This is not written by me. Source: http://science.skepticproject.com/forum/5526/flat-earth-society--debunked/

If you've dabbled in the internet's pseudoscience pages, you've probably encountered the Flat Earth Society. Their name is self-explanatory: they are a group of people who believe that the Earth is flat. For most people, this scores them a VIP seat in the bullshit box. However, there is a small group of people who don't dismiss their theories, and an even smaller group who accept it as truth. It should be painfully obvious that the Earth is round, but if you absolutely cannot see it, I will disprove the flat Earth theory.

Evidence for the flat Earth theory

On this (1) page, the FES outlines the evidence for their theory. I will briefly review it before debunking it. The FES's first piece of evidence for a flat Earth is that the Earth looks flat from the ground. They also offer the Bedford Level Experiment (2) as proof that the Earth is flat. In response to questions about how astronauts report a round Earth and pictures from space show a round Earth, the FES says that the pictures are faked and that the space agencies of the world are engaged in a conspiracy to falsely disprove the flat Earth theory. They say that the Sun acts as a spotlight and circles above the Earth, better explained by this diagram (3), and that the seasons are caused by the Sun's circle in the sky expanding and contracting. They also say that gravity does not exist, and instead what is felt as gravity is the upward acceleration of the Earth at 9.81 m/s^2. The Earth is supposedly being accelerated by dark matter, and it can supposedly accelerate forever due to Special Relativity.

Debunking the Flat Earth Theory

The very first claim is a qualitative analysis of the world. It basically says: the Earth looks flat, so it is flat! However, they fail to mention that a very large sphere would appear to be flat to someone standing on it. Either that or they think that a round Earth wouldn't look flat to those standing on it.

Their second argument about the Bedford Level Experiment is an outright lie. Before I go into detail about how they lied, I will first explain the experiment. The experiment's purpose was to determine if the surface of the water was curved or flat. Three buoys with long vertical sticks attached to them were placed in a river with negligible water flow velocity and were separated by 5 miles. A telescope was set up perpendicular to the river a mile away from the center post. If the water, and consequently the Earth, was flat, the posts should all appear to be the same height. However, the telescope showed that the center post was five feet higher than the other two posts, thus proving that the water's surface was in fact curved, and giving strong evidence of a round Earth. However, the FES makes a bald-faced lie and says that the experiment was faked and that the poles were actually at the same height. They give no evidence that the experiment was faked, and they give no evidence that a court determined that it was faked. In fact, on their Bedford Level Experiment page (4), there are no outside links at all, putting the page's credibility in question, especially since other reports by reliable sources conflict with it.

The FES also addresses the big question on everyone's mind: why do pictures from space show a round Earth? Their answer: the pictures are faked, and so is all space travel. This is an unfalsifiable statement, that is to say there is nothing that can possibly disprove it. This is usually a sign of a logical flaw. In this case, I believe the FES is saying the pictures are fake so that their theory can survive. Pictures from space of a round Earth would disprove the flat Earth theory. However, the people of the FES are convinced that their theory is right, so they see anything conflicting with it as wrong. Round Earth pictures from space conflict with the flat Earth theory, and since (in their minds) the flat Earth theory is real, the pictures must be fake. In their minds, any pictures of the Earth from space would show it to be flat, but since these pictures show a round Earth and are being presented by NASA, the pictures must be fake and NASA must be lying. That is the origin of their conspiracy theory, and it comes from the flawed belief that their theory is right and anything saying otherwise is wrong. Of course, there is no actual evidence that the pictures are fake and that NASA never sent astronauts to space, and lots of evidence of the contrary.

Another issue they address is how the day and night cycle works on a flat Earth. The FES says that the Sun acts as a spotlight on the Earth and it circles overhead (see the diagram in source 3). However, they completely fail to explain why the Sun is a spotlight, what causes it to rotate above the Earth, and why its orbit expands and contracts to cause the seasons. As will be discussed later, the round Earth theory can explain all of the observed motions of the Sun, moon, stars, and planets, the day and night cycle, and the seasons. Thus, the burden of proof lies with the FES to prove these wrong and their own theory right. They have failed at both of these.

Furthermore, there is evidence against these claims. If the Earth is flat, and the Sun is always circling above it, why do we see the Sun set? Even if its "spotlight" isn't shining on us anymore, it should still be overhead, albeit at an angle. But this doesn't happen. We see the Sun approach and pass below the horizon. For this to happen on a flat Earth, the Sun would have to actually pass below the plane of the Earth for us to see it pass below the horizon. But this isn't what the theory says. If the Sun actually were like a giant flashlight, and if we were about to pass outside of its light, it should appear to grow dimmer and eventually wink out somewhere in the sky. But this doesn't happen. The FES completely ignores the sunset, probably because it doesn't fit their theory. Unless they can explain this, their theory is incomplete.

