First, a quick disclaimer: I'm neither implying nor claiming that the writers were smart or organized enough to put any of this into the show. This is just a 'for-fun' thing that I did because I got bored.

So anyway, this is, to the best of my ability, an analysis of the canon technology, physics, sociology, and everything else I could cram in of the show. I haven't had time to do more than the first 6 episodes of the first season yet, but I'm posting this here as a sort of 'guide' in case any writer wants to know whether Equestria canonically has some material or has developed some process for a detail in their story. Apologies for any format problems, I swear it looked much better in the Word document and can't for the life of me figure out how to attach a file to these forum posts.

https://docs.google.com/document/d/16WvU7hI4pFn02EE0zKYzrWNpc3WBZQcLqFNNlkfLcEE/edit?usp=sharing

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electronic age

Equestria is not in the electronic age...

6328785
We have seen theam use elektricitet. So why not?

6328785
Electric streetlamps were seen in Manehattan, if I recall. While electricity isn't very widespread in Equestria, they have definitely invented it. Perhaps a better name would be 'Electric Age,' to denote the difference between complex circuitry and simple lightbulbs and power supplies.

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Industrial then. Electronic implies satellites level technology. Wireless.

6328807
If you are going to use a human Technological Age to approximate the ponies' one, then what you are looking for is the Second Industrial Revolution. This Technological Age covers the widespread use of the railway, the first steps of electrification (street lamps and such), paper making, and a lot of other technologies that in some way or another are used in the show. It basically covers the period between 1870 and 1914 (though of course a lot of these technologies we don't actually see the ponies use or use an alternative magical form if any).

6328811
Fair enough. I wasn't aware of any 'official' human Age to compare it to, so I was mainly just making up a name that would give some idea of where they were at. I'd also mention that in just the first 7 episodes, photobooths and refrigerators have both been seen, implying at least some level of automated technology.

Newer version:
https://docs.google.com/document/d/1D5_zkeAVVecFtJv_BQJXI5GQYyZioY5jGoiOGPOCpO0/edit?usp=sharing

Oliver pretty much make analysis on entire show (by episode), movies, and some of the books and comics. With pointing on technology ponies use, information when human invented same technology and when it become widely available.

Oh, and I'm pretty sure that pegasi flight at least partially magical - RD able to hover upside down or using only one wing.

6328826 Pegasus flight is definitely magical. That's why the pegasi couldn't fly when Tirek took their magic. Also, their wings are far too small to fly with using only physical means.

So, I have reached the page on vehicles being "integrated" (not a good word choice, but I'm writing this on the fly) with unicorn magic, and K wanted to point out that Tank's helicopter blade has a very clear magical energy in the glass tank, which would cause it to spin.

Mrs. Cake was called Chevron Swirl, I do believe, before she got her cutie mark

I shouldn't have pictured Steven Magnet with legs... my class thinks I'm weird

6328826
This is a fantastic resource! The only thing he appears to be lacking is calculation efforts, from the one episode I read (S5E12 - Amending Fences). Still, this will speed things up immensely on my end.

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You might think so, but nobody's ever explicitly stated such, not even the show writers. The closest they get is during Twilight's Kingdom, Part I, in which Celestia states:

Tirek has stolen enough magic that he now has the strength to steal flight as well. Without Pegasi to control the weather, there will be no rain in Equestria. There is word he has gone after Earth ponies as well. Without their strength, they will not be able to tend the land.

While this might seem pretty explicit, in that Tirek can 'steal flight', I'd make an important note that when Tirek saps a pony of their powers, he's doing two other things: Draining their physical strength, and growing larger. Pegasi drained of their strength would be unable to fly, but until he reached a certain size, they could simply fly over his head and escape his wrath entirely. In fact, Discord probably proved instrumental in avoiding this pitfall and allowing Tirek to progress in his conquest.

That being said, it's hard to say whether Rainbow is using magic to aid her flying or not. Certain species of birds can fly upside down (geese and ducks, mostly). As for using one wing, I've no idea. This would place the calculations I made as a 'minimum weight', as if pegasus magic aids in flight by reducing the effective weight of the pegasus in question, Rainbow could weigh significantly more.

6328839
...Do I need to bring up Bee Movie?

In all seriousness, though, the whole idea that a wing must be of a certain size to allow flight has been more or less debunked by now. It only applies to traditional flight mechanisms, which at the time were the only ones known, and ignores the unique wing patterns of bees and other insects. Granted, Rainbow's closer to a bird than an insect, but it's wrong to say it's impossible for her to fly with the wingspan she has.

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I could have sworn I used 'imbued', as that's what's in the Word document. Maybe something got lost in translation?
Anyway, like I said, this only contains data and speculation from the first seven episodes of the show, plus some information from the writers (Lauren Faust provided the statement about vehicles), so Tank hasn't even appeared yet. When he does, though, I'll be sure to make a note of that.

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I felt like imbued was the wrong word to use as Tanks helicopter has an obvious chamber full of a yellow energy, but yeah, can't wait for more!

I have a few issues with the planetary masses, and particularly the local gravitational acceleration (do they have ANY idea what a gravitational force of that magnitude would actually do?!). While I think they derived this from how Celestia and Luna raise and lower the moon (and the following assumption that the sun/moon rotate about the planet, which is not really a logical follow-up to the former), I don't really think that's what they're actually doing.

Rather, it's much more likely that they are changing what part of the sky is visible, relative to Equestria. It's always night or day somewhere on the planet; why not simply change what part of the planet's sky Equestria is looking at?

I base this argument off of several things, but one rather telling piece of evidence is in Season 4, Episode 1 ("Princess Twilight Sparkle, Part 1"). About 7:50 into the episode, there's a scene where both the sun and moon are visible in the sky... along with the "sky" being divided into night and day scenes. This is NOT what you would see if the sun and moon were physically placed near/next-to each other in the same visual plane.

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That's a good point, but it's possible for the sky to be split into two different colors - it happens here on Earth all the time, during sunset and dawn. While the sun isn't at its apex during those times of day, and thus the scene in S4E1 is pretty weird, I'm not sure I'd call it 'changing what part of the sky is visible', unless I'm misunderstanding what you wrote. Would Celestia and Luna be changing the visual perception of the sky itself (in which case, why have a physical sun or moon at all?), or would they be somehow changing which parts of the sky are seen at which locations (like a giant, remote camera that occupies the whole sky)?

Were the sun and moon to be placed physically (or in our case, optically would be a better term) near to each other in the Earth sky, it would be a) complete daytime and b) the moon would be nearly invisible. The fact that the moon's as bright as usual in this scene might imply that it gives off its own light somehow, instead of reflecting the light from the sun (which would honestly throw most of my math out the window, because I assumed tidal locking explained why the moon was always full).

My calculations so far do support the idea that Equestria's cosmic system is geocentric... barely. It works out to (at least, because this is a minimum estimate for an eclipse to be physically possible) 10 times lighter than the planet, which at the cosmic scale is barely even a difference. They might as well be a binary system. The moon is actually heavier than the sun (about half the weight of the planet), and a tiny bit closer too. This is all based on the sun and moon's sizes in the Equestrian sky, as well as rough guesses about the densities and therefore the Roche limits.

I revisited the gravity calculations, and it turns out it's actually higher than I posted. Much, much higher, at about 40 m/s^2 (over 4g). Don't misplace the 2, ladies and gents.

As for what a g-force of that magnitude would "do"... not much. People seem to have this belief that any g-force higher than 1g will squash you to a pulp, liquefying your insides as your body collapses in on itself. Unsurprisingly, this isn't actually close to what happens. At four times Earth's gravity, the main cause of death is that all the blood in your body will rush to your feet. This takes vital blood and oxygen away from your brain, as well as bruising the veins in the feet as they swell and possibly burst from too much blood. This will then cause you to lose consciousness, followed by a slow death as your brain, depleted of oxygen, shuts down.

But this makes a few key assumptions. First, that you were instantaneously or very quickly thrust into the higher-gravity zone, instead of slowly increasing gravity causing your body to adapt to the new pressures on veins and arteries; and second, that you're not wearing any protective gear. A simple pressurized suit goes a long way towards stopping most of those effects, as the increased compression on your veins forces blood back up to the brain, maintaining consciousness and precious, precious life.

Finally, it's definitively possible for humans to adapt (at least in the short term) to a higher-gravity planet. The Ames Research Laboratory, a subsidiary of NASA, recently published a study in which they found that a human test subject had survived 24 hours at twice Earth's gravity (19.62 m/s^2, approaching the gravity at Jupiter's surface) without any effects to the subject's health. From their data, they speculated that the absolute maximum that humans could adapt to (without any protective gear whatsoever) was around 3g (29.43 m/s^2). Past this, the aforementioned oxygen depletion cannot be avoided.

My gravity calculations in the updated version are based on two main sources: One, Spike jumping off a cliff in the Dragonlands and landing in a pit of lava (pretty conclusive), as well as an additional calculation based on the arc of Cadance and Twilight's ascent in A Canterlot Wedding - Part 1. Because I found two very different values for gravitational pull at these two locations (40.39 m/s^2 and 18.22 m/s^2, respectively), I concluded that the planet Equestria is on has an odd sort of egg shape, where the Dragonlands are closer to the shorter radius and Canterlot closer to the longer one. This is actually weirdly consistent with my theory that Celestia and Luna are moving the sun and moon to keep them from entering their respective Roche limits with Equestria's planet (and subsequently annihilating all three), so I was pretty pleased that a unifying theory could even be made for that.

All the new data can be found here, this time in a more helpful spreadsheet form. I'm still working on the analysis of every episode in Season 1, but I think I'll limit that to sociopolitical stuff unless something really interesting comes up.

I guess the takeaway from this, assuming my theory (which, again, I'm not saying the show writers intentionally put in there or even had any ideas about) is correct, is that humans in Equestria will actually be just fine as long as they stay in or near Canterlot and have a bit of time to adjust to the gravity there. If they start traveling south to the Dragonlands, though, they'll begin to experience the effects of the higher gravity and might run into some health complications. Also, Equestria's planet is egg-shaped and could be destroyed at any second if Celestia and/or Luna stopped pushing the sun and moon away from it for a while, but when hasn't Equestria been prone to disaster?

Let me get the largest elephant out of the room, first. You're trying to argue physically realistic orbital properties derived from a physically unrealistic set of circumstances. You cannot say "Celestia and Luna actually move the sun/moon" and then rationalize the orbital patterns of either, since "orbits" only happen under natural motion, and none of the ones you've described actually work (you seem weirdly fixated on the Roche limit as a defining factor for whether or not it would work, too). There are only two arguments to be made, then:

1. Either there are no actual orbital patterns involved (the sun and moon are artificial simulacrums), or...
2. There are actual orbital patterns involved, and rather than craft some very physically unrealistic/impossible circumstances under which unreal orbits can occur, we say that Celestia and Luna are only changing what is seen, rather than what is actually there.

I argue the latter, especially since it fits in with the tight artificial control Equestrians seem to wield over their environment, which does not appear to extend beyond their borders.

That's a good point, but it's possible for the sky to be split into two different colors - it happens here on Earth all the time, during sunset and dawn.

