You Don’t Weigh the Same Everywhere on Earth

Though your mass stays consistent no matter where you are on the planet, your weight fluctuates. In other words, you would weigh less at the equator than you would while standing at a pole. The credit of this goes to the amazing centripetal and centrifugal forces!

What’s Going on Here?

Let me explain. Imagine you are carrying a bag full of lemons. If you swing this bag at right speed over your head, the lemons will stay in the bag. And will even try to round out the circle again. Now, swing this bag too fast, the lemons will bust out through the bottom of the bag and get flung in all directions. Congratulations, you have just learned about the centripetal and centrifugal forces!

The force which causes the lemons to bust out of the bottom of the bag is the centrifugal force. While the apparent force which is equal and opposite to the centripetal force is called the centripetal force. It is the force which draws the lemons away from the centre of rotation and keeps them looping around in a circle and is caused by the inertia of the body.

This is the reason that when you weigh standing at the equator, you weigh less. At the equator, centripetal forces are acting on you as you spin around the centre of the Earth. It is this spinning that keeps you from flying off into space. At poles, this force is not acting. This is because the speed of rotation at poles is not that intense. Also, when you are at poles, you are actually closer to the centre of the Earth (remember, Earth is not a perfect sphere!), so the tad by which gravity is pulling you down is more strong. The effect this tad has on your weight isn’t too extreme (as in case of Moon and Mars). You would jest weigh about 0.5 percent more at poles. In other words, if you weigh 199 kg at the equator, you would be weighing 200 kg at a pole.

Wait — There’s More To This

Your location on the Earth isn’t the only factor which affects your weight. Altitude also plays an important role. We know that the gravitational force exerted on you varies inversely with the square of your distance from the centre of the planet. That is, if you move further from the centre of the Earth (say by climbing a mountain), you would become slightly lighter. While if you moved in the opposite direction, that it, towards the centre of the Earth (perhaps by venturing into the Death Valley), you would be a fraction of a percent heavier.

But this effect is much less than the difference between being at a pole and at the equator. At the equator, the radius of the Earth is 6,378 km. Now, assuming that you climb a 5-km mountain (something like Mount Kilimanjaro), it would put you 6,383 km (height of mountain) from the centre of the planet. Now, your weight would be decreased by a factor of (6,378 / 6,383)^2 =0.9984. That is a difference of 0.2 percent. To see that same change that you would see as you move from the equator to a pole, you need a mountain of whopping 32 km height. That would lead you to somewhere near the top of the ozone layer. Well, I would choose a sunny destination over the ride to Earth’s stratosphere any day.

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