Gravitational acceleration describes the rate at which an object’s velocity increases due to gravity. On Earth, this causes objects to fall towards the planet’s center. This acceleration dictates how objects move within Earth’s gravitational field, representing the acceleration an object experiences when solely influenced by gravity, assuming no other forces like air resistance are present.
The Standard Value and Its Effect
The commonly accepted standard value for gravitational acceleration on Earth’s surface is approximately 9.80665 meters per second squared (m/s²), often rounded to 9.8 m/s². This value signifies how much an object’s downward speed increases each second it is in free fall. For instance, an object dropped from rest would reach a speed of about 9.8 meters per second after one second, and 19.6 meters per second after two seconds.
The unit “meters per second squared” can be understood as meters per second, per second, illustrating the change in velocity over time. This consistent increase in speed applies to all objects in a vacuum, regardless of their mass, a concept famously demonstrated by Galileo. This acceleration gives objects their weight and dictates the trajectory of projectiles.
Factors Influencing Its Value
While 9.8 m/s² is a standard, gravitational acceleration varies slightly across Earth’s surface, typically ranging from 9.764 to 9.834 m/s². These variations arise from Earth’s shape, its rotation, and local geological conditions.
Altitude
Altitude significantly influences gravitational acceleration because gravity weakens with increasing distance from Earth’s center. As an object moves higher above the surface, it is farther from the planet’s mass, resulting in a weaker gravitational pull. This relationship follows an inverse square law, meaning that if the distance from the Earth’s center doubles, the gravitational force decreases by a factor of four.
Latitude
Latitude also plays a role due to Earth’s shape and rotation. Earth is an oblate spheroid, bulging at the equator and flattened at the poles. Objects at the equator are farther from the Earth’s center, which reduces the gravitational force. Additionally, Earth’s rotation creates an outward centrifugal force strongest at the equator, further reducing effective gravity there. These effects cause gravity to be lower at the equator (around 9.780 m/s²) and higher at the poles (around 9.832 m/s²), a difference of about 0.5%.
Local Geology
Local geology and the distribution of mass within Earth’s crust can also cause minor variations in gravitational acceleration. Differences in the density of rocks and subsurface structures can create localized “gravity anomalies.” Areas with denser materials beneath the surface may exhibit higher gravitational acceleration than regions with less dense rock formations.
Determining Gravitational Acceleration
Gravitational acceleration can be understood through Isaac Newton’s Law of Universal Gravitation. This law states that every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For an object near Earth’s surface, this law simplifies to an equation where gravitational acceleration (g) depends on the Earth’s mass (M) and its radius (r). The formula g = GM/r² highlights that Earth’s mass and physical dimensions are the primary determinants of this acceleration.
While theoretical calculations provide the physical basis, gravitational acceleration can also be determined through practical measurements. One method involves timing the fall of objects from a known height in a vacuum, a technique refined since Galileo’s early experiments. Another approach uses the precise measurement of a pendulum’s oscillation period. Modern instruments, such as gravimeters, provide highly sensitive measurements, allowing scientists to detect minute variations across Earth’s surface.