If the Earth is spinning at 1000 mph, why don't we fly off?

The title of this post is a question often posed by flat earthers to challenge the idea of a round earth. Because of its association with flat earthers, this question is often laughed at. I find this to be a shame, because its a quite interesting question. It also gives me the chance to do math and show off how smart I am!

I am going to start by answering a similar but related question. The earth is orbiting the sun at 66,660 mph [1]. Why doesn't the sheer speed of that orbit leave us all behind in the vacuum of space? The answer is inertia. Inertia is described in Newton's First Law of Motion: "An object at rest tends to stay at rest and an object in motion tends to stay in motion, unless acted upon by an outside force." How does that answer the question? Well, think about an airplane. Commercial airliners fly at about 600 mph. Do the passengers spend the entire flight pressed back into their seats at 600 mph? If one of them stepped out into the aisle, would he be propelled to the back of the airplane at 600 mph? No. Why? Because while the plane is moving at 600 mph, so are the passengers, the air in the cabin, and everything else in the plane. No additional force is required to keep them moving at that speed because of inertia. They will continue moving at 600 mph until acted upon by an outside force, i.e., the plane slowing down. In fact, if the plane were to vanish, they would continue moving at 600 mph until coming to an unpleasant stop due to the outside force of the ground. Military bombers have to account for this when they drop bombs. The bombs will keep moving at the speed of the airplane, so they have to calculate how far ahead of the target they need to be for their bombs to hit the target.

However, returning to the airliner, the passengers will be pressed back into their seats when the plane initially accelerates to 600 mph. This is because of Newton's Second Law of Motion, which states that Force = Mass * Acceleration. This tells us that force is only present when there is acceleration, and vice versa. So while the plane is accelerating, force is exerted on the passengers. While the plane is at a constant speed, no force is exerted on the passengers, and they are free to move about the cabin and eat disgusting airline food. Importantly, these effects are the same no matter what the speed is. A train traveling at 40 mph or a car traveling at 70 mph will have the same effects. This continues to be true no matter how large the number is. Inertia holds true whether you are traveling at one millimeter per millenia or 100,000 miles per second.

Returning to the question (finally!), we don't fly off the earth even though it is orbiting at 66,660 mph because it is traveling at a constant speed. If it were accelerating in some direction, we would feel a force. However, it is traveling at a constant speed, so we don't notice it.

Now, five paragraphs in, to the main topic. (Internet knights just love the sound of their own voice, don't they?) If the earth is spinning, that introduces a new consideration: rotation. Due to inertia, an object traveling in a straight line will continue traveling in a straight line, not a circle. So if the earth is spinning at 1000 mph, it should have left us behind long ago, right? Wrong. The big number of 1000 mph (1037.5646 if you want to be pedantic) looks impressive and scary. But when you do the math, it's anything but. Yes, the earth is spinning, but only once a day. That's 360 degrees per day, or 15 degrees per hour, or 0.25 degrees per minute, or 0.00417 degrees per second. So if we take your current velocity to be moving at an angle of 0 degrees, you are currently moving at 1037 mph at 0 degrees. Next second, you will be moving at 1037 mph at 0.00417 degrees, then at 0.00834 degrees, then at 0.01251 degrees, and so on. Notice what's happening? You're traveling at a constant speed, and your direction is barely changing. Going back to the plane example, if the pilot turned the plane 0.25 degrees every minute, would you notice? Not in the least.*

*Technically, you could if you put a level on the floor. Since planes bank in order to turn, you would notice the floor was slightly off level. However, my point is that you wouldn't feel your direction changing.

Intuitively, it's already clear why we don't fly off the earth. It's spinning so slowly that we can't even feel our direction changing, although we can measure it. But, for completeness sake, let's calculate how much acceleration we're all undergoing due to the earth's rotation. Let's also do the calculation in metric, because it's easier. The equation for centripetal force if acceleration = velocity squared / radius [2]. The earth has a radius of 6,378,000 meters, and it is rotating at 1,669.8 km/h or 463.83 meters / second. This gives us a centripetal acceleration of 0.0337 meters per second squared. That giant 1000 mph figure turned into a fraction of a fraction.

For the fun of it, let's find out how much force it would take to hold your average overweight American to the earth if gravity didn't exist. Suppose the overweight American weighs 100 kg. We can use Newton's Second Law of F=ma to find the answer of 3.37 Newtons, or 0.758 pounds. A quarter inch polyester ropecan hold 400 pounds, which is over 400 times stronger than needed [3]. So our conclusion is this: if gravity didn't exist, you could counter the acceleration of earth's rotation indefinitely using nothing more than string.

1. https://www.thoughtco.com/speed-of-the-earth-1435093

2. https://openstax.org/books/physics/pages/6-2-uniform-circular-motion

3. https://denverrope.com/rope-strength-guide/

I went out to a mesa overlooking the Wyoming prairie directly under the 2017 full eclipse.  From that advantage I could see about 40 miles in every direction as the shadow of the moon zoomed across the plains.  It will probably be the only time in my life that I could actually perceive the speed of the Earth relative to the Moon, sense the distance and mass  of that object as it darkened the world for 2 minutes.   In that brief discernment, I felt atomic- the tiniest of things.

So why doesn't a tiny fish next to a blue whale get tugged into its gravitational field? Why does a mosquito next to a skyscraper or mountain not either?

