Cosmology · 4:25pm May 14th, 2013
If there's one question I want answered about the universe of MLP:FiM, it's this: How does Equestria's sky work? What is the organization of its stars, planets, and heavenly bodies? How do the princesses fit into it all? Due to the paucity of relevant information, we can only speculate as to the answers. Happily, wild speculation is what I'm best at! I've actually come up with two possible explanations for what we've seen so far, one geocentric and one heliocentric, and I'll detail each with supporting evidence.
The first possibility, and to my mind the less interesting one, is that Equestria's cosmos works similarly to ours. The Sun at the center of the solar system (heliocentric), the Earth and planets revolving around that, and the stars scattered throughout space. There is certainly some evidence to support this; barring a few abnormalities, which I'll address shortly, there don't seem to be any differences between Equestria and Earth (the planet containing Equestria is also apparently called "Earth", but I'll treat it as Equestria for clarity).
On Earth, one of the most damning pieces of evidence in favor of heliocentrism was the discovery of the moons of Jupiter. Galileo Galilei, in making this discovery, proved that not everything had to orbit the Earth. This was an easily verifiable observation, in contrast to the mathematical proofs offered previously. How is this relevant to our discussion of Equestria? Well, in "It's About Time", Twilight makes reference to a "negative azimuth of the fourteenth moon". Equestria has only one moon; where, then, is this one? I posit that it is an analogue to one of the moons of Jupiter or Saturn, each of which has many more than fourteen moons. This, coupled with the aforementioned similarities between worlds, makes a heliocentric system at least plausible.
Fun fact: Twilight Sparkle is always relevant
What of the princesses, then? This is where this model takes a turn for the disturbing. If the Equestrian Sun and Moon are indeed massive, distant bodies, then the idea that they can be controlled by two ponies, immortal and powerful though they may be, seems a bit unlikely. Perhaps, then, they merely control the Earth's rotation; still impressive, but orders of magnitude less preposterous. Alternatively, the Sun and Moon are out of their control, and they merely take credit for a natural phenomenon. This is also feasible, perhaps, but it paints MLP:FiM in a much darker light, with the pony masses being fed lies by their rulers to keep them in line. As a counterpoint, when Discord takes power in "The Return of Harmony", he messes around with both Sun and Moon, implying that Celestia and Luna could certainly exert some control over them, or over the planet's rotation, whatever the case may be.
I'm going to blame Discord for impossible lunar phases
The second model is much more fantastic, in the sense that it could only exist in the realm of fantasy. In this model, Equestria itself is a planet much like Earth, but everything else is different. The Sun and Moon are smaller and closer, under the direct control of the princesses. They orbit Equestria, with the stars just a little bit further out (so they can aid in Nightmare Moon's escape). This fits more closely with the lore, which definitely gives Luna and Celestia complete dominion over the heavens. There's actually direct evidence as well, if you take the comics as canon.
COMIC SPOILERS
In the second arc of the comic, Princess Celestia actually pulls the Moon down to Equestria. Its curvature indicates that it's much smaller than Earth's moon, and the act of moving it without much apparent effort obviously favors the Princess-controlled cosmos.
END SPOILERS
"Oh no! A source of questionable canonicity!"
What about the "fourteenth moon", then? Well, geocentrism doesn't have to exclude the possibility of other orbits. It's also possible that Twilight is referring to lunar phases, but figuring out what she could mean in that context is baffling (not helped by her state of sleep-deprivation at the time).
There is another issue here, resulting from the superposition of a round planet with a Princess-controlled solar system; how do you define a day? On Earth, the global transition from one day to the next is defined by the International Date Line. A similar system could work in Equestria, with the date defined by Canterlot time; this, though, doesn't answer every question. If time zones exist in Equestria, then how does "raising the sun" work? The best I can think of is that the Sun has to be "boosted" every day at Canterlot dawn, and the Moon at Canterlot moonrise. This could also explain the Sun's change from unicorn control to Princess control.
Celestia, stop complicating things!
Alternatively, daytime is global in Equestria. Noon is noon for the whole world; time zones don't exist. This relies entirely upon magic to work, and it means that the Sun actually disappears at night. Basing any sort of model on this explanation is fruitless, given that it explicitly couldn't operate under any of our laws. As such, I won't dwell on it any longer than necessary.
In the first episode Nightmare Moon demonstrates her control over the night by causing it to last well into what should have been day. This makes the senario that you suggested, Luna and Celestia claiming power over a naturally occurring phenomenon, appear far less probable.
1079652 Yes, it's not an issue of if, despite what some have suggested, but exactly how. It's also mentioned the unicorns used to raise the sun. So for some reason it is required. That's not to say it always was, only that it is now. For instance since the sisters are roughly similar in power (probably) then logically the sum should be roughly the same size. One possibility is it's a fake sun since Equetria's original either burnt out or is otherwise gone. It could have been created by science if you want advanced ancients for a story, or it's a magical construct of some sort, maybe made by the sisters missing parents.
I have two theories on this.
Theory 1: Equestria is Heliocentric, but Discord screwed with the Stellar Fusion of the sun, making it unstable. In this version, Celestia controls the sun by making sure it doesn't destabilize and go supernova.
Theory 2: Equestria USED to be Heliocentric, but then Discord came to power and basically broke the Equestrian Solar System. In this version, Celestia and Luna do control the Sun and Moon like they do in the show, because as powerful as they are, they don't have the power to set things back to the way they were, so they make do.
In either version, the moon has a naturally erratic orbit, leading Luna to forcibly keep it in a stable orbit around the planet.
Theory One makes MUCH more sense to me as an Astronomy Nerd, personally. However, given the nature of the show, Theory Two (AKA, The One In Which Discord Beeped Up Everything,) is just as likely in-universe.