Hello everyone! I've found myself in a bit of a pickle I don't have the necessary physics knowledge to resolve, and this seemed as good a place as any to get input from people who are actually experts in that kind of thing. I know there's a big thread about the MLP sun-and-moon system, but the OP's initial conditions are sufficiently different from mine that I decided it would be better to post my own.

For a little while now I've been bothered by the ease with which assorted villains consider incapacitating or killing the Princesses, when it's been very much established that the Princesses are required to move the sun and moon and thus removing them specifically or Equestria in general from the world would have very negative consequences on everyone including the villains in question¹. This problem becomes even more pressing in a wider fanon world where Equestria is frequently one country among many others and has in its past fought major wars against neighbors that meant to conquer or eliminate it.

The solution I settled on was kind of an odd one- day and night are local phenomena confined to Equestria's general area, and other powers in the world have their own day-night cycles that they control through different methods³. I quickly realized that this would cause strange problems if the Sun and Moon were physical objects that physically moved over Equestria's land, since they clearly pass below a horizon but their movements would also be constrained to a small section of the world's total landmass⁴.

The solution to this problem was to make the Sun and Moon not physical objects but rather immaterial visual phenomena. No matter where one is in Equestria they will always appear to be in the same relative position, and you can fly towards them basically forever and never actually reach them⁵. There is a sort of parallel plane associated with each that is indeed physical (this is where Nightmare Moon ended up after her banishment), but it's not a place that can be physically reached from the normal world and I don't think that the visible Sun and Moon are actually any portion of these realms being directly seen⁵. I started referring to this as a 'dielectric' model because that's how I first thought of it operating- that there's some sort of element in the air (possibly a physical particle, possibly something like a luminiferous ether that's more just a quality of space itself) that has a 'sun pole' and a 'moon pole' on it and when Celestia 'moves the Sun' what she's really doing is aligning all those poles to a certain angle and that's where the Sun appears to be. This actually works fairly well for generating light and shadows, if all of the atmosphere is very dimly luminous and significant amounts of light are only put out when there is a lot of air in front of an object along that angle (i.e. it is exposed to the sky⁶).

But I don't think this would actually produce the single circular bright source of a visible Sun/Moon, and that's where I have to admit that my knowledge of physics simply isn't cutting it to actually describe this system in anything resembling clarity. There are concepts like spacial invariance in relativity that I think might be useful, but I freely admit that I don't understand them well enough to use them.

I'm not really looking for an explanation of this using terrestrial physics specifically, as I don't think our building blocks of four forces and a dozen-odd fundamental particles are really up to the task of creating something this... different. What I am looking for is more an attempt to make a model that is "physics-like", where the underpinnings of phenomena are described mathematically in a naturalistic way that could be discovered by the experiments of ponies⁷, and has the following features:

• Relies on processes that can be constrained to a physical volume or area on the ground⁸, or have influence that approaches 0 as distance increases.
• Produces some forces or emanations along a specific angular direction (i.e. light as described above, tides might also fall into this category).
• Produces a visible phenomenon with reasonably well-defined borders around a certain axis which changes based on that angle (i.e. the actual 'disc' of the Moon and Sun)
• That phenomenon remains at the same relative location regardless of the observer's location within the volume defined in Part A.
• Some explanation of how stars fit into this would be nice.

I realize this is all kind of abstract but I am truly stymied by it...

1. Looking strictly at canon sources the list of villains that actually do this is much smaller than I'd originally thought: Nightmare Moon was trying to freeze the day-night cycle from the getgo, Discord would almost certainly not care about the consequences of anything he did, and Tirek and the Storm King both fairly clearly desired to supplant the Princesses' role, leaving only Chrysalis, Sombra, and Cozyglow with this problem; the first two may have intended to capture at least one Princess alive and try to control her.²
2. This is further confused by the several times we see a Princess get incapped and the day-night cycle continue. It's possible that the Sun and Moon have some 'momentum' and will continue motion for a while if not immediately stopped like NMM did. This is a lesser issue from a fanon perspective, though, because it's easier to retcon since the fact that the cycle continued during those events is not really canonically important. Retconning the central problem of Equestria and only Equestria moving the Sun is a much bigger issue because it would require changing a major element of MLP's worldbuilding/lore .
3. For instance, the dome in the Crystal Empire may serve that function. The griffons once had a method of regulating day and night, but when their kingdom collapsed Celestia's nearby influence effectively spilled over into their territory. Some locations might not have concepts of day or night at all, or at least not the same ones Equestria does.
4. My model was based around a flat world of infinite extent, but if anything this gets worse with more normal geometries where the Sun and Moon are a large distance away from a sphere.
5. Although in fact they would become less distinct as you neared the edge of Celestia and Luna's influence; not sure what this would actually look like.
6. It is an interesting question, though, whether other places that have a sun and moon are tied to the same realms.
7. Although it would produce a weird effect where long caves or other closed spaces aligned east-west would get brighter near sunrise and sunset, and very tall closed towers would get brighter at noon.
8. While things that bring to mind historical scientific models from ancient history to the early Enlightenment add a nice flavor, I don't want to be bound to any one particular preexisting model because those models were created to explain a sun and moon like Earth's and these are very different.
9. I say area because the ground-surface or sea level may be physically meaningful. In fact, one of the ways that this physics differs from the terrestrial version is that certain axes might be 'favored' for some phenomena as opposed to the generally isotropic IRL physics. If it helps, think of ponies as having defined East and West based on some sort of measurement they conducted to identify a pre-existing universal axis, or land having formed at a specific level and sky above it because there is something underlyingly physically different about being above or below that level.

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Honestly, given it's canon that unicorns moved the sun and moon before the princesses turned up, I think you might be overthinking it. You don't need an elaborate local system, you just need the known historical fact that a group of ordinary magic users can duplicate the sisters' feat.

In my Bureau stories, Equestria is an artificial pocket universe that was designed by the Princesses based on brief glimpses of our earth through time. The 'sky' is a teal, frictionless crystal dome upon which the glowing, flat disks of the sun and moon can be slid by the will of the Princesses. The 'stars' are a life form that lives on the surface of the crystal dome, held there by local physics that provide an attractive force to the dome. They literally helped Nightmare Moon Luna escape from being an aspect of the moon. The land is a vast flat disk of matter which is hyperdimensionally wrapped around spacetime so that the underside of the land literally is the crystal dome that is the sky. Dig far enough down, and you would reach teal crystal, dig further and you would find yourself standing on the frictionless sky looking 'up' at the ground overhead.

The entire pocket universe is essentially like a ship, a vast ship that can travel between natural universes. The interior can be configured in any manner whatsoever - like a truly vast holodeck, only what is created is real and fully alive. Something not unlike a sapient, ego-less artificial intelligence maintains whatever is created by the Princesses, who have root access to the system. Indeed, they once were modules within the system of the ship, long, long ago.

That is how I deal with the issue of raising the sun. One story in my series explores all of this in great detail.