Gravitational Constant — Core Principles

Core Principles

The Universal Gravitational Constant, denoted by $G$, is a fundamental physical constant that quantifies the strength of the gravitational force. It is a key component of Newton's Law of Universal Gravitation, $F = G \frac{m_1 m_2}{r^2}$, where $F$ is the gravitational force, $m_1$ and $m_2$ are the masses, and $r$ is the distance between them.

$G$ is universal, meaning its value is constant throughout the cosmos, independent of the masses, distance, or the medium between them. Its approximate value is $6.674 \times 10^{-11} N cdot m^2/kg^2$.

This extremely small value explains why gravitational forces are only significant for very massive objects. The SI units of $G$ are $N cdot m^2/kg^2$ or $m^3/(kg cdot s^2)$, and its dimensional formula is $[M^{-1} L^3 T^{-2}]$.

Henry Cavendish first measured $G$ using a torsion balance. It is crucial not to confuse $G$ with $g$, the acceleration due to gravity, which is a variable quantity dependent on the celestial body and location.

Important Differences

vs Acceleration due to Gravity (g)

Aspect	This Topic	Acceleration due to Gravity (g)
Definition	Universal Gravitational Constant (G): A fundamental constant quantifying the strength of gravitational interaction between any two masses.	Acceleration due to Gravity (g): The acceleration experienced by an object due to the gravitational pull of a specific celestial body (e.g., Earth).
Value	Constant throughout the universe: $6.674 imes 10^{-11} N cdot m^2/kg^2$.	Variable: Depends on the mass and radius of the celestial body, altitude, and latitude. On Earth's surface, approx. $9.8 m/s^2$.
Dependence	Independent of masses, distance, medium, temperature, pressure, etc.	Depends on the mass of the planet, its radius, altitude, and rotational effects.
Units	$N cdot m^2/kg^2$ or $m^3/(kg cdot s^2)$.	$m/s^2$ (meters per second squared).
Dimensional Formula	$[M^{-1} L^3 T^{-2}]$.	$[L T^{-2}]$. (Same as acceleration)
Nature	Scalar quantity.	Vector quantity (directed towards the center of the celestial body).
Role in Physics	A fundamental constant in Newton's Law of Gravitation, defining the strength of gravity.	A measure of the gravitational field strength at a particular point, causing objects to fall.

The Universal Gravitational Constant ($G$) is a truly universal, fixed value that dictates the fundamental strength of gravity across the cosmos. It's a scalar constant, independent of any external factors, with specific units and dimensions. In contrast, the acceleration due to gravity ($g$) is a localized, variable vector quantity that describes the acceleration an object experiences due to the gravitational pull of a specific celestial body. Its value changes with location, altitude, and the properties of the planet. While $G$ is a constant of nature, $g$ is a consequence of $G$ and the specific mass and geometry of the gravitating body.