Variation of g — Definition

Definition

Imagine dropping a ball. It falls towards the Earth, speeding up as it goes. This speeding up is called acceleration, and when it's caused purely by Earth's pull, we call it the 'acceleration due to gravity', or simply 'g'. On average, at the Earth's surface, 'g' is about $9.8,\text{meters per second squared}$ ($9.8,\text{m/s}^2$). This means that for every second the ball falls, its speed increases by $9.8,\text{m/s}$.

Now, here's the interesting part: this value of 'g' isn't the same everywhere. Think of the Earth as a giant, slightly squashed ball (an oblate spheroid). Because of its shape and its constant spinning, the gravitational pull you feel changes depending on where you are.

First, let's consider altitude, or height above the Earth's surface. If you go up a tall mountain or fly in an airplane, you're moving further away from the Earth's center. Since gravity gets weaker with distance, 'g' will decrease as you go higher. It's like a magnet; its pull is stronger when you're closer to it.

Next, depth, or going below the Earth's surface. If you go down into a deep mine, you might think you're getting closer to the Earth's center, so 'g' should increase. But it's not that simple! As you go deeper, some of the Earth's mass is now *above* you, pulling you upwards, effectively cancelling out some of the downward pull. So, 'g' actually decreases as you go deeper into the Earth, becoming zero right at the center.

Finally, Earth's rotation and latitude. The Earth is spinning. This spinning creates a centrifugal effect that pushes things outwards, slightly counteracting gravity. This effect is strongest at the equator (where the spin is fastest) and weakest at the poles (where there's no outward push). So, 'g' is slightly less at the equator and slightly more at the poles. The latitude (your position north or south of the equator) determines how much of this rotational effect you experience.

In summary, 'g' is a fundamental constant for free fall, but it's not truly constant across the globe. It varies with your height, depth, and even your position on the Earth's surface due to its rotation. Understanding these variations is key to many physics problems and real-world phenomena.