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A flat earth calculation

There are people who believe that the earth is flat. More than once, I have seen a flat-earth believer attest that there is no such thing as gravity. I was always puzzled by what they meant by that.

But recently I read about one flat earth theory (I gather there are a few different variations) which claims that the flat earth is moving in a direction perpendicular to the plane of the earth, and is accelerating at a constant rate of 9.8 meters per second per second, which is equal to what we call the gravitational acceleration.

First, a quibble on my part. Even if that were true, the effect produced by that acceleration is something we would still call gravity.

But, aside from that, I thought it would be interesting to calculate how fast the flat earth is moving today, if it has been accelerating throughout its entire existence.

Since a lot of believers in the flat earth also believe in a young earth, I will take the age of the earth to be 6000 years, which seems to be on the low end of age estimates proposed by believers of the young earth.

Age of the earth in seconds:

(60 sec/min) (60 min/hr) (24 hrs/day) (365.25 days per year on average) (6000 years)
= 1.8935 x 10^11 seconds.

If we have been gaining 9.8 meters per second every second, then assuming we started at velocity 0, the current velocity of the flat earth is

(9.8 m/sec per sec) (1.8935 x 10^11 sec) = 1.8556 x 10^12 m/sec

Dividing by the speed of light, which is about 3 x 10^8 m/sec, we find that we are all currently moving at more than 6000 times the speed of light!

Caveats: I am assuming a disbelief in relativity theory. If relativity is taken into account, then I confess I am at a loss as to the precise calculations, as I have only studied Special Relativity, in which the acceleration is taken to be zero. In General Relativity, the mass of the earth would have to be taken into account, and I have no idea how the flat earth theory assesses that value. But I think it is fair to conclude that we would be travelling at pretty darned near the speed of light by now! Perhaps our resident professional physicist @GlitterEater could weigh in, assuming she has nothing better to do with her time!

Also, if the earth is older than 6000 years, or if our velocity at creation was more than 0, then our current velocity would be even greater than what I calculated.
JoyfulSilence · 46-50, M
The truth is that there is no such thing as gravitational force and gravitational acceleration. Rather, spacetime is curved, and matter (under the influence of no other forces) will follow a geodesic path in spacetime (I think it is the path of minimal "proper" time).

Space near the Earth is also curved non-uniformly, in a spherical arrangement. And the curvature increases as one gets closer to the Earth. The net effect are tidal forces, which cause objects to stretch in the direction of space-flow and compress perpenticular to it. This is called spaghettification. It is deadly near black holes.

An object floating freely in flat space is indistinguishable from an object carried along in a uniform gravitational field. This is Einstein's principle of equivalence. Also, a free stationary object in an accelerating ship in flat space would collide with the inside of ship when the ship accelerates to hit it, in the exact same way as if the ship was parked on an Earth with uniform gravty and the object fell.

But real gravitational fields are non-uniform, and we interpret this as tidal distortions. Of course, one must believe in a spherical Earth to get a non-uniform field.

As for us accelerating up in flat space, why do we not see the stars accelerating down? Or are they accelerating up, too? Why would they and the Earth do so, but not things on the Earth? What makes them so special? Yet if all things were accelerating up, then that would be indistinguishable from all things being in flat space. Unbolted things would float off, and we would not sense any "gravity." It would be a zero-g Earth.

And of course people circumnavigate the Earth, and watch videos live where it is night in one place and day where they are. Etc., etc.

As for special relativity, at relative speeds near the speed of light, an object moving toward or away from you will stop accelerating. Also, you would see its time stop, length contract to zero, and mass grow without bound (which prevents more acceleration). Yet for that object, all is normal, but they would see you stop accelerating, your time would seem to stop, length contract, and mass grow.
GlitterEater · 36-40, F
You're exactly right about everything in a Newtonian picture, but the world could have started with the Earth falling, so your calculated velocity is the change in velocity. I know you accounted for this with assuming we started at rest, just adding a side note.

Also, I agree that they are still describing gravity, they are just offering an alternative mechanism.

I'd have to think more about the details in the Relativistic picture, but it could be resolved in GR with Earth experiencing a constant 1g proper acceleration vs. coordinate acceleration. Flat Earthers reject GR so it's irrelevant to them (hence the alternative mechanism), but it's a fun question!
JoyfulSilence · 46-50, M
@DrWatson @GlitterEater

How do flat earthers explain gravity induced tidal distortions (spaghettification)?

Spherical masses explain it!
DrWatson · 70-79, M
@JoyfulSilence I will have to let them speak for themselves.
JoyfulSilence · 46-50, M
@DrWatson

Assuming they know how to speak, rather than just grunt and scratch their pits.
All of this is cool...........great you did the calculations......but why if flat earthers are soooooooooo interested and determined to prove all of us wrong.......why don't they ever send one of their own to the edge to take a ton of pics of the edge and then post them??? I'd pay for that trip.........when they get back with the pics.
@LordShadowfire That's convenient. ;-)
LordShadowfire · 100+, M
@anythingoes477 Isn't it just, though? The evidence is always just out of reach.
@LordShadowfire Just like conspiracy theories and evidence on Biden. We have it...we just doooooon't have it in front of us.
Interesting calculation!

However, the non-flatness of the earth is easily observed.

?? Go to Chicago. Head out on Lake Michigan on a calm day. Watch the city sink into the lake!! No, not really; it's just a bit beyond the curve of the Earth.


Go to Lake Ponchartrain.

Check out the power lines. Take some pictures.


[media=https://youtu.be/ipqronPSXGM]

Then check out the causeway. Take some pictures.

Did they build all these wind turbines partway under water? Nope. Curve of the Earth again.

DrWatson · 70-79, M
@ElwoodBlues Yes, I am aware of that. But it was the claim that gravity is a myth that I was wondering about.
morrgin · F
I love your detailed calculations. Have you heard all the Flat Earth puns? Like the Flat Earth Society says on their website that they now have over a million members globally?
we zooming thru space outward from a centre point of a 'big bang' yes?

yet every night i walk out side and all the stars are in the exact same position.
sailors have navigated the oceans for centuries of those same starrs.

stars that would change position and disappear out of our galaxy if we were indeed wizzing thru space on a outward trajectory.. ?...

im not saying the earths flat.

im saying theres a big farking huge chunk of information thats not been shared..
hunkalove · 61-69, M
That's really smart! Would you do my taxes for me?
DrWatson · 70-79, M
@hunkalove Sorry, but Einstein is a lot easier to understand than the tax code!
So you want GlitterEater to give u some attention.
DrWatson · 70-79, M
@NoThanksLeon She is a physicist, and more qualified than I am to talk about relativistic effects. She also has a sense of humor!
LordShadowfire · 100+, M
Added to my collection. This is brilliant!
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