Tidal Locking - Equestrian Orbital Mechanics

[SkySoldja 7]

Apologies for the missing equations, I am trying to figure out how to post the actual document itself.

 

 

 

 

 

 

 

 

 

My Little Planet: Entropy is Tragic

Volume One:

 

The Celestial Mechanics of Equestria

 

 

Introduction

I was first introduced to the pony show by a couple of friends of mine who had three little boys and a girl; the whole family loved the show. Now, this was early 2013 so I am a bit of a latecomer to the… um, herd. My own daughter loved the show (and books, and toys), and I shamelessly used her as an excuse to watch it as well. At first, I resisted participating in the fandom, but now that I’ve written an Equestrian orbital physics paper, I guess there’s no turning back.

I will start off this (very informal, plain-language) paper by briefly addressing a glaring issue from the show that caused me great mental distress, then explore the original pre-magic state of the Equestrian planetary arrangement, and wrap up by describing the magical process that changed everything and made life on our characters’ home planet possible. But first, a few side notes.

 

Perspective and Giants’ Shoulders

Science is not the only thing which fascinates me, about the show or in general. But there is a sprawling megapolis of pony fandom out there already analyzing every last drop out of this show in terms of characterization, narrative, world-building and theming. There may come a day when I can scrape together enough original thought on those subjects to add something worthwhile to the ponysphere, but for now this is where I think I can best contribute. I do really enjoy story-crafting, however, and I haven’t been this into a story since The Lion King.

I have read exactly one other work on the physics of the ponyverse, so it gets cited right up front. Check out “How Celestia and Luna "Raise" the Sun and Moon” by Comet Tail on the MLPForum[1]. Comet Tail and I approach the idea of Equestrian orbital mechanics from two different directions, I focus on tidal locking and Comet Tail on retrograde and erratic orbits, a concept I really enjoyed.

Last side note: I don’t consider any of this to be head canon. I think there is a difference between the extrapolation of concepts which the canon story directly implies—and even the analysis of those implications—versus real head canon, which implies the introduction of at least some new material into the story, characters, or world. Now don’t get me wrong, I likes me some head canons. I’m just going to limit the content of this paper to those things I consider direct extrapolation from the show’s story material, and straightforward analysis of that, and save the head canon for another edition.

 

 

The Curious Case of the Backward Moon

For all my enjoyment of the story, characters and world of Equestria, and even the scientific and philosophical implications of the world, I probably would never have committed any serious effort to exploring the subject of this paper if not for one blatant violation of sensible orbital mechanics which drove me crazy. And drove me to research.

From the first moment I heard that Celestia raises and lowers the sun and Luna the moon, what my brain heard was that Celestia rotates the planet and Luna revolves the moon. Not everyone made this assumption and there are plenty of geocentric model fans out there in the ponysphere, but that is what happened in my head. This assumption stood unchallenged until the ending of the season four two-part premier, where during the Summer Sun Celebration, Princess Luna lowers the moon for all to see, and then Princess Celestia raises the sun in the same part of the sky. It was as if the moon and sun had simply swapped places with each other, with no explanation. This happens a few other times in the show, but always as a cartoony effect easily dismissed as just a fun way to move the story (also, because Discord). But in S04 E02 it is a conscious act draped in a formal ceremony. So, the sun and the moon move across the sky in opposite directions? What does that even mean? After some thought, I decided that this was either the single best geocentric argument in the whole show, or a special event that isn’t representative of a normal day in Equestria.

Most of the time, a planet and moon both revolve and rotate in the same direction as the rotation of the star around which they orbit, all either clockwise or counterclockwise depending on if this is being viewed from the system’s ‘north’ or ‘south’. This is called prograde motion; when a body rotates or orbits in the opposite direction it is called retrograde motion. While retrograde orbit moons are present even in our own solar system, this phenomenon would not begin to explain a moon that appears to travel in the opposite direction across the sky as does the parent star from the viewpoint of the planet’s surface. This called apparent retrograde, and it is very different.

