Universal Law of Gravitation — Core Principles

Core Principles

The Universal Law of Gravitation, proposed by Newton, states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses ($m_1 m_2$) and inversely proportional to the square of the distance ($r^2$) between their centers.

Mathematically, this is expressed as $F = G \frac{m_1 m_2}{r^2}$. Here, $G$ is the Universal Gravitational Constant, a fixed value of $6.674 \times 10^{-11} ,\text{N m}^2/\text{kg}^2$, which signifies the inherent weakness of gravity.

The force is always attractive and acts along the line joining the centers of the two masses. This law is fundamental to understanding planetary motion, satellite orbits, and the acceleration due to gravity ($g = G \frac{M}{R^2}$), which varies with the celestial body and location, unlike the constant $G$.

The principle of superposition allows us to calculate the net gravitational force on an object due to multiple other objects by vectorially adding individual forces.

Important Differences

vs Coulomb's Law (Electrostatic Force)

Aspect	This Topic	Coulomb's Law (Electrostatic Force)
Governing Law	Newton's Universal Law of Gravitation	Coulomb's Law
Interacting Property	Mass	Electric Charge
Nature of Force	Always attractive	Attractive (opposite charges) or repulsive (like charges)
Strength	Weakest fundamental force ($G = 6.67 imes 10^{-11} , ext{N m}^2/ ext{kg}^2$)	Much stronger than gravity ($k = 9 imes 10^9 , ext{N m}^2/ ext{C}^2$)
Medium Dependence	Independent of the medium between masses	Depends on the medium (permittivity)
Shielding	Cannot be shielded	Can be shielded (e.g., Faraday cage)
Formula	$F = G rac{m_1 m_2}{r^2}$	$F = k rac{|q_1 q_2|}{r^2}$

Both Newton's Law of Gravitation and Coulomb's Law describe inverse square forces, meaning their strength diminishes with the square of the distance. However, they differ fundamentally in the property they act upon (mass vs. charge), their nature (always attractive vs. attractive/repulsive), and their relative strength (gravity is vastly weaker). Gravitational force is independent of the intervening medium and cannot be shielded, while electrostatic force is affected by the medium and can be shielded. Understanding these differences is crucial for NEET, as questions often compare properties of these fundamental forces.