Hmm

Nothing you wrote explained why we do not feel it especially if we are hurtling around the Sun and through outer space inside of a moving Milky Way that itself is hurtling.

That's because gravitational force is determined by the absolute masses of objects, not their masses relative to each other. The equation for gravitational force is F=g*m1*m2/r^2, where g is the gravitational constant of 6.673*10^-11, m1 and m2 are the masses of the two objects, and r is the distance between the two objects. I would encourage to take some different numbers and plug them into the equation to see what happens. I will also point out that because this is a mathematical equation, it is incapable of being logically inconsistent.

Actually, those cases are even easier. The earth takes 365 days to go around the sun. That's less than one degree a day. More specifically, it's 0.000011 degrees a second. The Milky Way is worse still. The solar system takes 230 million years to orbit the center of the Milky Way [1]. That is 0.0000000000000496 degrees a second (13 zeroes if you don't feel like counting). Yes, we're moving very quickly, but let me tell you something that the flat earth promoters don't.

It doesn't matter.

It really doesn't. Speed doesn't generate force. Acceleration - that is, change in speed and direction - does. The earth's direction as it moves around the sun and the solar system's direction as it moves around the center of the galaxy are changing at an imperceptible rate, and their speeds are constant. Look back at the equation for centripetal acceleration to see why. a = v^2/r. It doesn't matter in the slightest how big v is in absolute terms. What matters is how it compares to r. However, these numbers aren't independent of each other. They connected by angular speed, which is the degrees per second value I keep mentioning. The lower that number is, the lower the centripetal acceleration will be. So even we were moving at 99999999999999999999999999999999999999999999999999999999999999999999 lightyears per nanosecond (ignoring that you can't go faster than the speed of light), if the angular speed is low, the centripetal acceleration will be as well. Those enormous, scary numbers flat earth promoters show you are meaningless. They're the wrong numbers. What matters is our angular speed, and that number is ridiculously low.

1. https://en.wikipedia.org/wiki/Galactic_year

Use this:  https://www.omnicalculator.com/physics/gravitational-force ,to calculate the gravitational force between 2 objects.

That's a cool website, FLRW! Thanks. Yes, use that. Much faster than a calculator.

That explains nothing 

Mathematics equations can be internally consistent and externally irrelevant. Cheers.

Wrong numbers right ok.

The numbers are from NASA. The wrong flat earth numbers are from NASA. I am a flat earther, I know where we get the numbers from 

Agreed, but that's not the point I was making. I was making the point that, because of the nature of the equation, it is entirely consistent for us to notice earth's gravity but for a fly to not notice a mountain's gravity.

That's not what I meant by "wrong numbers". I should have explained that more clearly. I did not mean that the numbers themselves are wrong. The numbers are correct. What I meant was that they are the wrong numbers for determining whether or not we would fly off the earth. Linear speed does not determine centripetal acceleration.* Angular speed does. Although the linear speed of the earth is high, the angular speed is low, so the centripetal acceleration is also low.

*You may notice that the equation I'm using does use linear speed, as well as the radius. The angular speed is hidden in this equation because it is the relationship between the radius and the linear speed.

Inertia, or just relative motion. You would only fly off if the earth just stops spinning. If something going 1000MPH in a single direction and only in consant speed and direction, then you would not fly off assuming the acceleration is gradual enough for you to get used to. One example is airplanes. You don't get yeeted to the back of the plane midair.

Relatively speaking, nothing hurtles.

Hurtling is only a concept relative to you.

If a flat yet circular(cylindrical?) earth rotates along the circular axis while performing circular motion according to the sun(like if you strap a merry-go-round to a rollercoaster loop), why wouldn't that work?

I am sure there are someone with great knowledge in Physics. Right now, I want to know why this wouldn't work. If this does work for a flat earth, that means this is not valid disproof. I am not a flat earther, I just am a skeptic.

This post doesn't disprove the flat earth. It disproves a common objection to the round earth.

Depends what you mean. If you mean the the inhabited side of the flat earth was always facing toward the sun, then I'm not sure that would be a substantial change to the most common flat earth model. It would just mean that the earth was moving rather than the sun. It would still have all the drawbacks of the standard flat earth model. I'd have to think some more about what changes that would make. If you mean that the flat earth rotated so its face was sometimes pointed toward the sun and sometimes pointed away from the sun, then that would add an additional problem to the model. While the face of the flat earth was pointed away from the sun, the entire inhabited side of the earth would experience night at the same time, which is a bridge too far for most flat earthers.

This is easy - have you ever been in a lift/elevator in a big building? You accelerate - move at a speed - then decelerate. You cannot feel the speed you are traveling at, only the change in speed - only the force acting on you.  Repeat on a constant velocity plane, of train. Speed is irrelevant - only force matters.

Now, imagine you are on a roundabout or merry go round. It’s turning once per day. That rotation produces force. Would you feel it? What if the roundabout was twice as big, would you feel it? Twice as big gain? Would you feel it. 

What if you were in a plane traveling at 700mph turning fractions if a degree per hour; would you feel that?

What about in a car travelling 30mph, but taking a sharp turn quickly? Would you feel that?

Given the speed an object is traveling, and how fast it is turning: how could you tell whether you’d feel that force of not?

"Guys gravity doesn't exist, weight is what's pulling all these objects down!"