That's not an accurate analogy, as dawn and dusk result in a lighting gradient, due to the angle of entry from the sun's light into our atmosphere. This means it has to pass through much more atmosphere, which results in much more scattering (thus the color shift), and also results in less light reaching the further parts of the sky. This is not a sharp, instantaneous transition. However, in the aforementioned episode, the sky is literally split into two scenes. The night sky is right next to the sun, implying that the light simply is not being allowed to travel into that portion of the sky, as any kind of scattering would prevent its visibility.

While the sun isn't at its apex during those times of day, and thus the scene in S4E1ispretty weird, I'm not sure I'd call it 'changing what part of the sky is visible', unless I'm misunderstanding what you wrote. Would Celestia and Luna be changing the visual perception of the sky itself (in which case, why have a physical sun or moon at all?), or would they be somehow changing which parts of the sky are seen at which locations (like a giant, remote camera that occupies the whole sky)?

As I said before, "It's always night or daysomewhereon the planet; why not simply change what part of the planet's sky Equestria is looking at?" I remind you that Equestria is a nation, not the planet. When I said that, I was stating that Celestia and Luna's power only extend to the borders of their nation. Walk outside of it, and you may or may not see an entirely different day/night sky. In other words, the sun and moon are real physical objects, but where they are in reality may not necessarily correlate with where they show up while in Equestria.

It seems pretty clear that Equestria has a highly controlled, borderline-artificial environment. Even the seasons and weather are moved about artificially, rather than naturally, so why not the day/night cycle, too? Remember how they referred to the Everfree forest? They considered it creepy that the plants grow on their own, and the weather "had a mind of its own," meaning that they considered a non-controlled environment weird. You see similar hints at this in other areas, where the weather is not tightly regulated, like in Yakyakistan. In short, if the artificial and fairly strict control over their environment degrades beyond their borders, then it would follow that said day/night cycle control also degrades beyond their borders (assuming it a part of that same artificial control over their own environment).

Were the sun and moon to be placed physically (or in our case, optically would be a better term) near to each other in the Earth sky, it would be a) complete daytime and b) the moon would be nearly invisible. The fact that the moon's as bright as usual in this scene might imply that it gives off its own light somehow, instead of reflecting the light from the sun (which would honestly throw most of my math out the window, because I assumed tidal locking explained why the moon was always full).

It bothers me a bit that you'd freely admit the scene would be impossible in the event of the moon and sun being physically present in the same sky, and then follow-up with "maybe the moon has its own light source" instead of "yeah, that doesn't really work..." Also, Tidal locking would not explain a "full" moon. It would only explain why one face is always pointed toward the viewer; the "full" factor is determined by where the moon is with respect to the planet on its own orbital plane. This is one of those areas where we may have to assume some artistic liberty on behalf of the animators by cutting corners on things "they'll never notice." Or, we could assume that the night sky truly is artificial, to the point where they're not even projecting a different part of a "real" night sky from somewhere else on the planet. I remind you that the reason why the moon travels across the sky is because of the Earth's rotation under it. Which phase the moon is in (full, waxing, waning, etc.) depends on the moon's rotation around Earth:

My calculations so fardosupport the idea that Equestria's cosmic system is geocentric... barely. It works out to (at least, because this is a minimum estimate for an eclipse to be physically possible) 10 times lighter than the planet, which at the cosmic scale is barely even a difference. They might as well be a binary system. The moon is actually heavier than the sun (about half the weight of the planet), and a tiny bit closer too. This is all based on the sun and moon's sizes in the Equestrian sky, as well as rough guesses about the densities and therefore the Roche limits.

You are working regressively from the assumption that they both orbit the planet, and therefore inferring their masses and sizes from there. Plato would have agreed with you... and he was terribly wrong. Unless you wanted to argue that the sun were entirely artificial, it simply would not have the mass necessary to maintain any kind of fusion (Edit: think blackbody radiation!). For it to give off any visible light at all, there is a certain minimum mass required, which would far exceed the amount you're implying. So, no, that doesn't work out at all. Consider the apparent intensity and wavelength: there are some bare minimum requirements for it to be able to maintain either. Also, basing it on the apparent size in the sky is a very poor metric: even earth's moon and sun have roughly the same apparent size, but their actual sizes and distances clearly do not correlate with this.

As for what a g-force of that magnitude would "do"... not much. People seem to have this belief that any g-force higher than 1g will squash you to a pulp, liquefying your insides as your body collapses in on itself. Unsurprisingly, this isn't actually close to what happens. At four times Earth's gravity, the main cause of death is that all the blood in your body will rush to your feet. This takes vital blood and oxygen away from your brain, as well as bruising the veins in the feet as they swell and possibly burst from too much blood. This will then cause you to lose consciousness, followed by a slow death as your brain, depleted of oxygen, shuts down.

You completely missed my point. I wasn't even talking about humans; I was talking about basic physics as they relate to enthalpy (H=U+PV, which basically states the total energy content of a system as it relates to the amount of volume displaced), heat, energy, and/or the consequences to local chemistry. For example, the kinds of ice which would form, how water works as a solvent, etc. A local g of that level would exert too much pressure in the scale of a P-V diagram. Even water vapor would form a bit differently than it does on Earth. On that note of living things inside of such a gravitational well, though, I would recommend looking up how exactly trees move water to their upper boughs (kind of fascinating, actually; they use a negative pressure only possible because of the elasticity of water being able to store energy as particles are pulled apart). If the gravitational attraction is even close to what you mentioned, then they would hardly be able to grow beyond a few feet in height.

This also ties into atmospheric calculations. You could technically still have an atmosphere with earth-like density, but it would have to be a very, very thin layer. This has severe implications for how the sky would look: you would not have enough atmosphere to scatter light sufficiently for a blue sky. (Side note: while many people like to point out how low the clouds are in Equestria, I point out that 1.) the weather is artificial, and 2.) there are actually many cases in which the clouds appear at much higher, more "normal" altitudes, such as looking at the backgrounds while in Cloudsdale, or even looking at the movies)

Then there's geology. Rock formations would not be the same as you see in the series with such a substantial increase in local gravity, neither in terms of the layers, nor in terms of geological age factors, thus throwing almost every Maude episode out the window.

Then there's energy. With that much gravity, simply running across the ground would result in a LOT of waste heat. Ripples in water wouldn't propagate very far, either. Lighter-than-air skyships such as in the movie would be (more) impossible, as buoyancy forces would not be strong enough to provide lift. And many, many more things.

My gravity calculations in the updated version are based on two main sources: One, Spike jumping off a cliff in the Dragonlands and landing in a pit of lava (pretty conclusive), as well as an additional calculation based on the arc of Cadance and Twilight's ascent inA Canterlot Wedding - Part 1. Because I found two very different values for gravitational pull at these two locations (40.39 m/s^2 and 18.22 m/s^2, respectively), I concluded that the planet Equestria is on has an odd sort of egg shape, where the Dragonlands are closer to the shorter radius and Canterlot closer to the longer one.

Again, I'd point out the artistic liberty of animators. I find points of animation unreliable for determining the qualities of the world, since it's especially prone to deliberate exaggeration for dramatic effect, not to mention making motion physically accurate is not nearly as important as making it believable (two goals which often conflict in animation). It can seem silly to pick-and-choose which things to accept as "cannon" and which things to disregard as "liberties," but we kind of have to. Like when Big Mac is able to pull a barn, or uproot trees & boulders, but then struggles under the weight of a large cake (I forgot the name of the episode, but it's obvious the animators placed an exaggerated amount of physical exertion in order to add emphasis to the size of the cake). Unless you wanted to assume that cake to be made of lead (that would be... interesting...), there's little reason for him to be under such strain carrying it. Similarly, there are other points in the same "Dragon Quest" episode where gravity appears to be different than from the lava dive itself. I went off and calculated the acceleration due to gravity for the lava dive, and got the same answer as you. But if you try to calculate fall rates in the same area for different scenes (i.e., at different times/episodes while still at the same place, like different falling scenes in/around Twilight's treehouse)? Nope, they're horribly inconsistent. So, unless you wanted to say that gravity is constantly changing, I find basing it off of animations to be a very poor metric.

And no, you cannot argue for an egg-shaped planet, sorry. The inconsistency in fall speed occurs irrespective of location: you cannot use the comparative fall speeds in the Crystal Empire and Dragonlands to argue that point, either. Even a planetoid such as Pluto or Ceres has too much mass to allow anything other than a mostly spherical shape. You cannot argue for both a much, MUCH higher mass value and an egg shape: it's just not physically possible, even with absurd density or rotational values (an absurd rotational value wouldn't result in an egg, either, and the local g would be less at the equator).

Ultimately, starting with the assumption that the sun and moon rotate about the planet creates a massive number of inconsistencies which, in turn, require ever more complicated explanations in order to write them off. It seems far more sensical to me to instead assume the opposite, thus removing the need for an endless supply of excuses. Working regressively from the geocentric model assumption simply leads to too many contradictions and complications to be explained away :P

To the crux of our argument, however...

...is that humans in Equestria will actually be just fine as long as they stay in or near Canterlot and have a bit of time to adjust to the gravity there.

Yeah, that really isn't what I was arguing for or against in the first place. The issue I have with a geocentric model is the runaway effect of nonsense which follows, such as gravitational forces, properties of celestial bodies (size distance etc.), and properties of the local planet (densities, spin rate, etc.). But since you brought it up, you generated a rather facile argument by basing it purely on the local g effect on a human, while ignoring all the other implications this has for the environment, which in turn make it borderline inhospitable. Even then, you argued a ~40m/s^2 local g at the highest point, which, by your own admission, would not be bearable for a human: "From their data, they speculated that the absolute maximum that humans could adapt to (without any protective gear whatsoever) was around 3g (29.43 m/s^2). Past this, the aforementioned oxygen depletion cannot be avoided." So at the very least, a whole giant chunk of the planet is completely inhospitable to a human, while the rest is unrealistically difficult to manage. Granted, you admitted to this at the end of your conclusions, but still...

Still, if you want to argue for an egg-shaped planet... well, I guess that's your own headcannon, so fuckit, lol! I personally can't endorse it, but if you can write some interesting fiction based on that, then I suppose that's all that matters.

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This is all very true, and I both applaud and accept your comprehensive debunking of my arguments. It's why I started this thread, after all. That said, here are my attempts at rebuttals for some of the stuff you brought up:

I'd like to say that I can argue for an egg shape due to the idea of Equestria's planet (which I refer to as such because it's never been named, equivalent to saying "America's planet") is within the Roche limit of either or both of a physically present sun and moon. Because all materials at the cosmic scale act essentially like fluids, the planet would be deformed into a spheroidal shape the closer it came to the limit, and if kept at bay by some force from actually reaching the limit, the planet would retain this shape as far as I understand things. Being near the Roche limit would also necessitate something to push the planet away and prevent it from breaking up into a series of rings around the sun. Something like magic, which, if used in this manner, might also be needed to simulate a normal day/night cycle rather than the sun constantly looming closer and closer. Of course, using magic as part of an argument for the purposes of this thread would be rude, so I'll say for now that it's an only slightly supported idea rather than an actual theory. The differing gravities provided additional support for the idea, which is why I stuck with it until now.

