Gravitational acceleration and the gravitational constant are two fundamental concepts in physics related to gravity, but they refer to different aspects.
Gravitational Acceleration
Definition - Gravitational acceleration is the acceleration experienced by an object due to the gravitational pull of a massive body like the Earth.
Symbol: g
Value - On Earth's surface, the standard value of is approximately \(g = 9.80665 \;\;m / s^2\) (Metric) and \(g = 32.1740 \;\; ft / sec^2\) (English)
Variation - The value of g can vary slightly depending on altitude, latitude, and local geological structures. It decreases with altitude and varies with the distribution of mass within the Earth.
Formula - For an object near the surface of the Earth, \( g = (G \; m) \;/\; r^2 \)
Gravitational Constant
Definition - The gravitational constant is a fundamental constant of nature that appears in Newton's law of universal gravitation.
Symbol - G
Value - In the correct units, the gravitational constant is exactly 1! The value of G is approximately \(G = 6.67408 \;10^{-11} \;\; N-m^2 / kg^2 \) (Metric) and \(3.333 \;10^{-10} \;\;lbf-ft^2 / lbm^2\) (English)
Usage - G is used to calculate the gravitational force between two masses.
Formula - Newton's law of universal gravitation is given by \( F_g = G \; ( m_1 \; m_2 \;/\; r^2 ) \)
Key Differences
Nature - Gravitational acceleration g is a measure of the effect of gravity on an object, specifically the acceleration it experiences. The gravitational constant G is a universal constant that quantifies the strength of the gravitational force.
Units - g is measured in \(m / s^2\), while G is measured \( N-m^2 / kg^2 \) .
Dependence - The value of g depends on the mass and radius of the Earth (or other celestial body), whereas G is a fixed constant that applies universally to all masses.
To summary, g describes the specific gravitational pull at a point near a massive object like Earth, while G is a fundamental constant that applies to the gravitational interaction between any two masses.
