The Ball Earth Theory was designed to conceal that Humans appeared on earth in the 1800's.

But on account that many flaws existed in theory TPTB funded the society of flatness to compensate for the flaws. Both theories have flaws, namely both advocate 1 sun and 1 moon.

The following will reveal the flaws of 1 sun, 1 moon:

Flaw #1: If 1-sun was seen everywhere on earth, then those north of the equator (flat or ball) when facing the sun would see the sun travel from left (rise) to right (setting). And those south of the equator-line would see the sun travel from right to left. This not what happens, everyone everywhere sees the sun travel left (rise) to right (setting).

Flaw #2: The sun isn't hydrogen.

"Hydrogen flames in other conditions are blue, resembling blue natural gas flames."
[link to en.wikipedia.org (secure)]

There's no oxygen in outer-space, is there? Hydrogen fusion in space would reflect the color blue. Shouldn't the hydrogen sun burn blue? Of course it would.

Flaw #3: The suns are electric and why solar eclipses are possible. With only 1-sun everyone in daylight zone would see a Solar-Eclipse.

Here's the solar eclipse diagram.
[link to szsdneperska.edupage.org]

Looks a-lot like the new moon diagram.
[link to moonblink.info]

One of these is definitely wrong, right? Wrong! Both are wrong.

Flaw #4: The new moon would always cause a solar eclipse and a solar eclipse would be seen by everyone in daylight zone. And with 1-moon pulling on ocean waters would instantly cause a Low tide everywhere AT THE SAME TIME! Oceans are all connected, 1 body of water, and this not what really happens in the real world.

Here's a photo of the moon taken by the International Space Community.
[link to universe-beauty.com]

The moon is in direct line of sight parallel to the ISS which means the distance the moon's at isn't where the books say it is, in fact if you've flown in an airplane during the day you probably noticed the sun wasn't that much higher than the airplane. And if you took a photo of the sun and compared it with a photo taken from the ground of the sun around the same time perspective of how you see the sun shouldn't be noticeable if the sun is a Gazillion miles away, because flying 5mi up won't change much in its perspective of how the sun is seen from the ground or from an airplane. But it does.

Flaw #5: If there were only 1-sun and 1-moon you wouldn't be able to see the same stars 12 months, and at their same place due to the 23.4° tilt of earth's axis towards the sun or away. Because according to the following diagram we should be able to see different stars at different times of the year and at different angles. On the flat society earth you would see the same stars, hence why TPTB funded the program.
[link to www.buzzle.com]

Note: The stars would be seen lower in winter, higher in the sky in summer. But not in the real world. In real time the stars are always in their proper light-station order. There are multiple suns on earth, and moons, and star-systems for your geographical locations. In conclusion, the earth is an infinite flat plane extending forever in the unknown universe. There are many continents beyond ours with many suns, moon, star-systems. It is highly likely that more life such as ours existed before our own and are highly more developed and advanced.