You're correct that I more or less ignored the effects on local life of such high gravity, but I was mainly concerned with the effects on humans because... well, look at the forum we're in. It was based solely on gravity because that was the only data point directly from the show that could be taken: Air pressure/density, oxygen concentration, etc. are all stuff that can't be measured visually by anything in the show, as far as I'm aware.

Geological formations are radically different in Equestria's bedrock than on our planet even at a cursory glance (high prevalence of gemstones, which require high heat and pressure to form). From what I know of the hydrothermal process for growing artificial gemstones such as quartzes, the speed of crystal growth is proportional to the pressure used, meaning increased pressure will result in faster crystal growth (and, presumably, larger overall size). From this, I concluded that the idea of a higher gravity was weakly supported by this show canon. I'm not enough of a geologist to discern how this pressure would affect other local geology, such as rock formations being different, etc., so without any examples of rock formations on planets of higher (or lower) gravity, I'm unable to say anything contrary to your main point.

Per the sun and moon being tidally locked, look carefully at the diagram you posted: The full moon only occurs when the moon, earth, and sun are lined up so that the moon and sun are 180 degrees away from each other, with the observer in between. If the moon is always full in Equestria (a big assumption, but I've never seen it not full in the episodes that feature nighttime scenes), and reflects its light from the Sun, it follows that the sun must always be 180 degrees from the moon relative to the observer. Celestia and Luna might move the sun and moon, but they seem to do so following certain rules.

The calculations I make do account for the relative size not being indicative of distance and radius, and instead try to find those using other means and then make the data agree nicely. The reason I went for a geocentric model is that, in the current model, the mass of the sun works out to something like 16% of the mass of the planet (assumed to be the same as the Earth for now, which is a huge assumption that I intend to tackle once I figure out how to get a better number). The mass of the moon is actually more, at roughly half the mass of the planet, but we'll concentrate on the sun for now. From what I could gather, the minimum weight for sustained fusion to occur is an estimated 1.5912 x 10^29 kg (or 0.08 solar masses) according to Martin Cohen of Cambridge University (link here). This is 5 orders of magnitude above what I got for the sun's mass, which is a pretty big problem. I'll need to do some more math to determine, at a minimum, what the actual distance would have to be. Whatever it is, it would probably place the sun beyond the planet's Roche limit (unless their planet's sun was incredibly dense). This would also change things to a heliocentric model rather than a geocentric one.

If the force(s?) of gravity were inconsistent everywhere and at all times due to animation quirks, pretty much everything here would fall apart and this whole document would be entirely useless. I built this house on sticks and twigs, and I will live in it until it falls. ; )

That being said, I'd be immensely grateful if you could provide some sources of gravity being different in the same location. I knew the animators tended to exaggerate and don't exactly have a 'show bible' for this kind of thing, but how bad does it get?

In all seriousness, though, the idea of this thread is that assumptions will be made, disproven, and either replaced with improved assumptions or discarded entirely. Hopefully, at the end, the assumptions made will be more strongly supported than the ones at the start were. Maybe the whole thing's completely inconclusive (probably, all things considered). Maybe some stuff can be made to agree by playing with the numbers. Who's going to know until we try?

I'm going to post the updated version of all the math I've done here, but keep in mind this isn't taking into account any of the changes I said I'd make in this post, or anything you pointed out in yours - it's stuff that's been done in the interim. No idea how the new numbers will affect anything (though your note about the air pressure does give me some idea that that particular number needs some work).
https://docs.google.com/spreadsheets/d/1ayFwCF8E549fY8ka3JPPQ1stq4sCP-VCNfTp9h6GjRI/edit?usp=sharing

EDIT: Some preliminary results, based on messing around with the values for the sun:
Assuming identical density to our own Sun:

Distance/radius of sun if as massive as largest star known (315 M_Sol): R=4,733,829 km, D=27,846,182 km, M_planet = 1,995 M_Sol, p_planet = 0.0006316 g/cc

If as massive as Earth’s sun: R=695,000 km, D = 4,092,908 km, M_planet = 6.334 M_Sol, p_planet = 0.01121 g/cc

If at minimum mass for nuclear fusion (1.5912 x 10^29 kg, or 0.08 solar masses): R = 299,782 km, D = 1,763,464 km, M_planet = 0.5067 M_Sol, p_planet = 0.03963 g/cc

In all cases, Equestria’s Sun is 1/754^th as bright or as luminous as Earth’s.

The minimum-mass case is the most likely, as the density of the planet is (relatively speaking) the highest, and the solar mass of the planet is relatively the lowest. However, Earth weighs in at 3 x 10^-6 solar masses, meaning we would have a long way to go before approaching 'suitable' numbers.

Also, in this case, the equivalent radius for a sphere the same volume as the planet becomes 1,824,306 km, meaning Twilight and co. move very fast between towns and cities (the map of Equestria for the movie shows ice at both the top and bottom, which I take to mean that Equestria as a continent is roughly as big in terms of distances as the planet itself).

Basically, this doesn't work unless the laws of physics are violated and their planet's sun is allowed to sustain fusion at a smaller mass. Also, in all cases, the mass of the planet is higher than the mass of the sun.

Assuming mass of the planet is Earthlike (5.94 x 10^24 kg): R = 5,428.421 km, D = 31,925.83 km, M_Sun = 4.75 x 10^-7 M_Sol, p_planet = 16.268 g/cc

This is a little better in terms of density, but unless the planet's made of a gold, uranium or tungsten alloy, I kind of doubt it's that dense.

Assuming density of the planet is Earthlike (5.51 g/cc): R = 11,168.7 km, D = 65,698.25 km, M_Sun = 4.13 x 10^-6 M_Sol, M_planet = 2.62 x 10^-5 M_Sol

The mass of this planet relative to our Sun is pretty close to the relative mass of Earth, off by only one order of magnitude. Relative to its own Sun, though, it's 6.34 times more massive.

These calculations are all done assuming the density of their sun is the exact same as our own, which could be very, very wrong. I'm aware that this is little more than playing with numbers, but that's pretty much all one can do given so little data.

I built this house on sticks and twigs, and I will live in it until it falls. ; )

You, sir, have made my day :) To that end, I'll continue some debunking... but methinks I'll throw you a lifesaver. Who says the sun and moon need be ruled by natural principles? If the sun and moon are ancient magical constructs, then perhaps what Celestia and Luna are doing is actually more akin to "pushing buttons" than moving a physical object. It would save you the headache of trying to concoct "natural" explanations for either celestial body, while still retaining a physically "real" existence for both of them: the sun isn't actually undergoing any fusion process, nor does it have a substantial mass. Similar arguments for the moon. The only downside would be that the sun would be noticeably closer, to the point that there's a measurable parallax between shadows from different parts of the planet (the Earth's sun is so far away and so much larger that you can effectively treat all light from it as perfectly collimated).

Now, onto the other stuff...

You're correct that I more or less ignored the effects on local life of such high gravity, but I was mainly concerned with the effects on humans because... well, look at the forum we're in. It was based solely on gravity because that was the only data point directly from the show that could be taken: Air pressure/density, oxygen concentration, etc. are all stuff that can't be measured visually by anything in the show, as far as I'm aware.

You're mostly correct here. There's little evidence within the show to offer a good judgment on what effects gravity has at the planet's surface, at least in terms of physical phenomena. The only good example I can think of is the atmosphere. You cannot get a blue sky like Earth's without a rather particular composition and density. We can really only draw three things from it:

1. There's enough volume and density to the atmosphere to provide a blue sky.
2. It has enough pressure to prevent sublimation of many types of material, while not being so high as to significantly alter the way water behaves away from it does on Earth. In fact, the non-controlled weather very strongly implies a very, very close value to Earth's pressure range. Ice wouldn't form the same way otherwise (such as on lakes/bodies of water, or in the atmosphere as snowflakes), nor would waterways (streams & rivers), steam, or chemistry. Water's capacity as a solvent changes a bit with pressure.
3. It's composition is very similar to ours, as denoted by what color the sky is (at varying times of day).

Since the atmosphere's overall construction is (as far as I can tell) nearly identical to Earth, this would impose rather strict limitations on the planet's gravity. You can have very thick atmospheres, even with relatively low gravity (look up the moon Titan!), and you could technically have an atmosphere with the same pressure as Earth even with a very high gravity, but water vapor would not be able to the same kind of weather patterns. The planet would end up with very long and extremely high-velocity clouds within very low wind tunnels, due to the energy of the weather system being "squashed" to a much smaller volume space (higher energy densities on the weather systems=much more violent and powerful winds, storms, etc.). Since this doesn't match with observation, I would safely conclude that the observed atmospheric phenomena within the show (ignoring the ones which are controlled) supports an Earth-like gravitational well.

Geological formations are radically different in Equestria's bedrock than on our planet even at a cursory glance (high prevalence of gemstones, which require high heat and pressure to form). From what I know of the hydrothermal process for growing artificial gemstones such as quartzes, the speed of crystal growth is proportional to the pressure used, meaning increased pressure will result in faster crystal growth (and, presumably, larger overall size). From this, I concluded that the idea of a higher gravity was weakly supported by this show canon.

That's not entirely true. First, we need to make a distinction between "gems" and "crystals." "Gems" are minerals which can be, but are not always, crystalline in form. Similarly, not all crystals are gems. Obviously, in common parlance, the two terms are typically used interchangeably, and I doubt the show's writers actually know the difference. Still, there is a distinct difference between how gems and crystals form. Taking quartz as an example, while you can grow it artificially with pressure in a deposition chamber, the more common (and natural) way it forms is through precipitation at lower pressures, higher temperatures, and very high humidity.

Now, the show almost explicitly says "GEMS!" which (usually) require high pressure, but this does not necessitate high gravity. Quite the contrary, in order for you to get gems in such abundant supply right at the surface, what you need is some extraordinarily active convection currents through the mantle and crust. Not only would they have to be so active, they would also have to travel across a very large range within the planet's mantle and crust, meaning that those convection currents cover a substantial amount of the planet's depth. A high gravity planet would have the opposite effect: it would force the planet's convection currents to break up into more and smaller layers, preventing the circulation of materials from deeper in the mantle.

Having said that, the show's writers play pretty loose with these "gems." First of all, their fragility is much more typical of non-pressure formed crystals, rather than the sturdier stuff of pressure-cooked mineral-based gems, which form deeper within a planet and are brought to the surface via strong convection currents. And yet, they'll still refer to things as sapphires and diamonds with a kind of "rarity" (pun in intended!).

To top it all off, have you seen raw gems? They do NOT look like what they show in the series! Every time gems are "found" in the series, they're pre-cut! I'd argue something else is going on here. We could well blame magic for their formation, rather than natural geological processes, or some kind of unusual life form which grows them.

There's also a finer point I'd like to make about the first comment...

Geological formations are radically different in Equestria's bedrock than on our planet even at a cursory glance ...

Maud's episode with Starlight Glimmer and Pinkie (can't remember the name- Maud had graduated from college and Pinkie was trying to get her to move to Ponyville) and the conversations therein imply extremely similar geological processes to Earth's.

