Gravitational acceleration, abbreviated as \(g\), also called acceleration of gravity or acceleration due to gravity, is the acceleration experienced by an object due solely to the force of gravity. When an object is in free fall and other forces such as air resistance are neglected, gravity causes its velocity to change continuously over time. This acceleration is directed toward the center of the attracting body, such as Earth. Near Earth's surface, the standard value of gravitational acceleration is approximately 9.81 \(m/s^2\), meaning that the speed of a freely falling object increases by about 9.81 \(m/s\) for every second it falls.
Gravitational Acceleration Formula |
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\( g \;=\; \dfrac{ G \cdot m }{ r^2 }\) (Gravitational Acceleration) \( G \;=\; \dfrac{ g \cdot r^2 }{ m }\) \( m \;=\; \dfrac{ g \cdot r^2 }{ G }\) \( r \;=\; \sqrt{ \dfrac{ G \cdot m }{ g } } \) |
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| Symbol | English | Metric |
| \( g \) = Gravitational Acceleration (See Physics Constant) | \(ft \;/\; sec^2\) | \(m \;/\; s^2\) |
| \( G \) = Universal Gravitational Constant | \(lbf-ft^2 \;/\; lbm^2\) | \(N -m^2 \;/\; kg^2\) |
| \( m \) = Mass of the Celestial Body | \( lbm \) | \( kg \) |
| \( r \) = Radius (Distance from the Center of the Mass to the Point Where g is Measured) | \( ft \) | \( m \) |
Magnitude of gravitational acceleration depends on the mass of the attracting body and the distance from that body's center. As a result, gravitational acceleration is not exactly the same everywhere. For example, it decreases with increasing altitude above Earth and differs on other celestial bodies such as the Moon or Mars because their masses and sizes are different. Nevertheless, near Earth's surface, the value of approximately 9.81 \(m/s^2\) is widely used in science and engineering calculations.
The relationship between gravitational force and gravitational acceleration is described by Newton's law of gravitation and Newton's second law of motion. Gravitational acceleration is a concept in physics because it explains the motion of falling objects, the trajectories of projectiles, the behavior of satellites in orbit, and many other natural phenomena governed by gravity.
On Earth, the gravitational acceleration is a constant:
g = 9.80665 \(m/s^2\) (Metric)
g = 32.1740 \(ft/sec^2\) (English)