Regardless of direction, a spinning body tends to rotate significantly faster than anything orbiting it revolves. Take our own planet and moon for example. Earth ‘spins’ or rotates in exactly one day (that is the definition of a day, after all). The moon orbits Earth in about 29.5 of these days, so either way it revolves, prograde or retrograde, it will still appear to travel east-to-west across the sky, because that’s how everything that slow appears to move due to planetary rotation. So what would have to be going on for a west-to-east moving… anything?

Anything orbiting retrograde in respect to the direction of rotation of the orbited body will always appear to travel east-to-west, and anything orbiting at all at a lower angular velocity (fewer degrees per unit of time) will also appear to travel east-to-west. Only something orbiting in the prograde direction with a greater angular velocity than the rotation of the orbited body will appear to travel west-to-east. Around Earth, only artificial satellites do this. One simple reason for this is escape velocity. The further away you get from a gravity source, the less linear velocity (rate of motion through space) is required to escape its gravity well. A prograde orbiting body at geosynchronous-plus angular velocity at a distance (orbital radius) typical of moons would simply fly away into space. Or, more likely, into the nearest star.

Here’s an example. The equation for escape velocity (which is a misnomer, it should just be ‘escape speed’, because any direction that doesn’t cause a collision will result in escape) is:

 

Where  G is the Universal Gravitational Constant of 6.67 x 10^-11 m³ kg^-1 s^-2

            M is the mass of the body being escaped in kilograms and

            r is the radius, or distance separating the two, measured center-to-center in meters.

The average distance from the center of Earth to the moon is 384,399 km. At this radius, the moon’s orbit traces an ellipse 2.415250 x 10⁹ m in circumference (2πr), or about 1.5 million miles. At exactly geosynchronous orbit, or an angular velocity of 15° per hour (360° per 24 hours), this works out to be a tangential (linear) velocity of 27,954 m/s ((2.348949 x 10⁹ meters traversed) / (86,400 seconds in one day)), which is over 62,000 mph. The escape velocity at that same radius from Earth, a mass of 5.97219 x 10²⁴ kg, is 1,439 m/s, or about 3,200 mph. So just to maintain position in the sky, the moon would have to exceed its planetary escape velocity by over 19 times. To actually move from west to east, it would need to go faster still. While the home planet and moon of Equestria do not need to be exact copies of Earth and its moon for the story world to work, the magnitude of impossibility involved here leads me to the conclusion that the show writers never intended to imply that Luna (or Celestia, for the millennium prior to episode 1) causes the moon to cross the sky in a west-to-east direction, even with telekinetic magic. Yet this is exactly what seems to occur in the season 4 premier, part two.

My conclusion is that due to the chaos unleashed by the Plunder Seed vines’ entrapment of Celestia and Luna and their attack on the Tree of Harmony, the planet and moon of Equestria were left in very unusual positions relative to each other and their star. After all, directly after Celestia and Luna’s abduction, both the sun and moon were left hanging together in the sky, causing panic among the populace, and justifiably so. In this scenario Luna simply backed the moon down from its crazy position towards something more normal, followed by Celestia’s moving the planet back to its regularly scheduled rotation. Even this scenario involves Luna temporarily revolving the moon prograde at an insane velocity without shooting it across space like a severed tether ball, but temporary is better than routine. Either this, or the ponyverse really is geocentric.

Also, the writers probably just didn’t care, and my daughter wasn’t bothered in the slightest. And then I gave Hasbro some money for a toy for her, so I guess they win.

 

Formless and Void

The show’s world building has on more than one occasion implied that without magic, life on Equestria[2] would be difficult or completely impossible. I’ve already mentioned how extremely powerful magic is required to properly rotate the planet and revolve the moon. Both of these things are crucial for planetary life to thrive. The mortal and even non-magical residents of Equestria also seem to have a part to play, as evidenced by such episodes as Winter Wrap-up, Hearth’s Warming Eve and Hurricane Fluttershy. Magic or else considerable effort is necessary or at least really helpful in seasonal procession, cloud creation, and even animal migration and hibernation. To describe what Equestria might have been like prior to the influence of magic, I need to explain two concepts: entropy and tidal locking.

