What does the acceleration due to gravity depend on?

The acceleration due to gravity depends on the mass of the Earth (or other celestial body) and the distance from the center of that body.

Factors Influencing Acceleration Due to Gravity

The acceleration due to gravity, often denoted as g, isn't a constant value across the universe or even across the surface of the Earth. Here's a breakdown of what it depends on:

• Mass of the Celestial Body (M): The greater the mass of the planet, moon, or star, the stronger the gravitational force it exerts, and therefore the higher the acceleration due to gravity on its surface. A planet with twice the mass of Earth would have a significantly higher surface gravity (assuming similar radius).

• Radius of the Celestial Body (R): The acceleration due to gravity is inversely proportional to the square of the distance from the center of the celestial body. This distance is often approximated by the radius of the body. So, if a planet has the same mass as Earth but twice the radius, its surface gravity would be significantly lower.

Mathematically, the relationship is described by Newton's Law of Universal Gravitation, which can be simplified to find the acceleration due to gravity (g):

g = GM/R²

Where:

• G is the Gravitational constant (approximately 6.674 × 10^-11 Nm²/kg²)
• M is the mass of the celestial body.
• R is the radius of the celestial body.

What It Doesn't Depend On

Importantly, the acceleration due to gravity does not depend on the mass of the object experiencing the acceleration. This is why a feather and a bowling ball (in a vacuum) will fall at the same rate. The gravitational force acting on the bowling ball is larger, but its inertia (resistance to acceleration) is also larger, perfectly cancelling out the effect.

Variations on Earth

Even on Earth, g isn't perfectly uniform due to:

• Non-uniform Mass Distribution: The Earth's mass isn't distributed perfectly evenly. Areas with denser materials will have slightly higher gravitational pull.
• Altitude: As you move further away from the Earth's center (higher altitude), the value of g decreases, although this effect is relatively small for everyday altitudes.
• Earth's Shape: The Earth is not a perfect sphere; it's an oblate spheroid (wider at the equator). This means the radius at the equator is larger than at the poles, leading to a slightly lower g at the equator.
• Centrifugal Force: The rotation of the Earth creates a slight centrifugal force that opposes gravity, and this force is strongest at the equator.