@ The Heliocentric Model
The problem with this is that it is expressly “Not canon”.
And I doubt the show’s creators are going to say that “yeah, Celestia lied” or “we really meant she turns the earth”.
What exactly is the evidence for a heliocentric model here again anyways? The fact that they would be in earth’s position to see some “horse-head nebula”? No, that just means they’d be within the relative position of anywhere in our “solar-system”, compared to their world.
But more importantly, Celestia’s Talent is shown on her Cutie Mark to be the sun. Quite literally, she is the sun goddess. A verifiable Apollo for their world.
Would a pony who “turned the earth” get the sun as a mark?
Would a pony that “moved a giant rock in a circle” get the sun as a mark?
Would a pony that did nothing get the sun as a mark?
…I doubt it…
And more importantly, one of the major problems with the heliocentric “model” in this case, is that there are no “natural” seasons.
It’s mentioned in winter wrap up that seasons change in Equestria entirely through either magic or through a pegasus team; with earth ponies helping with some of the more mundane jobs.
If there were a heliocentric system in place, the chances of that being necessary are so incredibly small, as it would mean that the planet’s axis would have to be perfectly perpendicular with the line between them and the sun.
In fact, there isn’t a natural weather system to speak of. It’s all done either manually by pegasus, and natural precipitation seems to have been forgotten about. Note: hurricane Fluttershy, they get all their water using pegasus teams. Again.
And its often stated that the one place where things work entirely on their own for weather or whatever, is the ever-free forest; which is considered a place of weird significance, as if some “other” reality’s wild magic, such as a D&D world, worked on it instead of their own world’s magic. Counteracting some parts to be more natural for us, and making others even more mythical.
And don’t even get me started on how illogical it is for them to be able to grow both cherries and apples in the middle of a desert if we were talking a heliocentric model.
Equestrian ecology works nothing like ours… Literally… So the sun being moved around like some big flashlight isn’t that far fetched when the entire planet seems to have no natural rhythms that would indicate having the stability of a natural planet for us. To the point that on its own, the planet would devolve into a state of ontological stasis.
And instead of natural forces being able to be applied to the planet, the ponies seem to be living magical manifestations of what “should” be natural, placed into a living form. Pegasus for weather, Earth ponies for plants and animals, and possibly rocks. And Unicorns for the various metaphysical elements such as time.
In fact… every single aspect of the world… seems to run off of one thing…
Edit: I don’t want to say that Equestria Doesn’t spin, it might, and a few possibilities show the answer “Probably” as I went back and checked. But really, that just means the planet spins. And its quite possible that both sun and moon would be “geostationary natural satellites” that follow the same rotation as their planet, if it weren’t for outside intervention: A.k.a Luna and Celestia.