Class 9 > Unit # 06:Gravitation > Newton's Law of Gravitation

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Gravitation - Newton's Law & Comparison of 'g' and 'G'

Q.1 State and explain Newton’s Law of Gravitation.

Statement

"Everybody in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers."

Figure: Gravitational force of attraction between two masses $m_1$ and $m_2$.

Mathematical Derivation

Consider two point objects having masses $m_1$ and $m_2$ placed at a distance $r$ from each other. According to Newton’s Law of Universal Gravitation:

• The gravitational force $F$ is directly proportional to the product of their masses: $F \propto m_1 m_2$
• The gravitational force $F$ is inversely proportional to the square of the distance between their centers: $F \propto \frac{1}{r^2}$

Combining both proportions yields:

$F \propto \frac{m_1 m_2}{r^2}$

Removing the proportionality sign and introducing a constant $G$:

$F = G \frac{m_1 m_2}{r^2}$

Universal Gravitational Constant ($G$)

Here, '$G$' is the constant of proportionality known as the Universal Gravitational Constant.

• SI Value: $G = 6.673 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2$
• Nature: It is an extremely small value, which explains why we do not ordinarily feel gravitational forces of attraction between everyday objects around us, though it governs the large-scale mechanics of the universe. '$G$' remains strictly constant everywhere in the universe.

Q.2 Differentiate between “g” and “G”.

Universal Gravitational Constant ($G$)	Acceleration Due to Gravity ($g$)
It is a universal gravitational constant.	It is the acceleration due to gravity which determines the gravitational force acting per unit mass.
It has the exact same value everywhere in the universe.	It has different values at different places on Earth and across celestial bodies.
It has a value of $6.673 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2$.	Near the Earth's surface, its average value is approximately $10 \, \text{m/s}^2$ (or $10 \, \text{N/kg}$).

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