Per the sun and moon being tidally locked, look carefully at the diagram you posted: The full moon only occurs when the moon, earth, and sun are lined up so that the moon and sun are 180 degrees away from each other, with the observer in between. If the moon is always full in Equestria (a big assumption, but I've never seen itnotfull in the episodes that feature nighttime scenes), and reflects its light from the Sun, it follows that the sun must always be 180 degrees from the moon relative to the observer. Celestia and Luna might move the sun and moon, but they seem to do so following certain rules.

I think you misunderstood what I meant. Your original statement was

... because I assumed tidal locking explained why the moon was always full).

I was merely pointing out that tidal locking does not explain the moon being full: it would only explain one side of the moon pointing toward the planet, not its phase. You are correct in stating that the sun would always have to be a perfect 180^o to the moon... sort of. It would have to be off-center, other wise the moon would be in a permanent lunar eclipse.

From what I could gather, the minimum weight ...

Mass. MASS. MAAAASSS! Weight is a value of force; mass is... well, mass. We can blame the outdated imperical system we use in America for this misunderstanding: pounds are a unit of force, while our actual unit of mass is called the slug (which is why bullets are sometimes called slugs). Kilograms, however, are units of mass.
... *ahem* you can ignore that little rant if you want... >.>

That being said, I'd be immensely grateful if you could provide some sources of gravity being different in the same location. I knew the animators tended to exaggerate and don't exactly have a 'show bible' for this kind of thing, but how bad does it get?

That's going to be a bit tough. The lava dive makes a good study mainly because it's a relatively long falling scene, which makes measuring it pretty easy. Most other scenes where things fall are fairly short, but there's almost always books falling in Twi's library XD There's also the apples in/around Applejack's farm (Apple Orchards?), but I'm not sure how well we can use those, since 1.) the apples seem to fall at a flat velocity rather than accelerating through the fall, and 2.) we rarely get to see them at the start of their fall.

Having said that, it's pretty standard practice for animators to exaggerate falls, for two reasons in particular:

1. It's a simple and sneaky way to cut down on frame times, which frees up more animation time for other things. It's often quite small, but it adds up quickly, especially if you're running on a tight time-budget for the scenes.
2. It adds more "effect" than watching a realistic fall. Often, when you see a fall across any reasonable distance in reality (like from the roof of a small building), it doesn't really look that fast. If you animated things that way, it wouldn't "feel" like the fall had as much impact as you want people to recognize within the scene.

I'll have to do some searching myself to see what I can find, but I expect that journey to take a while :<

About those calculations.... "Oh, now you dun math'd, eh? You gunna make me break out the maths, ARE YOU?!"
density=ρ=M/V (substituting V for the volume of a sphere) -> ρ=M/(4πR³/3) -> ρ=(3/4)M/(πR³)

As a fairly crude calculation, you can see that density relates to radius as an inverse cube. If you wanted to keep the density constant while shrinking the mass, then the radius would change A LOT in order to compensate. For main-sequence stars and red dwarfs, the relationship between radius and mass is fairly linear (mostly). Following that, if you halved the mass of a star, keeping in line with that mostly linear relation on the radius would meaning halving the radius, too... which results in a density 1/4 of the original star, not 1/2. Similarly, doubling the mass and radius would result in quadrupling the density:

If M₁=M₂/2 and R₁=R₂/2, then applying a bit of basic algebra...
ρ₁/ ρ₂ = ((3/4)M₁/(πR₁³))/((3/4)M₂/(πR₂³)) = M₁R₂³/M₂R₁³ (substituting R₂ for 2R₁ and M₂ for 2M₁) -> ρ₁/ ρ₂ = M₁(2R₁)³/(2M₁)R₁³ = 2³/2 = 4 That is, the original density is 4 times the new density, or the new density is 1/4 the original.

Still, that linear relation isn't quite accurate... any star is really a balancing act between the force of gravity, and the force of fusion,. A lighter star tends to be much "puffier" (less dense), as the lower mass means less gravitational force to counteract the force of fusion. This also makes the star burn much more cool and very, very slowly. Red dwarfs, for example, are the longest-living stars in the universe: the ones floating around right now will still be there trillions of years after every other star has burned out.

Note the emphasis on being "more cool." When we say the star is much "dimmer," we don't just mean that it's producing less visible light: we mean that the spectrum of emission is shifted deeply into the infrared range. If the sun of Equestria's as-yet-unnamed planet (why, Hasbro? WHY DID YOU NEVER NAME THE PLANET?! WHY?!) were the smallest possible size necessary for fusion, then it would be noticeably more red. In fact, it would be a very, very angry-looking large red orb in the sky. The very smallest possible size a star can be and still have a fusion process is actually a red dwarf, after all.

As much as I'd love to show the math for that here (it's actually pretty fun to do), writing mathematical equations in fimfiction's forums is a pain in the ass (they've no support for coding which makes this practical). Instead, I'll link a paper from Caltech which roughly describes it: http://www.astro.caltech.edu/~george/ay20/Ay20-Lec7x.pdf

The most important part is assuming an equilibrium between the force of gravity and force of pressure, F_g + F_p = 0 -> GM(r)rAdr/r²+AdP = 0 -> dP/dr = -GM(r)r/r² Since this is a separable differential equation, you can re-arrange this and integrate to get an expectation value for the pressure of a given radius... which, in turn, gives you an idea of the amount of fusion energy required to generate said pressure and maintain that equilibrium. This helps a lot for getting an idea on the amount by which radius could vary as a function of mass, at least beyond red dwarfs (which are the only class of star small enough to still generate fusion reactions).

Another thing of note about those calculations... be careful when calculating "r" in terms of gravity. Technically, no body orbits another body: they all orbit the center of mass of their system of mass.
In the case of a system where one of the two bodies is way, WAY larger than the other, you can pretend that the center of mass of the system is approximately the center of that very massive object, yielding the classic F_g=GMm/r²
However, in the system you're describing, where the masses of the sun and moon are comparable to the planet, then the center of mass of the system will land outside of the planet's radius (again, this is assuming "natural" orbits governed by laws of gravity/relativity). For just two bodies, the "r" in F_g=GMm/r² would look like

My conclusion is this: either you...

1. Assume the sun and moon are real, physical objects... but completely abandon any kind of realistic setting regarding the sun or moon. You would have to assume both as artificial constructs (in a land of time traveling magic and other such wonders, why not?), likely involving magic. But you could never make them obey any kind of natural orbital pattern, especially if you want to move them at will while still assuming that they're real physical objects. Or...
2. Assume the sun and moon are not real, at least not in the classic sense. Either they're pure illusions, or they are illusory projections of something which is real. I prefer the latter, as this would leave fewer holes, requiring more explanations.

If you assume the first one, with the sun and moon (and their respective "skies") being magical constructs, then this may actually give you a lot more creative liberty in your writings. Assuming the latter also has its own interesting implications: what does it look like when you step outside of Equestria? Would it be like walking from one zone to another in WoW, the sky suddenly changing as you exit the domain of Equestria and step into the rest of the world?

I suppose what I'm trying to say is that either path is perfectly valid, from a story-telling point of view. Either one opens up a lot of options.

EDIT: actually, there is a third option. What if they're actually looping time on itself? The planet is caught in a perpetual moment in time, which would certainly explain always having the same lunar phase... and when we see an impossible mixed sky, we're looking through two different time-frame "windows" on different temporal states.

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Who says the sun and moon need be ruled by natural principles? If the sun and moon are ancient magical constructs, then perhaps what Celestia and Luna are doing is actually more akin to "pushing buttons" than moving a physical object. It would save you the headache of trying to concoct "natural" explanations for either celestial body, while still retaining a physically "real" existence for both of them: the sun isn't actually undergoing any fusion process, nor does it have a substantial mass. Similar arguments for the moon. The only downside would be that the sun would be noticeably closer, to the point that there's a measurable parallax between shadows from different parts of the planet (the Earth's sun is so far away and so much larger that you can effectively treat all light from it as perfectly collimated).

While I'm always hesitant to pull the "it's magic, I ain't gotta explain anything" card, it seems like this is the only explanation that fits so far, if only because it sidesteps the math entirely. Occam's Razor, and all that.

1. There's enough volume and density to the atmosphere to provide a blue sky.
2. It has enough pressure to prevent sublimation of many types of material, while not being so high as to significantly alter the way water behaves away from it does on Earth. In fact, the non-controlled weather very strongly implies a very, very close value to Earth's pressure range. Ice wouldn't form the same way otherwise (such as on lakes/bodies of water, or in the atmosphere as snowflakes), nor would waterways (streams & rivers), steam, or chemistry. Water's capacity as a solvent changes a bit with pressure.
3. It's composition is very similar to ours, as denoted by what color the sky is (at varying times of day).

Since the atmosphere's overall construction is (as far as I can tell) nearly identical to Earth, this would impose rather strict limitations on the planet's gravity. You can have very thick atmospheres, even with relatively low gravity (look up the moon Titan!), and you could technically have an atmosphere with the same pressure as Earth even with a very high gravity, but water vapor would not be able to the same kind of weather patterns. The planet would end up with very long and extremely high-velocity clouds within very low wind tunnels, due to the energy of the weather system being "squashed" to a much smaller volume space (higher energy densities on the weather systems=much more violent and powerful winds, storms, etc.). Since this doesn't match with observation, I would safely conclude that the observed atmospheric phenomena within the show (ignoring the ones which are controlled) supports an Earth-like gravitational well.

If we can take away from this point of evidence that the air pressure, gravitational pull at surface, and air composition of their planet is more or less identical to Earth, that does simplify a great deal of any math I'd do later on.

Incidentally, it's clearly seen in Winter Wrap Up that morning and sunset time feature a pale yellow-colored sky, rather than our orange. Is this possible given our air composition, or would a change be suggested by this?

You are correct in stating that the sun would always have to be a perfect 180^oto the moon... sort of. It would have to be off-center, other wise the moon would be in a permanent lunar eclipse.

Dag nabbit, I forgot how photons work again!

Mass. MASS. MAAAASSS! Weight is a value of force; mass is... well, mass. We can blame the outdated imperical system we use in America for this misunderstanding

Aagh. I'm an engineer, I should know better by now!

Having said that, it's pretty standard practice for animators to exaggerate falls...

This would probably mean that for the purposes of study, falling speeds shouldn't be used to determine gravity. Is there anything else to use, though? Some roundabout calculation that relies on other aspects of the world? The height of the trees seems like a potential starting point, though I'm at a loss as to how to actually squeeze a number out of it.

As for gravity being inconsistent everywhere and at all times, I hereby present my latest rock-solid theory on why this occurs:
The Comic Effect
Because 'destiny' is a real and tangible force in the show's narrative, it implies that comic relief can be a force as well. If we take all data from the show at face-value (in that absolutely nothing at any point is considered non-canon), it follows from these two points that there exists an actual, measurable effect on the residents and local laws of physics with regards to comedic or dramatic effect, similar to ponies breaking into musical or getting Cutie Marks that determine their life's path.

Gotta love unfalsifiable hypotheses.

This also makes the star burnmuch more cool...

