Flat Earth

This is not a creationist claim - despite what the Bible says - but I wanted to explore it anyway. It involves the same mindset of just believing, cherry-picking evidence and giving ad hoc explanations, without consideration for the consequences.

Note that this is responding to statements on the Flat Earth Society Wiki. If these guys had a coherent world view, we would expect each page to agree with the rest.That is, of course, not the case. Instead, each page addresses an issue, but its explanation often contradicts the explanation on another page.

From here:

The Sun is a sphere which revolves above the Earth on a path known as the ecliptic. Its path moves North-South over the year between the Tropic of Capricorn to the Tropic of Cancer. It illuminates a portion of the earth at a time and has daily cycle of one revolution per 24 hours.

We learn more here:

It has a diameter of 32 miles and is located approximately 3000 miles above the surface of the Earth.
...
The Sun's area of light is limited to an elliptic area of light upon the earth much like the light of a lighthouse is limited to a finite area around it.

So we have a spot light travelling on a circular path, way up in the sky, shining down on earth. So far so good...

What keeps the sun, moon and stars up?

Do they run on rails across a solid firmaments? Are they held in place by angels? As far as I can see, they do not say.

There is a page that seems to be trying to refute gravity, so it may be that they just float around up there, but that still does not explain why they follow those specific paths.

Phases of the moon

Here is one imaginative explanation:

The lunar phases vary cyclically according to the changing geometry of the Moon and Sun, which are constantly wobbling up and down and exchange altitudes as they rotate around the North Pole.

When the moon and sun are at the same altitude one half of the lunar surface is illuminated and pointing towards the sun, This is called the First Quarter Moon. When the observer looks up he will see a shadow cutting the moon in half. The boundary between the illuminated and unilluminated hemiplanes is called the terminator.

For a full moon, then, the moon must be higher than the sun... but it must also be directly above the sun - otherwise there will be some shadow visible. And yet we never see that! If the full moon is visible at day, it is on the opposite side of the sky.


Also, if the sun is like a spotlight illuminating a patch of the earth, then that spotlight is never on the moon(except when the sun is directly over it at a new moon), so where does it get its light in the first place?

This is a great example of the use of ad hoc explanations. The spotlight idea explains day and night, the bobbing up and down explains the phases of the moon (kind of), but they contradict each other!

Astral bodies bobbing up and down

There is another issue with the quote above about phases on the moon, and that is that the sun and moon are varying their height about the earth.

The first point is: Why? What causes them to go up and down? If they are running on rails, those rails look like a roller coaster!

The second point is that if the moon is higher than the sun at each full moon, then dips down to be lower at a new moon, then it is, of course much closer during a new moon, and it should therefore appear to be bigger. Do we see the moon getting bigger at each new moon, and small at each full moon? No we do not.

And apparently the sun is doing the reverse. That would mean the earth is much hotter during a full moon, as the sun is closer, it then cools during a new moon as the sun moves further away. Do we observe that? Of course not!

Lunar Eclipse 

In the RE model, a lunar eclipse occurs when the moon, sun and earth line up, with the earth in the middle, causing the shadow of the earth to fall on the moon.

In the FE model, that cannot happen, because both sun and moon are always above the disk of the earth. So instead they invent a satellite that "is called the Shadow Object or Antimoon". No one has ever see it, of course. It is another ad hoc explanation.

An Accelerating Earth

In the RE model, the planet's orbit is stable, and requires no energy input to maintain it.

At least some Flat Earthers reject gravity and say instead that the Earth is accelerating upwards at about 10 m/s/s, and, in accordance with Einstein's theory of relativity, this acceleration is indistinguishable from gravity (for example here). I am no expert in relativity, but from what I do know, this is reasonable.

However, that means there is a constant force pushing on the planet from underneath (or pulling from above). I wonder what that is?

What is the magnitude of the force? The maths is easy, just the mass multiplied by the acceleration.The mass of the Earth in the FE model is hard to say, but lets us suppose a disk, 4000 mile radius, 10 miles thick, with a density of 4 g/ml (which is a fair guess for stone, but much lower than iron). That works out to around 5x10¹⁷ tonnes, which requires a force of 5x10²¹ newtons.

