Introduction to Gravitational Constant (G):

The gravitational constant (G) is a fundamental constant in physics that appears in Newton's Universal Law of Gravitation. It quantifies the strength of the gravitational force between two masses.

Newton's Universal Law of Gravitation:

The law states:

F = G (m₁ m₂) / r²

Where:

- F = Gravitational force between two objects (N)

- G = Gravitational constant

- m₁, m₂ = Masses of the two objects (kg)

- r = Distance between the centers of the two masses (m)

Value of Gravitational Constant (G):

G = 6.674 × 10⁻¹¹ N·m²/kg²

Significance of G:

1. G is the proportionality constant that connects gravitational force to the product of two masses and the inverse square of the distance between them.

2. It is universal, meaning its value is the same everywhere in the universe.

Dimensional Formula of G:

The dimensional formula of G is derived from the gravitational formula:

G = F r² / (m₁ m₂)

Substituting dimensions:

- F = [M L T⁻²]

- r² = [L²]

- m₁, m₂ = [M]

Dimensional Formula of G = [M⁻¹ L³ T⁻²]

Experimental Determination of G:

Cavendish Experiment:

- Henry Cavendish in 1798 determined G using a torsion balance.

- A small bar with masses at its ends is suspended by a thin wire. Larger masses are placed nearby to attract the smaller ones, causing a measurable deflection.

Read Also: Notes on Acceleration Due to Gravity of the Earth

Factors Affecting Gravitational Force:

1. Masses of Objects: Gravitational force is directly proportional to the product of the masses.

  F ∝ m₁ ⋅ m₂

2. Distance Between Objects: Gravitational force is inversely proportional to the square of the distance.

  F ∝ 1 / r²

Applications of G:

1. Calculating the gravitational force between celestial bodies.

2. Understanding orbital mechanics, such as planetary motion and satellite trajectories.

3. Determining masses of planets and stars.

Gravitational Force vs Gravitational Constant:

1.Gravitational Force-Gravitational Constant (G)

2.Dependent on masses and distance-Universal constant

3.Measurable directly-Indirectly determined through experiments

4. Varies with different conditions-Always constant

Key Points to Remember:

1.   G is not the same as gravitational acceleration (g), which is specific to Earth's gravity.

2. G governs gravitational interactions at all scales, from atomic particles to galaxies.

3. Precise measurement of G is crucial for understanding fundamental physics and cosmology.

Conclusion:

The gravitational constant (G) is a cornerstone of Newtonian physics, providing the foundation for understanding gravitational interactions in the universe. It enables us to calculate the gravitational force between objects, from tiny particles to massive celestial bodies. The precise determination of (G) is essential for advancements in astrophysics, space exploration, and our comprehension of the universe's structure. By grasping the significance of (G), students can better appreciate the unifying forces that govern the cosmos.