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.
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.