Thank you all for a most interesting thread. I have been considering this question ever since the films.
There are two problems with most possible two and three star systems. Firstly there is the question of the relative sizes of the three suns, as viewed from Thra, and secondly there is the question of the direction of their relative movement.
Consider the first question: at the moment of the Great Conjunction all three suns and Thra are lined up perfectly and in order of size. ie the sun nearest to Thra is smallest and the sun farthest is largest, with sufficient difference in angular size as to appear like an eye.
For this to be possible Thra must be on an orbit outside all three. If Thra were orbiting its closest sun - the Dying Sun - then, firstly, it would have to be so close to that sun as to be tidally locked to it (so that sun would not move in the sky), much like planet Mercury is to our sun, and secondly - being closest to that sun - it would appear huge relative to the other two and easily big enough to eclipse them. Our own moon, for example, is tiny compared to the sun but being close to us appears exactly the same size such that it totally covers the sun during eclipses. The only way to get the ‘eyeball effect’ is for all three suns to be similarly distant from Thra ie it orbits all three of them.
Then there is the question of their relative motion. Seen from Thra directly up through the roof of the Crystal Chamber, the three suns do not approach each other in a straight line: they approach at 120 degree angles from opposite corners of an equilateral triangle. Since the Greater Sun is clearly the one around which both the other suns and Thra are orbiting then it would move across the sky more or less perpendicular to Thra’s own axis of revolution. Our own sun appears to move across the sky because the Earth is spinning on its axis. Thra must be similarly spinning because it has day and night.
Any objects orbiting a massive body (such as the Greater Sun) would normally tend to be on the plane of its ecliptic, having formed out of its protoplanetary dust cloud. Since both of the smaller suns appear to cross the path of the Greater Sun, from opposite directions, we must conclude that either both of them or Planet Thra itself are on highly eccentric orbits inclined at 60 degrees to the solar ecliptic. It may also be that Thra’s axis of rotaton is highly tipped so at least one of the lesser suns might be on Thra’s ecliptic plane.
We have to set aside concerns here about the temperature differences on Thra as it orbits three suns, and questions as to the frequency of conjunctions. Consider how frequently Planet Venus has its transits in front of the sun, if Venus is to be proxy to one of the lesser suns. Quite clearly both the Rose Sun and the Dying Sun must be emitting almost negligible heat otherwise they would be causing massive variations in temperature on the surface of Thra. We need to assume that Thra is on an earth-like orbit around the Greater Sun in order to give it the stability for life to exist.
A better model, I think, is to assume that both the lesser suns are effectively residual cores of dead novae, but still glowing brightly enough to be visible in the daytime sky, and that both are on highly eccentric, highly elongated, highly inclined orbits around the Greater Sun that periodically bring them inside the orbit of Thra. An orbit is effectively an oval shape and will be around a massive object close to one end of that oval. This would place them out in the void for most of their orbits but have them each occasionally rushing through the inner solar system like comets. If their orbits were long enough and both prime number periods then opportunities for both the cross the path of the Greater Sun simultaneously would be much rarer and possible within the thousand-year period of the Great Conjunction. It would naturally follow that such a conjunction would be accompanied with massive gravitational disruption that might even pull the planet out of its orbit and send it spiralling in to the Greater Sun. If the movement of these suns around the Greater Sun were, at that point, faster than that of Thra’s rotation on its axis, then they would appear (on the surface of Thra) to be travelling in the opposite direction to the Greater Sun. Mar’s moon phobos thus appears to be rotating in the wrong direction around Mars but this is simply because it orbits Mars faster than Mars is rotating. That would explain the three suns converging and crossing each other within a triangle, I think.
The big objection to such an arrangement, although that is the only arrangement that I can see might work, is that such elongated eccentric inclined orbits are, by nature, highly unstable. We must assume that the lesser suns were both ‘interstellar wanderers’ that were accidentally captured by the Greater Sun. There will be a strong tendency, at the far extremity of their orbits, for these suns to escape the gravity of the Greater Sun and return to wandering the galaxy. There must, then, be some other agency at work keeping such orbits as stable. Hmm. Something like a magic floating crystal might just do the trick.