Furthermore, what causes the Sun to move in a circle in the sky? Newton's first law says that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. If there were no forces acting on the Sun, it should either sit still or fly off in a straight line. So, there has to be something causing it to move in a circle. The FES doesn't say what. Is it a massive, invisible object over the Earth's north pole that the Sun orbits around? No, because they don't believe in gravity (discussed later). Is it some magnetic field that's causing the Sun to move in a circle? No, it couldn't be, because the Sun isn't solid, so there would be nothing keeping the particles in a perfect sphere, and they might stretch out to form some kind of a halo, and our compasses would always point in the direction of the field, which would have to be either towards the ground or towards the sky. Could it be some invisible electric charge above the North pole? No, because the Sun would still stretch out. Could it be the strong or weak nuclear forces? No, they don't act on a macroscopic level. Since there are no natural forces left, could it be a contact force? No, we don't see anything pushing the Sun, and if there were something, it would deform the Sun's spherical shape. Since there cannot be any natural or contact forces making the Sun orbit above the North pole, it is physically impossible for it to be happening. This means that the seasons can't be caused by the expansion and contraction of the Sun's orbit, which doesn't make sense in its own right, because the Sun can't orbit an invisible point above the North pole.

Their final piece of "evidence" for the flat Earth theory is what gravity is. They believe that there is no such force as gravity, and what we feel as gravity is instead the continuous acceleration of the flat Earth upwards at 9.81 m/s^2. They say that Einstein's special relativity says that an object can accelerate infinitely without reaching the speed of light, and that the acceleration is caused by dark energy. The FES grossly misinterprets what special relativity says about infinite acceleration. It says that an object can accelerate infinitely without reaching the speed of light, but the magnitude of its acceleration must decay exponentially. For example, you may reach 299,792,458 m/s (1 m/s less than the speed of light) at an acceleration of 9.81 m/s^2. However, you cannot continue accelerating at 9.81 m/s^2, because in 1 second you would be going 8.81 m/s faster than the speed of light. So, your acceleration would have to decrease, so that it would have to be less than the speed of light minus your current speed. Since the speed of light is 299,792,458 m/s, and the person's speed in this example is 299,792,457 m/s, the difference between the two is 1 m/s. So, the new acceleration would have to be less than 1 m/s^2. It could be 0.9 m/s² (although it may not be this), so that 1 second later the person would be traveling at 299,792,457.9 m/s, and the next second's acceleration would have to be less than 0.1 m/s^2. Therefore, an object can theoretically accelerate forever, but it cannot accelerate at the same magnitude forever. This means that, if the Earth is constantly accelerating upward at 9.81 m/s^2, after a certain amount of time it should approach the speed of light and "gravity" should appear to get rapidly weaker. How long would this take? We can find out using one of the "big four" kinematics equations (5). This one deals with objects at constant accelerations and can find the time it will take to reach a certain velocity. The equation is this:

vf = vo + a*t

Vf is an object's final velocity, vo is an object's starting velocity, a is acceleration, and t is time. We want to find how long it would take the Earth starting at 0 m/s to reach the speed of light, assuming its acceleration is 9.81 m/s^2. The speed of light will be vf, 0 will be vo, since it started at rest, a will be 9.81, since it is its acceleration, and t will be solved for algebraically. The equation now becomes:

299,792,458 = 0 + 9.81 * t

Just divide 299,792,458 by 9.81 and you have the time it will take in seconds for the Earth to theoretically reach light speed.

t = 30,559,883.6 seconds

Sounds like a lot, right? Let's do some conversions. 60 seconds are in a minute, so if we divide the seconds by 60, we get 509,331.4 minutes. 60 minutes are in an hour, so divide again by 60, and we get 8,488.9 hours. 24 hours are in a day, so divide by 24 and we get 353.7 days. That's right, it would take a little less than a year for a flat Earth accelerating at 9.81 m/s² to approach the speed of light and begin decelerating. We've all been alive for over a year, and we've all felt gravity just as strong as the year before. There is absolutely NO WAY that upward acceleration of 9.81 m/s² is causing what we feel as gravity. Not to mention, there is no explanation for how dark energy is supposedly causing the acceleration. This entire part is bogus. If gravity existed on this flat Earth, and if the flat Earth were not accelerating, gravity would still point to the center of the Earth, and the further away from the center someone walked, the more inclined gravity would be, until near the edges gravity would be almost vertical. There is no explanation for what we feel as gravity on a flat Earth, so the Earth cannot be flat.