Ah, now I see. Well then, ignore the first sentence of my post. One thing that worries me, however, is the change in the sun's size that you noticed. Going back to the "real world," because our sun is so far away, it or us would have to move many millions of miles in the few hours it took for you to see a change in size. This leads to one of several scenarios:
1. Either we or the sun is orbiting some very massive, very dark object, like a black hole. All that gravity would make the orbit very fast, allowing the changes you have observed. Plus, a black hole could distort the light coming from the sun, changing its size and position or maybe even absorbing all of it and making "periods of darkness."
2. MagicDuel's sun is actually very close to us, so it doesn't take much movement to change its size. The sun would also have to be very small to avoid frying us all into oblivion.
3. Something else completely?
Perhaps some more data would help. Is the path the shadow of the stick follows an oval, circle, or some sort of flower shape? Is the base of the stick inside the path, or do the shadows always fall to one side? This could help us determine if the movement is caused by rotation, precession, orbit, or a combination of two or three of these. Also, how much does the sun change in apparent size? You mention that it occurs in the same time period as the movement, but do the two cycles start at the same time? If we get lucky, we might actually be able to determine the exact nature of the motions of the celestial bodies, as well as the size of the earth and the sun (at least in units of "the stick" o.O), and perhaps the masses of the sun, earth, and moon if it exists. I hope you don't mind me borrowing the designs of some of the Instruments you used. I might have to imagine in a calculator, too