Law of Gravitation
The gravitational constant appears in the formula:
\( F = G \dfrac{m_1 m_2}{r^2} \)
Here, \( G \) determines how strong the gravitational pull is for given masses and distances. If \( G \) were larger, gravity everywhere would be much stronger. If it were smaller, gravitational forces would be extremely weak and planetary systems might not even form.
2.1. Why is G So Small?
The extremely small value of \( G \) tells us that gravitational forces are naturally weak compared to other forces of nature. For example:
- Two everyday objects barely attract each other.
- Gravity becomes significant only when at least one object has enormous mass—like Earth or the Sun.
3. How Was G Measured?
The gravitational constant was not measured by Newton. It was first measured over 100 years later by the English scientist Henry Cavendish in 1798 using a torsion balance experiment. Cavendish’s experiment was extremely delicate, as it involved measuring the tiny force between small lead spheres.
3.1. Cavendish Torsion Balance
In this experiment, Cavendish suspended a rod with two small masses attached. Two large lead spheres were placed nearby. The weak gravitational attraction caused a tiny twist in the rod, which allowed Cavendish to calculate \( G \).
3.2. Why This Experiment Was Important
By knowing \( G \) and using Earth-based measurements, Cavendish was able to calculate the mass and density of the Earth—something that had been unknown before.
4. Importance of the Gravitational Constant
The gravitational constant is a cornerstone of classical physics. Without knowing \( G \), we could not compute:
- The gravitational force between any two bodies
- The orbits of planets and satellites
- The mass of planets and stars
- The behaviour of galaxies
- The structure of the universe
Every gravitational calculation—from launching rockets to predicting tides—relies on the value of \( G \).
4.1. Why G is Universal
The value of \( G \) does not change with place, time, or environment. It is the same everywhere in the universe, making it a true fundamental constant of nature.
5. Moving Forward
Now that we understand the gravitational constant, the next topic explores the important distinction between mass and weight—two quantities closely related to gravitational force.