I did, in fact, attempt to relate the surface temperature of their sun to its radius and brightness, among other things. However, the resulting numbers were so unsolvable it gave me a headache, so I quickly abandoned that method. I got something like a surface temperature of 930 K - still possible for stars according to the 'hot-coffee' brown dwarf discovered by astronomers at the University of Hawai'i, but not terribly likely. Also, it'd be very deeply red in color, if not infrared.

(why, Hasbro? WHY DID YOU NEVER NAME THE PLANET?! WHY?!)

The eternal struggle. We could come up with a name just so we could refer to it in shorthand - popular suggestions are 'Equus' and 'Anima', from what I've seen.

1. Assume the sun and moon arenotreal, at least not in the classic sense. Either they're pure illusions, or they are illusory projections of something whichisreal. I prefer the latter, as this would leave fewer holes, requiring more explanations.

I like this theory, if only because spatial warping is shown relatively often in the show itself. It would be quite easy for Celestia or Luna to open a 'window' at a set distance to an existing star or moon. Though, this begs the question of just how far away Luna was really banished. Did she go through the window, too?

EDIT: actually, there is a third option. What if they're actually looping time on itself? The planet is caught in a perpetual moment in time, which would certainly explain always having the same lunar phase... and when we see an impossible mixed sky, we're looking through two different time-frame "windows" on different temporal states.

This would be 'possible' from the standpoint of the magic required to do it, but strikes me as just a touch too complex. If time magic is involved, then Star Swirl's research into time travel would be somewhat supportive of this, as he was the first unicorn to raise the sun and moon before Celestia and Luna (according to the admittedly not-quite-canon Journal of the Two Sisters, which describes the process as requiring multiple unicorns around a central one, all of whom would suffer burnout after 2-5 attempts except the central caster). However, if the sun and moon were 'caught' between points of time, how would light from the sun reach the planet? It, too, should be 'frozen', as otherwise two options present themselves:
-Either the photons are still considered part of the sun, in which case they would all be sucked back into it as soon as everything was 'reset', or
-The sun would not be constantly at the same parameters after each loop (having permanently given off photons, something would have changed).

I think the second theory is the best one. If an illusory 'window' were opened onto a nearby parent star (perhaps one that is too far away otherwise, as we would see two suns were this not the case) and a similar one opened onto a nearby planetoid that could then be considered a 'moon', conventional physics goes out the window and Celestia and Luna can move the sun wherever they darn well please. Though that does bring up the question of just where this sun and moon actually are relative to Equestria's planet - is their moon orbiting some different planet entirely? Is it marooned in space? Is their star simply the closest one, but not close enough to be considered a 'sun'?

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That's not how you spell her name.

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Aagh. I'm an engineer, I should know better by now!

SOMEONE I CAN TALK TO! ( BS in physics :D ) Please don't make that horrible joke... you know the one. "What's the difference between a physicist and an engineer? The engineer has a job." =_=

I did, in fact, attempt to relate the surface temperature of their sun to its radius and brightness, among other things. However, the resulting numbers were so unsolvable it gave me a headache, so I quickly abandoned that method. I got something like a surface temperature of 930 K - still possible for stars according to the 'hot-coffee' brown dwarf discovered by astronomers at the University of Hawai'i, but not terribly likely. Also, it'd be very deeply red in color, if not infrared.

Blackbody radiation -> Planck's Law/distribution -> Wein's Displacement Law: λ_mT = roughly constant = 2.898x10^-3mK ... roughly the peak of the energy distribution of Planck's Law (aka the "most probable" value of a photon) .

So, for a body of temperature 930K, this comes out to about 3116 nm wavelength of light, well into the infrared range. Only a tiny fraction of the emitted light would be visible :<

Alternatively, you could stick to blackbody radiation, using the Stefan-Boltzmann relation, describing the power output of a thermal body across its surface area (written in terms of "luminosity"): P = σT⁴ (where σ = 2π⁵k⁴/(15c²h³) ) -> L = 4πR²σT⁴

This will give you a rough relation between luminosity, temperature, and radius... for sun-like stars. The radius-temperature relation breaks down a bit as you walk off of / toward the edges of the main-sequence stars, as other forces come into play. Still, it yields a useful simplification: R_o, T_o, and L_o are in terms of solar Radius, Temperature, and Luminosity, respectively.

Aside from that, there's two ways to approach the mass-luminosity relation (and, in turn, radius-luminosity). First is through empirical data, which shows a largely logarithmic relation, but you can look up graphs/distribution charts to give a rough idea of where you may want to place your star. Second is through a brute-force calculation, which actually involves something I had mentioned before about balancing gravitational and pressure forces, F_g + F_p = 0

This basically means assuming hydrostatic equilibrium; how you solve for this depends on what exactly you assume for pressure values. If you ignore pressure values generated by radiation, nuclear decay and fusion, etc., instead making a crude assumption of an ideal gas, then dP/dr = -GM(r)r/r² can be solved to give a VERY rough value of R = (3M/4πρ)^1/3.

Plugging in the Stefan-Boltzmann relation, you can get an even more crude relation: L ~ M³. There's actually a wikipedia article which covers the steps of derivation for that over here, if you're interested.

Some roundabout calculation that relies on other aspects of the world? The height of the trees seems like a potential starting point, though I'm at a loss as to how to actually squeeze a number out of it.

Methinks there's a video about that... remember when I mentioned that water can store kinetic energy, similar to a spring? Yeah, that's the only reason water can be drawn so high up through a tree: if you used "suction" (difference in pressure between the atmosphere surrounding the tree and the inside of the tree) to drive the water upward, then you could never draw something with greater force than the difference between 1atm and vacuum.

Even then, there's still limits on how high a tree can pull water up. You can still have relatively tall trees, even within a high gravity well, but it's a matter of energy balance... and a varying the gravity will both change how much energy is required to raise that water up (in raw energy wasted just fighting gravity to achieve a height), as well as how efficiently water can evaporate at different heights (which also effects the necessary energy, and changes chemistry/structure values for the tree). If the amount of energy required to move the water up exceeds the amount of energy a tree gains through photosynthesis in the same process, then the tree will have no reason to grow that high. Unless you want to say "because magic!"

Considering that the apple trees in Sweet Apple Acres are about the same height as Earth-based apple trees in a similar orchard, and the height of trees in the Everfree forest (an even better example, since these trees are "unregulated"), it would seem to support an Earth-like atmospheric pressure-gravity relation (remember that hydrostatic relation between F_g and F_p? It shows up everywhere in nature!).

This would be 'possible' from the standpoint of the magic required to do it, but strikes me as just a touch too complex. If time magic is involved, then Star Swirl's research into time travel would be somewhat supportive of this, as he was the first unicorn to raise the sun and moon before Celestia and Luna (according to the admittedly not-quite-canonJournal of the Two Sisters, which describes the process as requiring multiple unicorns around a central one, all of whom would suffer burnout after 2-5 attempts except the central caster). However, if the sun and moon were 'caught' between points of time, how would light from the sun reach the planet? It, too, should be 'frozen', as otherwise two options present themselves:
-Either the photons are still considered part of the sun, in which case they would all be sucked back into it as soon as everything was 'reset', or
-The sun would not be constantly at the same parameters after each loop (having permanently given off photons, something would have changed).

Well, time moves relative to the observer. To a viewer on Equestria, it would seem as though the sun is simply "starting over" from the same temporal setpoint, though time appears to continue moving forward relative to the sun.

Think of the grandfather paradox... which actually isn't a paradox. Say you go back in time 50 years, to year "100" on the calendar (just to make the math neater), and kill your grandfather, thus preventing your father's birth and yours. Well, relative to the people you left, time is still moving forward; the effects of having killed your grandfather never reach them, because such effects move forward at a rate relative to the observers in YOUR timeframe.

For example, time moves forward one month: you've been arrested and charged with premeditated manslaughter, while the family you left (50 years in the future) have spent the past month looking for you. 10 years later, in the year 110, you're rotting in prison; the family you left is mourning the 10th anniversary of your disappearance, in the year 160. Finally, 50 years later, in the year 150, time in your frame of reference has advanced to the same point you left... you're probably still in prison in this timeframe where your father never came into existence, but the people you've left? They're in the year 200! Your father (in that timeframe) is a sad old man who never found where his son disappeared to... though perhaps it's best he never does.

You see, time doesn't magically "stop" for the reference frame you left: it will continue to move at a rate relative to the observers in that frame. This is why Hollywood-style time-loops bug the crap out of me... THAT'S NOT HOW TIME WORKS! At least not according to special or general relativity.

However... it's clear this point was never made to the writers :| We already have Twilight's episode involving a time loop (S2 E20 "It's About Time"), which violates the way time actually works. There are no self-fulfilling prophesies (aka, "closed" time-loops, or "self-correcting" time-loops) in the real mechanics of time, but that's exactly what they invoke. And then they BREAK that later with Starlight Glimmer's "The Cutie Re-Mark" parts one and two: no closed time-loop / self-correcting timeline!

So, I think it's safe to say "because magic!" in this instance. Clearly, magic-induced time travel can have varying non-consistent effects, depending on how it's performed. Getting the sun/moon stuck in a time-loop would violate conservation of energy, but methinks its safe to say we're past that when invoking magic-induced time travel :)

I think the second theory is the best one. If an illusory 'window' were opened onto a nearby parent star (perhaps one that is too far away otherwise, as we would see two suns were this not the case) and a similar one opened onto a nearby planetoid that could then be considered a 'moon', conventional physics goes out the window and Celestia and Luna can move the sun wherever they darn well please. Though that does bring up the question of just where this sun and moon actuallyarerelative to Equestria's planet - is their moon orbiting some different planet entirely? Is it marooned in space? Is their star simply the closest one, but not close enough to be considered a 'sun'?

Yup! It's the one I've been arguing for, too! I like to play around with it in some interesting ways; if you had a gravimetric sensor, you'd see where the moon actually is... and probably respond with "WTF?"

I'm kind of eager to for season 8, actually. They may finally be venturing outside of Equestria and into the world at large... while I doubt the show's writers will invoke any kind of satisfactory consistency with things like raising/lowering the moon, it may still be interesting! Do other cultures, which maybe never heard of Luna or Celestia, have entirely different myths surrounding these bodies and their motion? Do they even see the same motion or Sun that Equestrians see?

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"What's the difference between a physicist and an engineer? The engineer has a job.

Can't really make this one, being unemployed. Come to think of it, none of the engineers I graduated with had that sort of attitude. Maybe it comes with age and cynicism?

Still, it yields a useful simplification:R_o, T_o, and L_oare in terms of solar Radius, Temperature, and Luminosity, respectively.

We know the surface temperature of the star (or at least have a rough guessing range), but the luminosity could vary a lot. We could say that the light reaching Equestria is about as bright as it would be on Earth, but without knowing the 'windowed' distance to the star we couldn't deduct luminosity (and therefore radius).

Yeah, that's the only reason water can be drawn so high up through a tree: if you used "suction" (difference in pressure between the atmosphere surrounding the tree and the inside of the tree) to drive the water upward, then you could never draw something with greater force than the difference between 1atm and vacuum.

