I'd like to paint a picture of the simplicity, elegance and explanatory power of the heliocentric, round earth model.
We need very few, simple starting ingredients for this model. Everything we see in the world is derived as a consequence, quite easily explained with simple reasoning, geometry, and known physics. There are no conspiracies, there's basically 100% consensus among scientists, and the world. To assume any of the hundred or so incomplete flat earth models is to assume so much more, leave so much unanswered, and come up with such weird, complex hypotheses without evidence that it's simply not likely.
Here are our ingredients:
1) Gravity. Approximately, it's just a force that acts between everything. All matter attracts all other matter in a very predictable, calculatable way. We can measure it in the laboratory (see the Cavendish experiment) and use it to make all sorts of mathematical predictions about the solar system, which are then confirmed, so to put it in doubt is really quite something. We also have a solid explanation for what causes it: general relativity, which is also heavily confirmed and seems to be generally accepted by flat earthers anyway.
2) Laws of angular momentum, uncontested.
3) A cloud of gas and dust. Basically, a clump of stuff. Really not much to ask for. Moreover, we have thousands of photos of such objects (nebulae) in the universe and plenty of good explanations for where they come from. You can even see them for yourself with an ordinary telescope, such as the Orion Nebula. We also have photos of nebula undergoing the processes I'm about to describe. I'm also going to assume that the cloud is rotating a little. Still not much to ask for. Why should it be perfectly still?
So, with those ingredients, here's a very rough and quick explanation of how the solar system forms:
Under gravity, the cloud starts to collapse inwards, simply because all the particles attracted to each other. The forces average out so that they generally move towards a central point, so the vast majority of stuff collects there. Such a large amount of matter makes for powerful gravity, heat and pressure, and a star forms: the sun. It is powered by nuclear fusion, a well known principle: it's how hydrogen bombs work, and how we might power the world someday. Meanwhile, some of the remaining stuff doesn't quite go into the centre, but it does collapse into a disk, spinning faster than the original cloud. The reason for this is related to angular momentum. Essentially, it's like spinning dough to flatten it into a pizza. It's really not surprising. Again, gravity causes tighter and tighter clumps, and these form planets and other stuff like asteroids, all orbiting around the sun. Some clumps also form moons orbiting around the planets. In these early stages, everything is still very crowded. One large body collides with the earth, tilting its axis, and the debris form our moon. Eventually, things calm down, although we still get hit by asteroids now and then. Gravity pulls large bodies into a spherical shape, although we can observe that for example the Earth isn't quite spherical because the spinning makes it bulge. The planets, moons and even the sun spin because they preserve the angular momentum of the original protoplanetary disk.
See how simple, coherent, and reasonable that was? See how little I had to invoke? The way the world is is easily explained, compared to wondering what the UA is or why the Earth is flat and so on. Now, just from this, we can explain all of the following observations. And by explain I often mean we can make detailed mathematical calculations and predictions that fit perfectly with the observations.
1. We know why the Sun is by far the largest object in our vicinity. We can tell how big it is based on its apparent size and the fact that we can quite easily measure its distance by several methods. Aristarchus of Samos first estimated the distance and size of the sun in 250 BC, and his result was vastly lower than the actual distance known today.
2. We know why the Sun is hot and bright.
3. We know why all the planets move in the same direction in the sky from night to night (that is, all the planets orbit the sun in the same direction).
4. We know why this is sometimes violated, i.e. apparent retrograde motion. It's simply because we aren't at the center: the planets orbit the sun. We can build a precise mathematical model of how they do so, and how we orbit as well. Newton did so based on his law of gravitation and showed that the orbits are ellipses with the sun at one of the foci. Einstein refined this with general relativity to explain why Mercury doesn't fit exactly. So we can calculate exactly how the planets and the earth orbit, predict how the path of the planets in the sky should look, and get it spot on every time. That's why we can have software that will tell you where the celestial bodies will be in the sky without having to check by observation. And we know exactly why this calculation works. Moreover, the same principles can be applied to the orbits of moons around other planets.
5. We know why we can see the planets and the sun spin, and again we know why they pretty much all spin in the same direction.
6. We know why the orbits all lie roughly within the same plane. This is actually quite something, if you think about it. Assume FET is correct. Why is it that, despite heliocentrism having no relation to reality, if you were to assume that it's true you suddenly get all the orbits lying in the same plane? Seems like a massive coincidence.
7. We were able to predict where Neptune would be in the night sky based on gravitational perturbations of the orbit of Uranus.
