The cause of the earth's magnetic field is not actually known, but there are theories proposed that would explain it. It is thought that some large quantity of ferrous material in the earth's core is moving to produce this field, but how much iron, where exactly it's located and how fast it's moving are all unknowns and up for speculation. One thing scientists can agree on is that wherever this iron is precisely, it exists at a temperature of over 1,000 degrees Fahrenheit, or perhaps even 2,000, which would mean it would be molten at atmospheric pressure, however, since it is expected to have an ambient pressure of hundreds of atmospheres, the liquidity/solidity or whatever state it is in cannot be certain. In any event, since the magnetic poles of the earth are observed to in fact be moving, we can reasonably presume that the ferrous or iron mass deep within the earth must not only be moving so as to generate this field but must be moving in a variable manner, that is, moving differently today than it has moved in previous centuries.
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Since it is essentially unknown what forces are acting on the iron inside the earth, we cannot know for sure what kinds of changes the magnetic field will undergo in the future. We can presume to expect it to move in a somewhat predictable manner, but as you can see from the image above, in the years 1732 (George Washington's birthday and the square root of 3), 1859, 1890 and 1900 the north dip pole changed direction of drift quite abruptly and without apparent or observable cause as far as we know (the birth of Washington or the square root of 3 can't explain a pole shift), therefore a similar change could likewise occur in our present age and we have no way of predicting it or even of anticipating when or whether it will occur.
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1.  So the its ok that sun, moon, planets and starts in the sky area all globular, "hanging in space", but its a ridiculous conclusion to think we are a "ball hanging in space."  The logical answer is that a flat dinner plate supported by pillars that is floating in space.  

2.  Pagan or not, it doesn't invalidate the conclusions.  Pythagoras was a pagan but a ² + b ² = c ²...every single time.

3. "against infallible teachings " I assume you are referring to the Holy Bible.  Leo XIII's Providentissimus Deus clearly had the flat earthers in mind when he wrote:  Full text here.

(52) To understand how just is the rule here formulated we must remember, first, that the sacred writers, or to speak more accurately, the Holy Ghost "Who spoke by them, did not intend to teach men these things (that is to say, the essential nature of the things of the visible universe), things in no way profitable unto salvation."(53) Hence they did not seek to penetrate the secrets of nature, but rather described and dealt with things in more or less figurative language, or in terms which were commonly used at the time, and which in many instances are in daily use at this day, even by the most eminent men of science. Ordinary speech primarily and properly describes what comes under the senses; and somewhat in the same way the sacred writers-as the Angelic Doctor also reminds us - `went by what sensibly appeared,"(54) or put down what God, speaking to men, signified, in the way men could understand and were accustomed to.
19. The unshrinking defence of the Holy Scripture, however, does not require that we should equally uphold all the opinions which each of the Fathers or the more recent interpreters have put forth in explaining it; for it may be that, in commenting on passages where physical matters occur, they have sometimes expressed the ideas of their own times, and thus made statements which in these days have been abandoned as incorrect. Hence, in their interpretations, we must carefully note what they lay down as belonging to faith, or as intimately connected with faith-what they are unanimous in.

Thank you for the reply Hap, I had forgotten about this.  
So a couple of things here. I'm going to throw some stuff out there and ramble.  If the stars are just lights, what produces their lights?  Why wouldn't I say that the sun, moon, and planet are globular.  Years ago, I was able to see the spot on Jupiter, the rings on Saturn, spots on the sun.  It was a unique opportunity to be able to use such expensive equipment shared by a astronomy hobbyist.  If their rotations and revolutions can be observed then why wouldn't I assume the rest were spherical.  

Before I run off with an idea, which I am prone to do...am I understanding that you are saying that you believe the sun and moon to be flat circles as well?

Heh...you caught me at a crossroads.  I'm actually beginning to think this may be true.  Not flat, but concave.  The principles of the way light reflects, a convex or even circular moon would scatter light out in a way that it probably wouldn't travel far.  Instead, the light is concentrated (most visibly at full moon) and reflected like a concave surface might do, so that it is crisp and intense. There is more to this but it takes a video to get the full gist) The reason it looks convex or like a ball is a simple illusion, like the optical illusion drawings that could be viewed either direction.  So it looks convex, but may be concave. Truly, I don't know the reality of this, and I am open to information that brings light. (pun, sorry) 

So let me throw something else into the mix.  The firmament that everyone brings up.  I am assuming you don't believe in the probes, hubble, satellites, etc that take pictures.  Then keeping it straightly earthly, if its suppose to divide the waters and Heaven/earth etc, how are we able to see through it with such clarity?  How are we able to observe the planets, comets, etc with such clarity if there is a solid mass blocking us in?

All of the celestial bodies are in/under the firmament.  Scripture and Augustine agree the firmament itself is a (humanly) impassable boundary between heaven and earth, above which, is the water with which God replenishes the earth, found in Genesis 1:5-14.  To say the stars are 'in' the firmament also works because the firmament is a dome within which they circle.  Many Fathers elaborate on this in great detail. 
  
Its been months since we were back this far in the discussion, but I believe what I was referring to was people were just dismissing certain things because the person who did the experiment was not Catholic, or that a certain bit of math was being discussed by a non Catholic.  I believe I was trying to make a point that just because the science was discovered/developed/endorsed by a non Catholic doesn't invalidate the validity of the math.  

You point is taken.  I agree.  But! The contradictions of heliocentrism promoted throughout the centuries also happens to include the fact that its forwarded by anti-Catholic pagans, in a way that constitutes a conspiracy of epic proportions.  Now that the conspiracy has emerged, taking the word of one of the conspirators is hardly wise.  Your next question should be, "can you prove there is a conspiracy?"  I can...but will you listen?  If you don't, I can't prove it to you.  However, that doesn't mean it doesn't exist.     

3) We can skip No 3.  I originally brought this up in November and it has since been discussed ad nauseam.  Last I saw, docs on the web wouldn't suffice, originals requested...different translations, etc.  I have nothing new or beneficial to contribute, so I'll drop this.

No worries.  Its kind of a moot point because someone was using PD to prove the Church doesn't want us using Scripture in a scientific way.  The argument has no bearing on what we're discussing here. 

Thanks for your reply Hap.  I've have actually seen a concave universe video, so I have a rough idea what you are talking about.
What conspiracy are you referring to?...there are several out there.  Can't promise that I will accept for agree but I promise to hear it out.

It is ironic that you mention Protestantism.  You are the one thinking like a protestant, using you own interpretations rather than the principles of the Church.

Thanks for your reply Hap.  I've have actually seen a concave universe video, so I have a rough idea what you are talking about.
What conspiracy are you referring to?...there are several out there.  Can't promise that I will accept for agree but I promise to hear it out.

If Bede said that, he forgot something.  The Church Fathers all describe a dome over earth with water above that, BECAUSE Scripture says so.  There is no "space".  A dome over a globe is not only a contradiction, but the globe doesn't even claim it, let alone the water above the dome. Augustine says the firmament exists, sun moon and stars within. The globe model says the sun is 93,000,000 miles away in space and ginormous.  So, the firmament is greater than 93,000,000 miles and modern science doesn't even mention it?   Rather, earth is not a globe.