That is a fascinating video. Another point for Equestria having an Earthlike surface gravitational pull, then.

Think of the grandfather paradox... which actually isn't a paradox. Say you go back in time 50 years, to year "100" on the calendar (just to make the math neater), and kill your grandfather, thus preventing your father's birth and yours. Well, relative to the people you left, time is still moving forward; the effects of having killed your grandfather never reach them, because such effects move forward at a rate relative to the observers in YOUR timeframe.

To me at least, this implies a timeline 'split': One 'branch', from the perspective of the grandson, loops backwards to reconnect with the point of the split to form the second branch, which then continues as 'normal' (well, as normal as jail for murder can be to a person). The second branch, from the perspective of everyone else, is also continuing as normal, with the exception that the grandson has inexplicably vanished.

The Cutie Re-Mark appears to have a more roundabout approach, in that Twilight and Starlight, across many separate iterations, eventually close the loop and reset everything back to what it once was. Honestly, I'm not sure what to make of that episode's delving into time travel - why would traveling back to that moment to prevent Rainbow's Rainboom again and again result in different outcomes? Where one resulted in Chrysalis' takeover of Canterlot, but another resulted in Nightmare Moon's defeat of Celestia? Wouldn't it all be the same, every time, because all timelines lacked the new Elements of Harmony and therefore couldn't combat even the first threat (Nightmare), leaving her to deal with subsequent ones? Gah.

I really need to watch the MLP movie - a lot of new locations spring up (Abyssinia, Mt. Aris, etc.) but I'm not sure whether they're in Equestria or not. From what little we've seen of non-pony, separate cultures, nobody so far has presented their own, conflicting theologies on why the sun or moon move - not even Zecora, who would have had reason to mention it at some point or another. Everyone just seems to universally accept that Celestia and Luna are responsible for the task.

But going back to the sun and moon: How big is this 'window', and how might it behave? Our best answer comes from that screenshot during Princess Twilight Sparkle:

There appears to be a gradient between day and night here, though it's nowhere near as big as one here on Earth and the Sun and Moon are entirely too close together. (Also, the moon appears to have a slight crescent on it. So much for my theory of tidal locking - really should have checked this one earlier). So, assuming the windows typically looked something like this, where the actual 'view' of a sky color extended across roughly half the planet's circumference:

Where the yellow zone represented the 'daytime sky' and the dark blue zone represented the 'nighttime sky', respectively...

Would the two intersecting 'windows' depicting day and night sky look like this (a 'rigid' barrier between the two):

Or this (a more 'flexible' or even 'miscible' barrier)?

And in both cases, what would be seen in the pink zone?

I think the show points more closely towards the first (rigid) idea, as the gradient between the 'day' and 'night' zones appears to be very small, and observers caught in the 'middle' zone appear not to see 'day' and 'night' skies superimposed on one another. But why would they behave 'rigidly' at all? Why wouldn't they simply blend across the entire sky, or create a 'twilight' zone? (I'm so funny, I know.)

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Yeah, I don't know how to spell her name...

Oh god... this blog turned into my science homework again...

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https://derpibooru.org/tags/chiffon+swirl
http://mlp.wikia.com/wiki/Mr._and_Mrs._Cake

Easy ways to check the spelling of pony names: The wiki and Derpibooru.

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Thanks!

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We know the surface temperature of the star (or at least have a rough guessing range), but the luminosity could vary a lot. We could say that the light reaching Equestria is about as bright as it would be on Earth, but without knowing the 'windowed' distance to the star we couldn't deduct luminosity (and therefore radius).

Yeah, as I pointed out earlier, the temperature you stated would yield a peak thermal emission wavelength at 3116nm; the vast majority of the light would be invisible mid-range infrared, with very little in the visible range.

Actually, if you intend to do any writing in fiction involving stars, it would be useful to remember Wein's Displacement Law, so I'll write it again:
λ_mT = 2.898x10^-3mK -> λ_m = 2.898x10^-3mK / T , where λ_m is the "peak" wavelength of transmission, i.e., the center of the top of the curve for a blackbody's thermal distribution.

To me at least, this implies a timeline 'split': One 'branch', from the perspective of the grandson, loops backwards to reconnect with the point of the split to form the second branch, which then continues as 'normal' (well, as normal as jail for murder can be to a person). The second branch, from the perspective of everyone else, is also continuing as normal, with the exception that the grandson has inexplicably vanished.

That's mostly correct, with one caveat. To say it's a "split" would be to imply a previously linear path. Time is not linear in the least; all possible states exist at all times. If you want something especially mind-bending, then I'd suggest watching this PBS Spacetime episode on the "Quantum Eraser." Really, you should; that special delayed-choice experiment was groundbreaking research, and these guys do an excellent job of explaining/summarizing it. Quantum mechanics is like the honey badger of temporal mechanics... "honey badger don't care!" It also rather flatly implies that there is no true linearity in time; that's more or less an artifact borne out of how we perceive time.

About that sky projection... I'm not sure it's necessarily sitting at a specific distance from the surface. More likely, it's an enchantment across the kingdom, covering a whole volume space. That is to say, no matter where you are within Equestria, you would see the same image; there wouldn't really be any kind of parallax. "Projection" was a poor choice of words, as that can easily be misinterpreted as a flat image at a set distance, which isn't quite what I meant (pointing back to my statement of a volume-space illusion).

Then again, I kind of doubt this; the show's writers want to make Equestria as analogous to the US as possible, which likely means invoking time zones as well. They'd probably do that and still have everyonepony see exactly the same day/night split in the sky! Storytelling is their primary focus: realism takes a back seat compared to that.

Once you step outside of the kingdom (into the pink area), the sky may or may not return to it's "true" value... assuming the day/night cycle within Equestria is not in sync with the "real" position of the sun/moon. If it is at least roughly kept in sync, then you might not actually see a difference. I'd like to imagine that, looking back at Equestria from inside that Pink zone, it would look like it's in the same day/night phase as where you're standing... but after you walk across into Equestria's domain of influence (and assuming that they're not in sync), then it would suddenly become some other time of day/night, whatever Equestria happens to be set to at the time.

I'd also like to assume then, that, although Celestia and Luna have absolute control over Equestria's day/night cycle, they at least try to keep it in proper sync with the rest of the world.

From what little we've seen of non-pony, separate cultures, nobody so far has presented their own, conflicting theologies on why the sun or moon move - not even Zecora, who would have had reason to mention it at some point or another. Everyone just seems to universally accept that Celestia and Luna are responsible for the task.

I watched that movie, and I can at least say this: it's quite the opposite. The rest of the world seems largely unaware of Celestia or Luna's existence. For that matter, the area they ended up in didn't seem to know much about ponies or even magic. Then again, the story was also massively inconsistent: somehow, the rest of the world knew the main villain quite intimately (the effects of his rule were quite wide-spread), while Equestrians seemingly never heard of him, and the rest of the world hadn't heard much at all about Equestrians... despite the kingdom of hippogryphs being an ancient and close affiliate of Equestria, and at least locally known in mythology/legend.

Having said that, nothing at all is mentioned about the sun or moon's behavior from the other cultures. If you combine what's either unawareness or apathy toward Equestria with the lack of any statements toward the sun/moon's "weird behavior" (I would really expect such odities to become part of cultures outside of Equestria), then either

1. They just never thought to make any mention of it throughout the story (deeper world building it wasn't important to the movie's plotline), or...
2. Such weird behavior is considered "normal," as if a fancy of temperamental gods, or...
3. Such behavior was never observed.

I don't think we really have enough to go on in order to make a statement on any of those :|

ANYWAYS!

First, a quick disclaimer: I'm neither implying nor claiming that the writers were smart or organized enough to putanyof this into the show. This is just a 'for-fun' thing that I did because I got bored.

Well, I think we can both concur the writers either weren't smart enough to consider such things, or it just wasn't important enough to them XD

Also, I hope I have un-bored you by now :D

What do you think you'll do with all of this new information/feedback? I personally think it makes for some interesting fiction, if you go with "The Sky is an Illusion!" route: what would a spaceship see? Or someone punching high enough through the atmosphere that they exceed the range of the spell?

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Side note: part of the reason why I'm avidly interested in this is because I do intend to write a HiE story at some point... branching off from a rather deep "Treadfall" series, taking place circa 2913. Hard sciences only, no FTL travel or grey-goo, roughly 83 years after the human race finished its "First Stellar War," with the aftereffects having massive and seemingly permanent effects on the way humans do things.

I'm wary talking about it, as it's a rather large and long story that I'd like to publish, so I don't really want anyone stealing the idea off of me :<

About that sky projection... I'm not sure it's necessarily sitting at a specific distance from the surface. More likely, it's an enchantment across the kingdom, covering a whole volume space. That is to say, no matter where you are within Equestria, you would see the same image; there wouldn't really be any kind of parallax. "Projection" was a poor choice of words, as that can easily be misinterpreted as a flat image at a set distance, which isn't quite what I meant (pointing back to my statement of a volume-space illusion).

Fair enough. The question I was asking doesn't really change with regards to a flat projection at a fixed distance or a filled volume that experiences the enchantment, in that I'm curious as to why the 'boundary' of each behaves so seemingly rigidly.

Once you step outside of the kingdom (into the pink area), the sky may or may not return to it's "true" value... assuming the day/night cycle within Equestria is not in sync with the "real" position of the sun/moon. If it is at least roughly kept in sync, then you might not actually see a difference. I'd like to imagine that, looking back at Equestria from inside that Pink zone, it would look like it's in the same day/night phase as where you're standing... but after you walk across into Equestria's domain of influence (and assuming that they're not in sync), then it would suddenly become some other time of day/night, whatever Equestria happens to be set to at the time.

The only real way to prove this would be to have a character mention that the time of day changed as soon as they set foot (hoof?) onto Equestrian soil, so I guess we'll hold out for S8's hot take on the matter.

I watched that movie, and I can at least say this: it's quite the opposite. The rest of the world seems largelyunawareof Celestia or Luna's existence. For that matter, the area they ended up in didn't seem to know much about ponies or even magic. Then again, the story was also massively inconsistent: somehow, the rest of the world knew the main villain quite intimately (the effects of his rule were quite wide-spread), while Equestrians seemingly never heard of him, and the rest of the world hadn't heard much at all about Equestrians... despite the kingdom of hippogryphs being an ancient and close affiliate of Equestria, and at least locally known in mythology/legend.

Maybe this is just because I've been watching S1 a lot lately, but that doesn't seem terribly out of place to me. S1 makes a point over and over that Equestria is extremely culturally isolated from the rest of the world. Fluttershy didn't know what a dragon was in S1E1, and nobody knew what Zecora was (Rarity even assumed the stripes on her body were aesthetic rather than what she was born with). Twilight knew, but given how much time she spent in books and/or around Celestia pre-S1E1, it's fairly possible that she might have picked knowledge about zebras up there.

As for the rest of the world not having heard of Equestria, that does seem a bit strange, and definitely points in favor of Celestia and Luna only affecting the local perception of the sun and moon. Astronomers outside the kingdom, upon viewing a sun and moon seemingly adjusting themselves to very precise but arbitrary positions, might otherwise exclaim "What in blue blazes?" and start trying to figure out the source. Temperamental gods aside, I don't think any culture could go for very long without trying to figure out why it was happening, whether by establishing cultural myths or investigating evidence and discovering Equestria.