8. We know why the moon is bright (reflection) and why it and the planets have phases.
9. We know what causes lunar eclipses, and we can predict exactly when they will happen because we know when Earth will be in between the sun and the moon. Think about that. It's one thing to say you don't know what causes lunar eclipses. It's another thing to say that this unknown phenomena, whatever it is, happens to occur exactly when we would expect it to under RET. And here's another amazing coincidence if you assume FET: when you observe the height of a lunar eclipse, you can call a friend in a certain place on the earth and he can tell you that the sun is directly overhead. That place happens to be the exact location diametrically opposite you if you assume RET. Finally, look at photos of lunar eclipses where the moon at several times has been superimposed. That is quite clearly the shadow of something round.

10. We know what causes the sky to turn red as the sun sets. This also tells us why the lunar eclipse appears red: the atmosphere of the earth scatters sunlight so that red light remains, falling on the edges of the shadow on the moon.
11. We know why the sun sets in the first place. Or rather, we know why everything sets and rises, why the whole sky rotates around a celestial pole. If you were in a car and everything looked like it was moving past you, would you assume that everything really was moving past you, all in essentially perfect unison, or that you were moving? Please note that there are two things to explain as to why the sun (and everything) sets: why the sky seems to move, as I said, and also why there is a horizon to set below. Both are explained at the same time. Interesting extra piece of evidence for this: if you watch the sunset lying down, you can then stand up quickly and see it again.
12. We know what causes the tides: we can predict them based on the moon, and we can predict how they get stronger when the sun and moon align.
13. We know what causes the seasons: the difference in temperature, the lengths of days, the height of the sun, and the different seasons at different hemispheres, all follow very easily. We don't need to wonder why the radius of the sun's orbit changes over the year.
14. We know why hurricanes rotate, and why they rotate in different directions in different hemispheres: the Coriolis effect.
15. We know why the Bedford Level experiment generally confirms these days that the earth is curved. Oh, and if you trust the experiment from centuries ago as it was originally performed, it's pretty weird to then not trust later reproductions and all the other experimental evidence for a round earth that I'm mentioning. That is, you believe some ancient scientist got it right and was honest, but NASA has it wrong or are involved in a giant conspiracy theory? Or, you don't trust claims about traveling around the world because you haven't done that yourself, but you haven't done the Bedford experiment yourself yet you trust half of the results for that?
16. We know why the earth looks flat. It's big.
17. We know why it doesn't really, i.e. you can hold a ruler up to the horizon and see the curvature.18. We know why ships and skyscrapers sink over the horizon as they do, and not shrink.
19. We understand Foucault's pendulum.
20. We know how we went to the moon.
21. We know why we can use satellites for all sorts of things, e.g: how Hubble produced photos of space that weren't possible at the time with land based telescopes, although today's land based telescopes see the same pictures. GPS. Google Earth.
22. This is why we have photos of a round earth. Thousands of photos. And films. Look at films taken from the ISS. There's really a huge quantity of stuff to fake.
23. We know why gravity isn't perfectly uniform.
24. We know how time zones work.
25. We know how it is possible to circumnavigate the globe in either direction, and why doing so will cause your calendar to be off by one day.
26. We know why we observe different sets of stars in different hemispheres, and why the stars in the skies change continuously as you travel, exactly as you would expect them to on a round earth, forming a celestial sphere. That is, we see similar stars in Australia and South Africa, because they're both close to the South Pole and so the skies in both places are close on the celestial sphere. On a Flat Earth, North Pole centered map they're much further apart and a similarity in night skies is really weird and unexpected.
27. We know why you can have triangles with angles that sum to more than 180 degrees.
28. We know why the Earth has a magnetic field, we know where its south pole is, and we know why the magnetic poles line up with the coldest areas. And we know why we have aurorae.
29. We know why there's an asteroid belt between Mars and Jupiter.
30. We know why no one has ever been beyond Antarctica.
31. We know why we observe parallax of nearby stars, and we know why the timing of this matches up with the timing of the seasons.
No bendy light, dark energy, aetheric wind, anti-moons, massive conspiracies, nothing. All these observations follow simply and directly from the ingredients I gave, with just a little bit of well understood physics here and there. If the earth isn't round, then that is an INCREDIBLE coincidence. Meanwhile, flat earth theory requires numerous weird, ad hoc, complex, unsubstantiated, unexplained hypotheses to explain these observations. Like assuming that a mysterious force exists beneath the earth, forever pushing harder and harder to maintain an impression of constant acceleration for us as we approach the speed of light. And these are constantly thoroughly refuted on this forum by round earthers, or even rejected by fellow flat earthers, like bendy light. Why? Why do you insist on this inchorent theory which none of you can properly formulate or agree on, compared to a theory that we've known to be true for centuries which has mountains of evidence and is constantly used by science and industry every day? FET doesn't hold a candle to RET.
http://xkcd.com/258/RE believers, please help me extend the list!