The energy required to push the disk with that force over a meter is then 5x10²¹ joules. That is quite a lot. Where does it come from?

Oh, and remember it is pushing the sun, moon and stars too... You might think that if you get rid of gravity then you did not have to worry about what keeps the sun up there; there is no gravity to pull it down, so no problem, it just floats around up there. Not so. If the earth is accelerating at 10 m/s/s, then it will not take long until we collide with the sun, unless it too is accelerating at 10 m/s/s.

If fact, the acceleration of the sun is rather more complicated than that, because it is also travelling in a circle, and it is also bobbing up and down every month!

A Stationary Earth

That same web site also makes a big deal about how the earth is stationary. This is to use the Michelson-Morley Experiment. The experiment showed that the speed of light is the same in all directions. This led to Einstein's theory of relativity - which Flat Earthers use to support their accelerating Earth idea.

However, on this page, they reject Einstein's relativity, and say that what the Michelson-Morley Experiment actually proves is the planet is stationary.

So not accelerating.

Satellites

Flat Earthers reject all space flight... so what about satellites? How does GPS operate without satellites (given the "S" stands for "satellite")? What do satellite TV dishes point to, if not a satellite?

I find it telling that their Wiki has nothing on this topic.

The Conspiracy

Naturally there is a conspiracy, but who is behind it all? NASA, apparently.

There is a Space Travel Conspiracy. The purpose of NASA is to fake the concept of space travel to further America's militaristic dominance of space.

The story goes that people erroneously believed the world is round anyway. Then NASA came along, had a number of fails, due to the planet being unexpectedly flat, so they decided to fake it being round to "further America's militaristic dominance of space". It seems to imply that the faking does actually achieve that dominance of space... which makes as much sense as anything.

Perhaps they mean that dominance of space will dissuade enemies from attacking, and therefore the illusion of  dominance of space will do likewise. That is reasonable as far as it goes, but...

Do these people realise the USSR had a space program, and had a man in space before NASA did? I found nothing about the USSR space program being faked, but obviously the commies would want their own domination of space, right?

But wait... If both the Soviets and the Americans were faking their dominance of space, they must have both known the other was faking it. So who were they trying to fool?

If it is all faked, why did the Soviets not get to the moon? There is no technical reason if it just requires a studio.

Size of the conspiracy

Who knows the truth?

Obviously all those people at NASA... and the Soviet space program. A huge number of people in telecommunications, including anyone involved in GPS, satellite broadcasts, satellite TV engineers.

Meterologists, physicists, geographers, cartographers... Anyone who has been to Antarctica and failed to report back about the wall of ice. Airlines who know the real distances between cities.

There are private companies, such as SpaceX, and organisations in other countries, such as ESA, that launch rockets.  They too must be working hard to help NASA to further America's militaristic dominance of space.

Which is odd when you consider how many of those people will not be American.

How big is the curvature?

A big part of the Flat Argument is that you cannot see the curvature of the earth.

Below I calculate how much curvature there is - eight inches over a mile. A mile is quite a distance; have you ever tried to look across a flat, smooth mile? If you are looking at the sea, the waves are going to be more than eight inches high.

And if you look at a ship heading away from you, you will see it sink below the horizon (though you will need a telescope to see it properly).

Despite what Flat Earthers claim, engineers do take the curvature of the Earth into consideration when building bridges. For example, the towers of the Verrazano-Narrows Bridge are more than an inch and a half further apart at he top, rather than the bottom.

Calculation

In the Round Earth (RE) model, the Earth has a radius of 3959 miles, giving a circumference of 24875 miles. If you travel 69.1 miles, you have travelled along an arc of 1°. For one mile, that would be 0.0145°.

The curvature, i.e., how much the planet falls away compared to a perfectly level line, is given by trigonometry:

d = r(1 - cos A)

So for the 0.0145° arc, 1 mile, the curvature would be 1.3x10^-4 miles, or 8 inches.