Entropy is essentially disorder, with a certain sense of inevitability. When a system is highly organized and complex, it is said to have very low entropy. A brass watch is complex and organized, so it has low entropy, while that same amount of brass melted and re-solidified as a nugget has higher entropy, because it is simple and disorganized. The second law of thermodynamics teaches us that the overall entropy of a system always increases when left to spontaneous (naturally occurring) forces. By investing organized effort, a system can undergo a local and/or temporary decrease in entropy (increase in order), but only at the cost of enough expended useful energy that the overall effect of a larger system is an increase in entropy.

The same holds true at the scale of a planet or star system; entropy increases over time. Rotations slow down, satellites either escape or fall into their planets or stars, and ultimately, the star itself dies in one of a number of ways. Of course, the law of entropy does not take into account magic, but more on that in a moment.

The second concept, tidal locking is a result of tidal bulging and braking, the subject of some discussion in the piece by Comet Tail which I referenced earlier. As a moon rotates and revolves it tends to flatten a bit due to the gravity of its planet (provided its planes of rotation and revolution are sufficiently aligned). Like any other macroscopic physical object, moons do not have uniform density, so different longitudinal cross-sections will present more or less mass than its average density would present, so this flattening is likewise not uniform. The cross-section that is flattened the most is referred to as the major axis, or simply the ‘bulge’.

Once a tidal bulge emerges, it begins to alter the angular velocity of the rotating moon. As the rotation swings the major axis closer and closer into alignment with the planet’s gravitational pull, the angular velocity increases slightly, in a way falling into place. As the inertia of the moon’s rotation then begins to pull the major axis out of alignment, the angular velocity decreases, now fighting gravitational drag. This effect is referred to as ‘tidal braking’.

The cumulative effect of repeated tidal braking is that the moon favors its major axis more and more, which in turn increases the severity of the bulge more and more. Eventually, the planet’s pull on the major axis is actually stronger than the force of rotational inertia, and the moon slips into a rotation period equal to its revolution period, thereby ‘tidally locking’ onto its planet. In this arrangement the same hemisphere of the moon is permanently facing the planet as in the case of our own moon.

Before a moon has tidally locked to its planet (or a planet to its star), it is possible to roughly[3] approximate the time until it does so with the formula:

 

Where  w is the rotation rate (in radians per second) of the satellite

            a is the average of the perigee and apogee of the satellite’s orbit (in meters)

            I is the satellite’s moment of inertia (in square meter kilograms), which can be estimated as (0.4)(m_s)(R²)

            Q is the dissipation function of the satellite (no units), which can be estimated as 100

            G is the Universal Gravitational Constant

            m_p is the mass of the orbited body (in kilograms)

            k₂ is the tidal Love number of the satellite (no units), which can be estimated as much less than 1 (typically around 0.1 for a mostly solid satellite)

R is the average radius of the satellite (in meters) and

m_s (from the description of I) is the mass of the satellite (in kilograms).

Examples of tidal locking are all over our solar system. Earth, Mars, Jupiter, Saturn, Uranus and Neptune all have moons tidally locked to them, and Pluto and its satellite Charon are tidally locked to each other.

What does this have to do with Equestria? Well, hopefully it’s clear that these two concepts are related. Tidal bulging, braking and locking are all examples of the unstoppable march of entropy on a lunar and planetary scale. As time goes on, orbital mechanics slip from complex arrangements into straightforward ones, which are sadly ineffective at supporting life. A tidally locked moon is not unusual, but an otherwise M-class planet tidally locked to its star would be completely uninhabitable, a blistering super-desert on the sun-ward hemisphere and frozen perpetual night on the other.

This is the cataclysm that Celestia and Luna guard their subjects from, absolute extinction across the entire planet.

 

 

Let There be Magic

There isn’t too much detail I can offer as to exactly how the alicorns would have gone about decreasing entropy and resetting the required rotations and revolutions without getting into head canon territory, which I pledged not to do in this volume. But here’s what I have:

According to what I perceive the story has told us about its world, this was the original, no-magic state of the Equestrian solar system. A planet locked onto its star, unable to rotate beyond its revolution around the star, unable to support life. A moon not only locked onto its planet Earth-style, but also tidally ‘pinned’ in place between the planet and the star, its revolution in sync with the planet’s revolution. This moon would appear to hover directly above the planet’s surface at exactly the sun-ward pole, casting an unmoving solar eclipse shadow on the surface of the planet’s desert side, creating a small area of shade, assuming a roughly Earth-like size-and-distance arrangement. Solar magic is required to rotate the planet any faster than its one day per year rate, and lunar magic to revolve the moon any faster than its one month per year rate.

