Gravity is a fundamental force that shapes our universe, influencing everything from falling apples to the orbits of planets. Within the study of this force, two symbols, ‘g’ and ‘G’, frequently appear, often leading to confusion. While both relate to gravity, they represent distinct physical concepts. Understanding the difference between these two symbols is key to comprehending how gravity operates on both a local and universal scale.
The Concept of ‘g’
The lowercase ‘g’ represents the acceleration due to gravity, a measure of how quickly an object’s velocity changes when solely under the influence of gravity. On Earth’s surface, the approximate value of ‘g’ is 9.8 meters per second squared (m/s²) or 32 feet per second squared (ft/s²). This means that, ignoring air resistance, an object in free fall near Earth’s surface increases its speed by about 9.8 m/s every second.
The value of ‘g’ is not perfectly constant across Earth’s surface; it exhibits slight variations. Factors such as altitude, the planet’s rotation, local geological features, and the Earth’s non-spherical shape can influence its precise measurement. For instance, ‘g’ is slightly less at the equator than at the poles due to the Earth’s bulge and rotational centrifugal force. This acceleration is directly relevant to calculating an object’s weight, which is the force exerted on it by gravity (Weight = mass × g).
The Universal Constant ‘G’
In contrast, the uppercase ‘G’ denotes the universal gravitational constant, a fundamental constant of nature. This constant describes the strength of the gravitational force between any two objects in the universe. Its value is fixed and applies everywhere, regardless of location or the masses involved.
The approximate value of ‘G’ is 6.674 × 10⁻¹¹ N·m²/kg². This constant is a central component of Newton’s Law of Universal Gravitation, which mathematically describes the attractive force between any two objects with mass. The formula for this force is F = G(m₁m₂)/r², where F is the gravitational force, m₁ and m₂ are the masses of the two objects, and r is the distance between their centers. Henry Cavendish first accurately determined the value of ‘G’ in the late 18th century using a torsion balance.
Distinguishing ‘g’ from ‘G’
The primary difference between ‘g’ and ‘G’ lies in their nature and application. ‘g’ is an acceleration, specifically the acceleration experienced by objects due to gravity at a particular location, while ‘G’ is a universal constant that quantifies the strength of gravity itself. The value of ‘g’ varies depending on the celestial body and location, such as 9.8 m/s² on Earth’s surface, but it would be different on the Moon or Mars. Conversely, ‘G’ maintains the same value throughout the entire universe, never changing.
Their units also reflect their distinct roles. The unit for ‘g’ is meters per second squared (m/s²), indicating an acceleration. Meanwhile, the unit for ‘G’ is Newton meters squared per kilogram squared (N·m²/kg²), which allows the calculation of force from masses and distance in Newton’s law.
The Interconnection of ‘g’ and ‘G’
While ‘g’ and ‘G’ are distinct quantities, they are mathematically related. The acceleration due to gravity, ‘g’, on the surface of a celestial body is derived from the universal gravitational constant, ‘G’, along with the mass of the celestial body (M) and its radius (R). This relationship is expressed by the formula g = GM/R².
This equation demonstrates that ‘g’ is not an independent quantity but rather a specific manifestation of the more general law of gravitation governed by ‘G’. For example, Earth’s mass and radius, combined with the universal constant ‘G’, determine the average value of ‘g’ on our planet’s surface.