# Gravitational Acceleration vs Gravitational Constant

on . Posted in Classical Mechanics

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.