It seems most likely that once the alicorns (whoever they were and wherever they came from) decided to revive Equestria’s ability to sustain life (for whatever reasons), they would have first begun to accelerate the rotation of the planet, as this is absolutely necessary and the change requiring the most energy. But there’s a problem. The moon is locked on to the planet’s tidal bulge axis too strongly. As the alicorns accelerate the rotation of the planet, the moon tries to match angular velocity to maintain its position relative to the planet’s surface. But the star’s gravity pulls it back, threatening to tear the satellite apart. So the alicorns would then have to exert magical force to slow down the moon’s revolution as the planet continued to spin faster and faster. The moon’s orbit would still be accelerating (from one per year to the order of 10¹), just not as rapidly or as high as the acceleration of the planet’s rotation (from one per year to the order of 10²).

With the planet now rotating hundreds of times per revolution and the moon now revolving tens of times in the same time period, key changes begin to happen. The hemisphere-spanning super glacier begins to melt, evaporate, and partially refreeze in a daily cycle, causing intense flooding and erosion. The desert cools and gigantic storm fronts race around the globe as the planet’s rotation and cycles of heating and cooling the atmosphere rapidly change temperature and pressure. The revolving moon now pushes and pulls the emerging liquid water in a tidal bulging sequence of its own, beginning to delineate land from sea.

Assuming the planet has the internal structure of one at all capable of sustaining familiar life, the now spinning core begins to assert a discernable geomagnetic field and trap energetic particles into its magnetosphere and plasmasphere. This provides an increasingly strong shield against dangerous particles and electromagnetic radiation from space, restoring some habitability to the planet.

After these and many other effects have emerged and stabilized, two last pieces of the puzzle remain, neither of which is assigned a patron alicorn in the show like Celestia and Luna. The first of these is planetary tilt. At full planetary tidal lock, there would be no rotational tilt, no angle separating the planes of planetary rotation and revolution. But tilt is required for seasonal procession, and Equestria definitely has seasons. The final element of a restored living planet is of course biological life. How the various life forms were created or restored must remain purely in the realm of head cannon, however. All we know is that on Equestria all of ponykind, and perhaps other sentient species are active participants in the march of time. Seasons, weather and the life cycles of other forms of life are enabled and guided by mortal hooves.

 

Well, there you have it. I hope you’ve enjoyed my paper and that whatever amount of time you just spent reading it was not wasted. I would (probably) enjoy your comments and questions.

 

 

 

Next:    Devolution, Natural Selection and Immortality

Soon:   Talent, Choice and Cute Marks of Destiny

Later:   Twilight and the Divine Harmony

 

 

About the Author

The author is currently serving as a Senior Scientific and Technical Analyst at the National Air and Space Intelligence Center in Dayton, Ohio. He holds a Bachelor of Arts in Business Administration from Malone University in Canton, Ohio as well as Associate of Applied Sciences degrees in Intelligence Studies & Technology and in Scientific Applications Technology. He and his wife live in the Dayton area with their daughter, who loves the ponies, especially as toys gathered around a play tea set.

[1] http://mlpforums.com/topic/27530-how-celestia-and-luna-raise-the-sun-and-moon/

[2] For the rest of this paper, rather than invent a name for the planet, I will refer to both the realm ruled by Celestia as well as the actual planet which hosts that realm as “Equestria”. Which is meant should remain clear in context.

[3] No, really, it’s pretty rough: http://en.wikipedia.org/wiki/Tidally_locked#Timescale

 

[Zefir 34]

 That is quite a work. Comprehensive, detailed, also sadly hard to understand to someone with basic physics education, let alone any random user who happens to stumble upon this topic. There are quite a few terms and concepts introduced, and while they are properly explained, they still solidify the appearance of insurmountable wall of text.

This piece deserves far more attention than it is getting, however it's posted in place used mostly for discussion involving the show alone, without involving any scientific fields in it.  