The writers make quite a bit of effort to relate Equestria to North America, but I'm beginning to think it's closer to the size of Great Britain. How else could civilizations with airships ignore it for so long? Of course, the 'official' map depicts both the north and south of Equestria as having icy areas, but the 'official' map is never the most reliable thing.

I'm wary talking about it, as it's a rather large and long story that I'd like to publish, so I don't really want anyone stealing the idea off of me :<

They'd have to replicate the science behind it first, and even then you could probably simply outwrite them. No worries there.

What do you think you'll do with all of this new information/feedback? I personally think it makes for some interesting fiction, if you go with "The Sky is an Illusion!" route: what would a spaceship see? Or someone punching high enough through the atmosphere that they exceed the range of the spell?

I would imagine someone entering or exiting their atmosphere would see the sun or moon 'jumping' to a new position, as well as possibly changing size and distance. It would probably be pretty jarring and unsettling if it did - imagine looking up one day and finding the sun was twice as big.

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lol you all forgot the biggest part of the sun/moon thing

it takes Celestia 10 seconds to move the sun (AS SHOWN IN THE SHOW).

light don't move that fast

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That actually fails to prove or disprove either theory. In awesomesauce4's theory, the sun is very close to the planet, enough that the light delay would be unnoticeable. In my theory, I'm stating that Celestia and Luna are actually shifting an illusion, which would obviously be unaffected by any kind of light lag.

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Well said. There's no way to prove or disprove either theory without more information, so I'll move on to other stuff for now.

Maybe you could weigh in on another theory I've been working on: Is the 'golden material' seen in Equestria really gold?
It pops up all over the place in S1E1, mostly in Canterlot. Some examples of its use include:

-Twilight's chariot (S1E1). This includes the wheels, axles, and harness.
-Celestia/Luna's chariot (S1E2). This features non-golden accoutrements, but is still mostly a uniform material.
-Celestia's raiments, seen from S1E2 onward.
-Bits, the Equestrian form of currency.
-Armor of the Royal Guard, seen in S1E1 onward.
-A golden ring with a large diamond set onto it, as well as another golden band, dreamed about by Rarity during S1E3.
-A stand made apparently for reading scrolls, owned by Celestia and first seen in S1E5.
-Most of the treasure in a dragon's hoard, seen in S1E7.
-The nozzle on the hose attached to the side of Twilight's treehouse, seen in S1E8.
-Zecora's dzilla rings, seen during her debut in S1E9.
-Certain musical instruments, such as cymbals and a tuba, seen in S1E10.
-The horn of a gramophone (S1E12)
-And, presumably, others from episodes I haven't watched yet.

Evidence supporting that this is gold:
Strong evidence:
-The use of it as a currency. A stylized kids' show about a magical land full of gems, princesses and fantasy would indeed feature gold coins.
-Celestia's raiments. Again, a Princess would be wearing gold (though if it were pure gold... That's gotta hurt her neck).
-The treasure of a dragon's hoard being made of the same material. Traditionally, dragons hoarded gold and other precious metals either solely due to their perceived wealth, or because they subsisted on them as a food source. Spike is known to eat gems, so the latter could be possible.

Weak evidence:
-None of the golden objects seen in the show have any kind of oxidation on their surface. While this is likely an animation consistency rather than an actual feature, this might imply that, like gold, the metal used resists chemical attack in the long term. Oxidation and corrosion of metal is shown a rare few times in the show - a rusty iron/steel plow in S1E3, for example, as well as the Statue of Liberty lookalike in Manehattan.

-When dropped onto a surface, bits make a very quiet sound, inconsistent with the ringing of brass. Again, this is likely the result of a stylistic choice by the storywriters rather than any actual physical occurrence, but gold is known to make much less of a 'ringing' sound compared to brass (this is used to detect fake gold coins/bullion via the 'ping test'). However, this sound is also inconsistent with a 3-inch diameter coin weighing nearly a kilogram hitting a wooden surface...

-A distinctly bronze horn is seen during Trixie's debut in S1E6, having a darker tint than the typical 'golden' material that is depicted. This is, as far as I know, the only time such a darker golden metal is shown.

Evidence against this being gold:
-Gold would, quite simply, be too heavy to be used in most of these applications. Wearing a solid piece of gold that thick would easily injure Celestia/the Royal Guards if they tried to lift their necks, and using it to make chariots and other vehicles would make them incredibly difficult to push or move (coefficient of static/dynamic/rolling friction and thus force applied all depending on the total weight of the object itself). Traditional peytrals weighed somewhere around 15 pounds, and I couldn't find what traditional chariots weighed (they were made of wood, so at a rough density comparison, they would be 0.044 times as dense as a solid gold chariot of similar make). In order for gold to be used as a chariot, magic for weight reduction and surface protection would have to exist. Both of these have been hinted at, but not explicitly shown to apply to these vehicles.

-Gold is too malleable to be used as a proper engineering material. Gold, on Earth, can be dented with a fingernail, shaved by a knife or screwdriver, and beaten so thin by a hammer that it would qualify as 'foil' instead of 'sheet metal' (the basis of gold leaf). Because of this, any object that was actually made of gold would have to be reinforced on the outside by some means to prevent mechanical wearing and subsequent failure.

-Zecora's dzilla rings, as well as Pinkie's tuba and cymbals and the gramophone horn, are all traditionally made from brass. The latter two are not apparently due to any special acoustic property of brass, as the shape of an instrument plays a much larger role in how it sounds than the material from which it is constructed.

-Brass alloys can look very visually similar to gold, and an alloy of approximately 85% copper and 15% zinc is visually indistinguishable to 23k gold (used as a substitute for gold leaf, among other things).

My current attempt at a 'unifying theory' for all of this is that the Canterlot mountain, and by extension Equestria, has a plentiful supply of native gold or gold minerals such as auricupride, callaverite or petzite. This is then processed into a variety of equipment and aesthetic materials such as bits, chariots, stands, etc., most of which remain in Canterlot to contribute to the opulent 'palace' look while necessary commodities such as bits (the national currency) are shipped statewide. In contrast, gold is scarce in other places such as Griffonstone and possibly the Dragonlands, making bits an extremely valuable currency to own (and, to dragons, possibly a good source of food). Because Canterlot has so much gold available, and gold is so much easier to work than other metals once smelted, its use has turned to engineering products such as chariots, possibly with magical reinforcement to avoid mechanical failure of golden objects.

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Hmmm... that's actually something I wondered about, too. The show's writers play pretty loose with stuff like material types, but I think it's clear that gold and other valuable/rare elements and materials are common enough that their value falls well below what they have here on Earth. For example, the gold-woven fabric Rarity was using (which Sweetie Belle mutilated for the CMC capes). Valuable enough to make Rarity angry when it gets ruined, but not anything like the career-ending loss in assets it would have been here.

It's also one of the few instances where the show explicitly states "yeah, that's made of gold." Outside of that, it's tricky to say when gold is actually being used. Methinks the show's artists/writers prefer the appearance of gold for purely aesthetic purposes, without any consideration to the actual material properties of gold....

I'd suggest gold-plating or gold-leaf, rather than solid gold, for most objects. Especially in the instance of anything which requires good structural properties (wheels, tools, etc), or things with weight restrictions (armor). Gold has that remarkable property of being one of the most malleable of all materials known to man; you can hammer that stuff out to a ridiculously thin (two molecules thick) layer, and it will still retain ductility (which actually makes it one of the few metals that can be practically woven into a fabric). Since it's apparently so abundant as to make the material trivial to use (I wouldn't be surprised if there was magic involved in that, such as transmutation), it would follow that applying it to everything they want would also be trivial.

Otherwise, it would make sense to say that most of the things in Equestria are bronze, but not drawn/depicted in a way which would make that obvious.

Side note: there is a practical reason for using bronze for instruments. Shape may dictate the type of wavelengths permissible and the style of resonance within a cavity, but material changes how that instrument can transmit sound. An instrument made of rubber, for example, would absorb most of the sound, particularly at certain wavelengths (some notes would be far more flat than others). There's also noticeable differences between a carbon-fiber instrument and a wooden one. Carbon fiber gives a very "sharp" feel to the individual notes, while wood gives an illusion of softness/fullness because of how it rounds notes toward the ends of its range. Deeper notes simply sound better with wood, while they certainly sound more clear/crisp with carbon fiber. Brass has the right balance of hardness and ductility to allow a very wide range of vibrations to move through it, resulting in a wider range of sounds which do not get flattened/absorbed by the material itself. It's also why a gong (one of the larger ones) is typically made of cast-iron

In order for gold to be used as a chariot, magic for weight reduction and surface protection would have to exist. Both of these have been hinted at, but not explicitly shown to apply to these vehicles.

Well, it doesn't have to be made of gold for magical protection to be placed on it. I'd assume they'd like to place that on regardless of what it's made of.

My current attempt at a 'unifying theory' for all of this is that the Canterlot mountain, and by extension Equestria, has a plentiful supply of native gold or gold minerals such as auricupride, callaverite or petzite. This is then processed into a variety of equipment and aesthetic materials such as bits, chariots, stands, etc., most of which remain in Canterlot to contribute to the opulent 'palace' look while necessary commodities such as bits (the national currency) are shipped statewide. In contrast, gold is scarce in other places such as Griffonstone and possibly the Dragonlands, making bits an extremely valuable currency to own (and, to dragons, possibly a good source of food). Because Canterlot has so much gold available, and gold is so much easier to work than other metals once smelted, its use has turned to engineering products such as chariots, possibly with magical reinforcement to avoid mechanical failure of golden objects.

This seems a reasonable conclusion, though I wouldn't rule out the use of alchemical transmutation, since that would also fit MLP's general theme. Still, there may be issues with using it for engineering purposes; unless you've got a unicorn handy at your blacksmith's shop, he wouldn't be able to run his business.

This would likely mean blacksmiths need to pay for an enchanter's service, which is an extra cost on their overhead. So, any blacksmith which uses regular steel (and can do so proficiently) would have a sizable advantage over other blacksmiths, which would drive them toward the same practice. Though, that would also depend on how cheap and reliable said enchanter's services are.

You could argue that steel working is not a well-refined art, and therefore expensive, as it would require a lot of individual experimentation. Scratch that: I just thought of their railroads. You can't produce the steel necessary for that without a well-refined steel crafting art -_-

You'd also have to consider the weight of gold while it's being worked, though. I imagine trying to work a solid-gold wheel would be an enormous PITA, and I don't think it can be enchanted until after the product is finished. I can't recall a solid example where blacksmiths are portrayed in the show, but I would expect them to be earth ponies... imagine moving that around with your mouth o_o

So, I go back to my previous statement: it's more likely that they're making extensive use of gold leaf or gold plating, with exceptions to when the show explicitly states "this is made of solid gold." Gold seems abundant enough that this is not unreasonable, and it's useful for preventing corrosion on surfaces.

Either that, or the brass alloy you had already mentioned.

