Gravity is a universal force that governs the motion of celestial bodies, keeping everything from planets to people grounded. The acceleration due to gravity, often denoted as g, is a measure of how quickly an object’s velocity changes when it’s under the influence of Earth’s gravitational pull.
On the surface of the Earth, this value is approximately 9.8 m / s2, but it changes when we move above or below the surface. Let’s explore why and how.
Acceleration Above the Earth’s Surface
When you move away from the Earth’s surface, such as climbing a mountain, flying in an airplane, or venturing into space, the force of gravity decreases. This happens because gravity is inversely proportional to the square of the distance from the Earth’s center, as described by Newton’s law of gravitation: g = G M / r2
Here:
G is the gravitational constant.
M is the Earth’s mass.
r is the distance from the Earth’s center.
As you increase r, the denominator grows, causing g to decrease. For example, at an altitude of 100 kilometers, gravity is slightly weaker than at sea level, though it’s still significant. This is why astronauts experience “microgravity” in orbit; they are far enough for the pull to weaken but not absent.
Acceleration Below the Earth’s Surface
When you move below the Earth’s surface say, descending into a mine gravity behaves differently. The force now depends only on the mass of the Earth within the sphere of radius r (your distance from the Earth’s center). The remaining outer mass no longer contributes to the gravitational pull due to a principle called spherical symmetry in gravitational fields.
Mathematically, the formula becomes: g = G M / r2
Where Mr is the mass enclosed within radius r. Since the density of the Earth isn’t uniform, g decreases non-linearly as you go deeper. Near the core, g drops significantly because much of the Earth’s mass is above you, counteracting the pull of gravity.
Acceleration Due to Gravity Below and Above Earth
Variation in Acceleration due to Gravity:-
Due to rotation of Earth: The acceleration due to gravity at latitude lamda is given by glamda = g – Re 2 cos2lamda
Where is the angular speed of the Earth.
At the equator, lamda = 00 Glamda = ge = g – Re 2 cos200 =
g – Re 2
At the poles, lamda = 900 glamda = gp = g – Re 2 cos2 900 = g
The value of acceleration due to gravity is minimum at the equator and maximum at the poles. Thus g increase as we move from equator to the pole. gp = ge = g – (g – Re 2) = Re 2
Due to shape of the Earth:- Earth is not a perfect sphere but it is an ellipsoid. The earth’s radius is 21 km larger at the equator than at the poles. Thus the earth has an equatorial bulge and is flattened at the poles. Both rotation and equatorial bulge contribute additively to keep the g smaller at the equator than at the pole.
Key Insights
Above the Surface:
Gravity decreases with altitude.
The decrease is more gradual when closer to Earth but becomes significant in space.
At twice the Earth’s radius (2R), gravity is only a quarter of its surface value.
Below the Surface:
Gravity decreases with depth.
It’s proportional to the distance from the Earth’s center, assuming uniform density.
At the Earth’s core, g is effectively zero because the gravitational forces from all directions cancel out.
Practical Implications
Understanding these variations has practical applications:
Satellites and space missions rely on precise calculations of gravitational forces to maintain orbits or travel to other planets.
Engineers consider gravity’s decrease with altitude when designing tall buildings or geophysical equipment.
Subterranean explorations or drilling projects use gravity’s variations to model Earth’s inner structure.
Note:-
The acceleration due to gravity isn’t a fixed value it’s a dynamic measurement influenced by your distance from the Earth’s center. Above the surface, it diminishes with altitude due to the increasing distance from the Earth’s core.
Below the surface, it weakens as less mass contributes to the gravitational pull. These principles reveal fascinating details about how gravity works, both on and off our planet, offering insights that enrich fields from astrophysics to engineering.
The acceleration due to gravity on the surface of the Earth is approximately 9.8 m / s2. This value represents the rate at which an object accelerates towards the Earth when in free fall, assuming negligible air resistance.
Gravity decreases as we move above the Earth’s surface. This is because the gravitational force is inversely proportional to the square of the distance (r) from the Earth’s center. As altitude increases, g decreases gradually.
Gravity decreases with altitude because the distance from the Earth’s center increases. According to Newton’s law of gravitation, the gravitational force diminishes as the square of the distance grows larger.