 

 

What does raise questions is the assumption that Equestria's universe can be so directly compared to our own. After all, celestial bodies do not behave in the same way, with Equestrian's sun and moon shining their own light, an aura almost. Also the sheer precision and expertise that is required to maintain a system like that, especially if all the elements were moving, would be impossible to achieve, even for immortal demigods (which may be possible, however is still unlikely, especially considering not seeing what you are supposed to move).

 

 

Another problem is the idea of pre-magic Equestria. I do not believe that magic was an alien, or non existent element anywhere in this universe's timeline. It seems to be present everywhere, even if separate from forces commonly known to us. Each and every single aspect of Equestria's existence seems to be regulated by magic. It's not merely right conditions of the inhabited planet, but the sheer magical force itself keeping its citizens alive (which is shown in Twilight's Kingdom). Magic is used for literally everything, one way or another. That suggests a different perspective to this realm's inner workings. It is no secret that this show wasn't made as a complete, self compatible masterpiece. Most of the writer's probably don't know enough about physics and astrology to even consider the effect of shifting celestial bodies by two immortal mares, instead turning to ancient myth-like logic, requiring only a basic understanding of things around them, filling any gaps with simplistic yet imaginative magic.

 

 

But overall I think this is quite well put together, in depth and very informative perspective on Equestria's solar system. I look forward to more works like that. 

Edited December 25, 2014 by Zefir

[Alleviate 342]

I like to keep science and magical talking ponies separate, not to say I don't indulge in a little application of learning myself, from time to time. Sadly, as I am only at AS Physics level currently, I'm taking a little while to work my mind through all of this. 

 

Overall, the only workable comparison we currently have is our own, when it comes to the celestial bodies and the universe in general, but, due to what we've seen from the show, and a little assumption, I think it can be safely said there are large similarities, though also large differences. I have to say, I am a fan of the geocentric plan of the Equestrian universe (GODPONIES, 'nuff said.)

 

Just wondering if anyone's ever even thought about the conversion rate of magic (Of the various sorts) to more standard measures of energy and power...

 

 

 

Next:    Devolution, Natural Selection and Immortality Soon:   Talent, Choice and Cute Marks of Destiny

 

These concepts both interest me hugely. The biological sciences of Equestria I have my own theories on, I eagerly await. Especially the idea of a Natural Selection process in a land governed by super-powered, eternal, generally benevolent princess.

 

It's late and I feel I ramble. Consider this work mentally pinned, and I shall research unto full understanding, at least, what I can reach before the end of the holidays.

[sweetolebob18 724]

Well, I've always (if 6 months = always) been a firm believer in the "Equestria is flat & Celestia & Luna actually raise the sun & moon" school of thought.

 

One thing I've often wondered, though.  IRL you've got 4 forces. Strongest to weakest they are Strong Nuclear (binding force of atoms), Electromagnetism, Weak Nuclear (chemical reactions) & Gravity.   I've always wondered where Magic fits on that scale.

 

Clearly, magic can overcome gravity (that's how they lift stuff, including the sun & moon), but where is it in relation to the others?  Also, do the sun & moon cause the tides in EQ, or is there a Sea Pony equivalent of Luna & C who does that? 

[truth is life 76]

A tidally locked moon is not unusual, but an otherwise M-class planet tidally locked to its star would be completely uninhabitable, a blistering super-desert on the sun-ward hemisphere and frozen perpetual night on the other.

 

Not quite, actually! Atmospheric effects can keep temperatures fairly clement all over the planet (as on Venus, which although not tidally locked to the Sun still has a very long solar day, lasting 116 Earth days, but which has a virtually uniform temperature due to trapping and transport of heat by the Venusian atmosphere). I have seen computer modeling that indicates this could occur on less extreme planets as well, especially planets with oceans (which are very efficient transporters of heat). Besides that, there's the possibility of inhabiting the twilight areas between the day and night poles, which would not necessarily be particularly extreme in temperature or environment. Tidal locking would probably be problematic mostly because it either means the planet is so close to its star that it is not habitable in the first place, or it is close to a red dwarf, which are more commonly flare stars.