EDIT: more rambly than usual for me. I am le tired.

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Gold plating/leaf is a good point. In a 'real' world, it would rub off rather quickly on a chariot wheel, but I suppose the whole 'magical protection' thing could take care of that, depending on how strong it was.

Considering that most of the 'golden' objects are found in or originate from Canterlot (as far as I've seen in S1, anyway), couldn't most smiths be unicorns? In that case, they would likely have little difficulty lifting the gold objects with telekinesis.

Alchemical transmutation has been shown in the show (beginning of S1E6 - Boast Busters), but we haven't seen it from an engineering or manufacturing perspective.

I'd originally thought that iron was more scarce than gold in Equestria, but the railroads also smacked that theory out of the air. Gold-plated steel, then, would be a more logical choice for the chariot - a combination of aesthetic, surface protection from oxidation, and higher engineering strength. This might indicate other objects, such as brass instruments, are also gold-plated for aesthetic purposes. (I imagine cyanide gets quite a lot of use in Canterlot...)

It doesn't tell us much about the availability of other metals, though. So far, I've seen things that are definitively made of alloys of aluminum (kitchenware) and iron (farm implements, decorative black ironwork, other kitchenware), but not much else. We can't assume their availability of materials is exactly Earthlike, because of all the gold and gems. Not sure how close we can get while still accounting for those. If other elements we consider 'valuable' (Ag, Pt, Ru/Rh/Ir/Os/etc. to name a few) are common there, what's rare? We could say boron is a viable candidate, as all the valuable diamonds shown in the series thus far are blue-tinted rather than strictly white (on Earth, only diamonds containing a few ppm or more B have this color), but that's a weak observation to make a scientific statement about.

One could tally all the gems that have been discussed/referenced in the show thus far, and figure out which elements in what relative quantities could be needed for those to be widespread (or, in the case of a 'rare' gem, which might be scarce). So far, I came up with Si, Al, C, Au, Fe, Cr, Be, Cu, and possibly B, from mentions of diamond, sapphire/ruby, emerald, topaz, opal, and turquoise throughout the show. Of those, Be seems to be more common than normal (emeralds being easier to find), while Si seems to be about as common as on Earth (but in better conditions to form gems like opal/corundum variants).

Any evidence I might be missing? I haven't watched much of the later seasons, and one would think any episode with Maud Pie in it would provide better insight into the geology of Equestria.

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I imagine cyanide gets quite a lot of use in Canterlot...

Nah, you don't have to use cyanide to do that. Especially if they're using a "gilding" method.

Then again, Thermal Fisher seems to use a less hazardous process involving high voltage (and a nickel adhesion layer), so that may involve unicorns which can use some sort of lightning spell: https://www.thermofisher.com/blog/metals/how-gold-plating-is-done-step-by-step/

So far, I've seen things that are definitively made of alloys of aluminum (kitchenware)

I'm not so sure about that... I hate using aluminum in my kitchen. It has a greater tendency to warp, it discolors/corrodes more easily, and can often lend the food an odd and unwanted taste when something is being cooked for a longer duration (especially with lots of water, vinegar, wine, or salt). Pretty much everything I use is stainless steel (sometimes copper-plated to absorb heat better), cast-iron, or ceramic. Then again, maybe I'm the exception... *shrugs*

Anyways, throwing that tangent aside...

We can't assume their availability of materials isexactlyEarthlike, because of all the gold and gems. Not sure how close we can get while still accounting for those. If other elements we consider 'valuable' (Ag, Pt, Ru/Rh/Ir/Os/etc. to name a few) are common there, what'srare?

Remember that point I made about strong convection currents across the mantle and crust being required for an abundance of gems so close to the surface? That's because most gems form across various strata across the crust (lithosphere) layer, while diamonds and peridot form in the mantle. The gems which form in the crust still require materials drawn from deeper inside the planet (thus the need for active convection currents; those heavier elements would otherwise end up locked close to the planet's core), but they do not require much or any pressure by comparison. Largely, other precious stones such as agate and opal rely on precipitation and evaporation to form.

We can surmise an active core and convection layer through the use of magnets in the show... and the fact that they still have an atmosphere. You need a decently strong (it would seem to be Earth-like) magnetosphere for both of these things, which infers an active planetary core.

There's just one problem with this, though. Earthquakes/tectonic instability. With exception to the dragonlands, it could be that Equestria was once a very geologically active place (and no longer is), but if that process were still going on, I would find it unlikely that such would go unnoticed.

Still, we can tinker with this a bit to see what kind of things are more abundant or less. I'll have to re-watch some of Maude's episodes and cross-reference what's seen with actual geology to come up with a stronger conclusion.

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Nah, you don't have to use cyanide to do that. Especially if they're using a "gilding" method.

Then again, Thermal Fisher seems to use a less hazardous process involving high voltage (and a nickel adhesion layer), so that may involve unicorns which can use some sort of lightning spell:https://www.thermofisher.com/blog/metals/how-gold-plating-is-done-step-by-step/

True... but cyanide in MLP would be funnier. Electroplating would be pretty easy for pegasi to pull off, given their control of weather (I distinctly remember a lightning bolt in a jar in one of the episodes, but for the life of me I can't seem to find the screenshot). It might be a collaborative effort?

I'm not so sure about that... I hate using aluminum in my kitchen. It has a greater tendency to warp, it discolors/corrodes more easily, and can often lend the food an odd and unwanted taste when something is being cooked for a longer duration (especially with lots of water, vinegar, wine, or salt). Pretty much everything I use is stainless steel (sometimes copper-plated to absorb heat better), cast-iron, or ceramic. Then again, maybe I'm the exception... *shrugs*

Anyways, throwing that tangent aside...

I base that on the weight and color of a few of Pinkie's baking dishes. They're more or less identical to some I have in my kitchen, and Apple Bloom is shown supporting them on her head with little struggle (where cast iron, copper or ceramic would have certainly caused some problems). Again, this might be a quirk of animation, but I think it unlikely considering how visually similar they are to the ones I have.

EDIT: I have just been informed that those types of pans are actually made of steel, and the ones i have are mysteriously lighter than they should be given their thickness (or maybe I'm just misjudging their weight). Never mind!

There's just one problem with this, though. Earthquakes/tectonic instability. With exception to the dragonlands, it could be that Equestria was once a very geologically active place (and no longer is), but if that process were still going on, I would find it unlikely that such would go unnoticed.

I would imagine that with Equestria's thoroughly-controlled climate, they might have found a similar way to suppress or reroute tectonic activity, at least at or near the surface. Still, no evidence of that exists, and it could be that we just haven't seen it yet. From an Earth perspective, I've lived my entire life without experiencing an earthquake, and I live on the West Coast of the U.S., pretty close to the Ring of Fire.

From what I looked up on Wikipedia, diamonds are typically associated with kimberlite, which forms in something called a 'kimberlite pipe' that is violently ejected from a subterranean volcano deep within the mantle and solidified in an inverted-cone shape. If diamonds are easy enough to find that Rarity can grab a few for jewelry purposes from the Diamond Dogs, then it might be that kimberlite pipes are more common in Equestrian geology. Peridotite nodules can also be found in these same columns, but the show's never explicitly mentioned peridot (it might, however, show up in one of the images down below).

From the MLP Wiki page that has all the transcripts for every episode, I found that characters mention the following geological phenomena:

Maud: "This is a sedimentary rock."

Rainbow Dash: "Nope, I mean igneous. It's a kind of rock. Ask me how I know that."

Maud: "Isn't it obvious? There are specks of extrusive andesite on your hoof. It's a mountain rock."

Maud: "If you thought quartz was high on the Mohs hardness scale, wait 'til I tell you about corundum."

Igneous: "Surely thy name is not but Granny Smith. I am called Igneous Rock Pie, son of Feldspar Granite Pie."

Apple Bloom: "What does the rock look like?"
Maud Pie: "It looks like something that formed when volcanic lava cooled quickly."

Applejack: "I didn't mean to cause a fuss... Why don't we just open presents around the flag pole? It'll be fun, you'll see!"
Maud Pie: "Excuse me. You planted your pole on a fault line."

Maud Pie: "The first one is about rocks. They're all about rocks. 'Hearth's Warming is great. Like calcium silicate. What a wonderful day. As good as mica or clay.'"

Rarity: "Maud, darling! It's lovely to see you again! Oh! Congratulations on your rocktorate. What are you doing now?"
Maud Pie: "Talking to you."
Rarity: "Oh, y— Right. Well, if your trained eye happens to see a chartreuse gem, I'm desperate to find one."
Maud Pie: "I found one."

Rarity: "Oh, you're an absolute darling! This will surely make my gown stand out at Countess Coloratura's album release party. Do you know how rare this is?"
Pinkie Pie: "Just another day in Ponyville!"
Maud Pie: "That's actually a really common gem."
Pinkie Pie and Rarity: "Huh?"

[rocks crumbling, gems falling out]
Maud Pie: "These are all really common gems."

Maud Pie: "Rocks take on different properties when interacting with magic. With the right stone, you could rule all of Equestria if you wanted to."
Starlight Glimmer: "You're messing with me."
Maud Pie: "Am I?"
Starlight Glimmer: "So other than rocks, what else are you into?"
Maud Pie: Minerals. "Plate tectonics. Oh, and stand-up comedy, of course.

Starlight Glimmer: "Why do you find rocks so fascinating?"
Maud Pie: "Each one has a different story to tell. Like Boulder here. This tells me he's over two thousand years old. [to Boulder] You don't look a day over six hundred."
Starlight Glimmer: "Wow. You can tell that from a line?"
Maud Pie: "I didn't get a rocktorate because I can shred on guitar like nopony else."

Rarity: "Oh, no-no-no-no, no, not true. There's beauty in everything. Even these blah rocks aren't really blah. If you look closely, you can see flecks of gold in them. And the way the firelight dances on the cave wall, shadow and light? Ooh, it's so gorgeous! Sweetie Belle, have I ever told you about my favorite legend?"

Sunburst: "Starlight, what happened? Maud and I found some fascinating sedimentary stratum, but when I turned to show you, you were gone."

Sunburst: "We had to take out a few spaces to get it to fit, but you hardly miss them. Maud made the dice."
Maud Pie: "Pumice is the lightest igneous rock. It seemed the best choice."

Per the images of what Maud claims is a 'common' chartreuse gem, the only chartreuse gemstones I could find are peridot, chrysoberyl, enstatite, grossular garnet, idocrase, sapphire, and sphene. Of those, considering what else we know about Equestrian gems, grossular garnet and sapphire are two very likely alternatives. It could be that greenish-yellow sapphires just aren't very valuable in Equestria (same as on Earth, actually, as they're one of the more common kinds). Alternatively, also like Earth, garnets could be not very valuable compared to other, 'better' gemstones.

EDIT: Here's the latest version of that document I'm still writing about my observations of each episode. I'm not exactly happy with some of the conclusions I've made so far, but this contains my best guess about everything up until S1E15 (Feeling Pinkie Keen).
https://docs.google.com/document/d/1QMNiz2wAoHKgTr7N7eC7Ob0d9cDnI9gmJSCpbrASdl4/edit?usp=sharing