# The Enemy’s Gate Is Down

In Physics by Brian Koberlein11 Comments

I’ve been getting a flurry of emails and comments recently from folks who don’t believe the Earth is round. It’s pretty straightforward to demonstrate to yourself that the Earth is indeed round, but this time the argument is about gravity and Earth’s (supposed) rotation. Water droplets on a ball will fly off if you rotate the ball due to centrifugal force. If the Earth rotates once a day, then stuff on the equator is moving at over 1,000 mph, while stuff near the poles is barely moving. How can gravity be strong enough to keep things from flying off the equator without simultaneously crushing things at the poles?

The basic idea of gravity is that masses are mutually attracted to each other. As Newton described it, masses exert a force on other masses depending on how much mass it has, and how far away it is. Near the surface of the Earth, the gravitational force is about 10 times your mass. This number comes from that fact that force is a product of mass and acceleration, and the acceleration of gravity is about 10 meters per square second. That means that if you took a mass and let go of it, its speed would increase by about 10 meters per second (22 mph) each second. If the Earth weren’t rotating, the force of gravity would be basically the same everywhere on the planet, and “down” would always be toward the center of the Earth. But the Earth is rotating, say the scientists, so surely that would have an effect, right?

It turns out centrifugal force is easy to measure in the lab. Just swing a mass and measure how much the mass seems to pull outward. Yes, I know some of you will point out that this actually involves centripetal force, but the end result is the same. A common introductory physics lab involves performing just such an experiment to see how the speed of an object affects the centrifugal force. What you find is that the force depends upon the square of the speed divided by the radius of the circular motion. At the equator an object is moving about 1,000 mph, and it’s moving in a circle with a radius of about 4,000 miles. Plug these into our equation and that gives 250 miles per square hour. That sounds huge, but if you convert it to metric, you get 0.03 meters per square second. So gravity pulls an object at the equator with a force of about 10 times its mass, while the centrifugal force is pulling it away from the Earth at about 0.03 times its mass. Yes, things at the equator are moving fast, but the radius of the Earth is so large that it doesn’t produce much centrifugal force.

Saturn’s fast rotation means it is wider at the equator than the poles.

Since centrifugal force is only about 0.3% of the gravitational force, gravity always dominates, and we don’t notice the centrifugal force in our everyday lives. But modern gravitational measurements are extremely sensitive. We’ve measured the variation of gravity all over the globe, and we find it varies with latitude just as predicted by Newtonian gravity and centrifugal force. Earth’s rotation means you are slightly lighter at the equator, but Earth would have to rotate much, much faster to overcome gravity. Earth isn’t the only place where centrifugal force has an effect. Saturn, for example, has a day that is only 10 hour long, and as a result it’s equator is moving at more than 23,000 mph compared to its poles. That isn’t enough to make things fly off Saturn, but it does mean that the centrifugal force at the equator is about 19% of Saturn’s surface gravity. As a result Saturn bows outward at its equator.

So Earth’s rotation really does mean that you weigh less at the equator. The effect is small, but we can measure it, and it confirms once again that the Earth is round.

1. Your title is a bit provocative. Nice choice of words. I am still in awe of the (seemingly, at least) increasing number of people who staunchly refuse to believe that the Earth is round. No matter what evidence or even easy to do experiment they’re shown, it all just bounces off their craniums like science off a ducks back. And the funniest part is they cite ‘celebrities’ who believe it as proof they are right. I may be wrong here, but in absolutely no paper nor textbook do I recall Tila Tequila as a contributing author.

1. I feel the earth is round but not like a ball but yet a ball cut in half. More like a water balloon filled with water all the water is at the bottom in a round shape but nothing but air at the top an not a full balloon.. Not a scientist but just my theory of the earth’s shape…

2. Not heard the ‘Celebrities must always be right!’ argument before. That’s a whole new level of stupid. Here in England a few years ago there was a primetime sports commentator called David Icke who suddenly announced that the World was run by Big Green Lizards in disguise. One of the more important Big Green Lizards was apparently the Queen of England, who in a feat of heroic self control didn’t have him arrested and carted off to a funny farm somewhere. And she remains without visible scales. At least in public.

3. “So Earth’s rotation really does mean that you weigh less at the equator.”

Also, Earth is not a perfect sphere. North-to-South is a few kilometers less, as its diameter at the equator. Meaning at the poles there is more mass between you and the center of Earth and more distance. All-in-all this also increases your weight at the poles.

“Taking into account both of the above effects (centrifugal at equator, and more mass below your feet at the poles), the gravitational acceleration is 9.78 m/s^2 at the equator and 9.83 m/s^2 at the poles, so you weigh about 0.5% more at the poles than at the equator.”

Ok i am nitpicking. But i am thinking of buying gold at the equator, and than sell it from my Northpole shop. I win about 5 grams of gold for each kilo i resell, right? 🙂

Thanks for this and your other million good articles

1. Your gold scheme probably would not work if the sellers and buyers insist on using balance scales 🙂 That actually measures the mass regardless of the acceleration of gravity (you just need a tiny bit of it to keep the objects from flying away 😀 )

2. “North-to-South is a few kilometers less, as its diameter at the equator. Meaning at the poles there is more mass between you and the center of Earth and more distance. All-in-all this also increases your weight at the poles.”

Doesn’t the first part of your statement imply that there is actually “less” distance between you at the pole and the center of the Earth?

In fact what makes you “heavier” at the pole, due to the “shape” of Earth (if it is bulging around the equator), is the that you are “closer” to the “center of mass” rather than the amount of mass between you and the center of Earth. The amount of mass between you and the center of Earth (assuming the shape is at least “symmetric”) is the same no matter where you are on the surface (if you go underground, all bets are off! 🙂 ). It is always “half” the entire mass. But that, in and of itself does not lead to any conclusion about how much you’ll weight.

But when you are at a pole, you are “closer” to all the particles of mass (of Earth) on average and since gravity decreases with distance, then you weight more.

4. Truly amazing that people still think the world is flat. With so many simple ways to prove to ourselves that it is spherical, it would be interesting to see their proof that it is flat.Would love to see their proof that it is flat.

1. I also was curious about what their proof could possibly be. Alas, I’m sure I became stupider for finding out…Also I’m sadly disappointed at how many people are rejecting (even basic) science (what? you mean provable evidence is important?) and how many more vocally believe in pseudo-science.

5. @Alipasha Sadri You are right about that….i mixed it and wrote a wrong statement. Indeed when Earth is slightly “flattened” because of its rotation, it means that the diameter from north to south is less…..not more as at the equator (how stupid of me). I do believe it leads to less mass below your feet, but closer to the center of gravity.
Luckely the part i qouted from that link is correct…i saw more links when googling saying about the same.

Thanks for correcting that!

6. Knowledge is limited by time and space and is renewing with passage of time. Science and mathematics are a way to scale the natural phenomenon and the minutest elements of particle that constitute the world and the universes . To days knowledge is transforming the
understanding at a rapid speed due to technological advancement in communication,visualisation and formulations. The knowledge of creations and the devine origin are fathomless oceans and yet to be explored ! To days understanding will keep changing with new wave
of knowledge & understanding in a rapid speed.

7. I was recently asked if I could, through a simple experiment, prove that the earth was round. I suggested that a sail boat with flags tied onto it’s mast at different heights when sailing away from shore (or any point) would show the flags lowest on the mast disappear over the horizon before the taller ones.
The person who quizzed me did not feel that my demonstration would prove anything.