 

Also, I want to correct you on one point, because it's a common misconception. A magnetosphere is not required to shield planetary surfaces from cosmic radiation; the bulk of that protection is provided by the sheer mass and bulk of the planet's atmosphere. Any planet that has an atmosphere thick and massive enough to create habitable pressures at the surface will also suffer essentially negligible levels of cosmic radiation. Earth's atmosphere, for example, provides the equivalent of 63 half-value densities against cosmic gamma rays (okay, gamma rays are not common), reducing their intensity by a factor of 2^63, or some trillions of times. (Additional evidence for the non-necessity of the magnetosphere in providing radiation protection is the fact that there have been a large number of magnetic reversals, involving weakened magnetic fields, in Earth's history, with no noticeable effect on life). A magnetosphere is important to retain an atmosphere for cosmic periods of time except in exceptional cases (like Venus), but in the relatively short run isn't crucial.

 

Personally, as a physicist myself, my view is that the MLP universe pretty clearly does not work on anything like our own rules in any but the broadest sense, and that the show works on cartoon logic anyways, so it doesn't really make very much sense to try to quantify their capabilities and construct realistic models for how their world could work.

[SkySoldja 7]

Wow, long time between logins. Real life is so needy sometimes.

 

 

 

the appearance of insurmountable wall of text. This piece deserves far more attention than it is getting, however it's posted in place used mostly for discussion involving the show alone

Zefir: Thanks for the comment! Yeah, the “school paper” format doesn’t translate well into a forum. I would love to find both a better format and location to post. I chose this forum area because that’s where CometTail’s piece was, but I’m all ears for suggestions. I’m pretty new here, as I’m sure is evident. As to holding Equestria to most of the same laws of physics which govern our world being unnecessary, I totally agree. And the fact that magic is so ubiquitous on Equestria is a legit strong argument for that perspective.

But this highlights a quirk which may or may not be unique to my perspective, and explains why I would make a really poor critic of the show. First, I have an immersive enough imagination that I have a very “magic window into another time and place” approach to watching the show, meaning I almost never have the “that makes no sense” reaction to things. I just accept that it makes sense in that world even if I don’t get it right away. On the other hoof, I have enough scientific interest/education/competence that there are some things that I just cannot abandon. The heliocentric model didn’t just turn out to be the model that describes our experience, it’s the only one that works. Period. So I’m stuck. Tell me magical talking candy-colored ponies inhabit a world of dragons, phoenixes, equine pixies and spontaneous singing, and I’m all on board. But tell me that celestial mechanics don’t work the way they should and I pitch a fit. Oh, well. It will make for some interesting papers, at least.

 

 

 

These concepts both interest me hugely. The biological sciences of Equestria I have my own theories on, I eagerly await. Especially the idea of a Natural Selection process in a land governed by super-powered, eternal, generally benevolent princess.

Shardikku: Thanks for the comment! I think CometTail or else somepony in his comments did some math and came up with some impressive megawattage. And I’m glad you’ll be interested in the next papers, I hope they hold up. I’m working on the next one right now; I wasn’t totally sure anypony would be interested so I only wrote the one ahead of time.

 

 

 

IRL you've got 4 forces. Strongest to weakest they are Strong Nuclear (binding force of atoms), Electromagnetism, Weak Nuclear (chemical reactions) & Gravity.   I've always wondered where Magic fits on that scale.

Sweetolebob18: Thanks for the comment! I’m actually including the four fundamental forces in my current paper. Stay tuned! I’m not sure if there’s an Alicorn of the tides or anything, but I have seen some ads for a comic story that addresses “Aquastria” and its equine demigod. Celestia’s cousin, no joke, if I remember correctly.

 

 

 

Not quite, actually!

Truth is Life: Thanks for the comment! Interesting information on the uniform temps on tidally locked worlds. I wonder if it might be a bit more delicate for worlds in the terrestrial goldilocks zone? Venus’ climate may be more uniform thanks to its thick atmosphere, but that mean surface temp is 462° C. Here on Earth, for example, the temperature changes significantly with the daylight terminus, even though we have a dizzying 24 hour day. I don’t think tidally locking onto our star would give us a more uniform temperature. As to the necessity of a magnetosphere, I’d be interested to see the breakdown of “short-term” and “cosmic scale” as you are using the terms. I have always read the ionosphere, magnetosphere, and plasmasphere presented as fairly important to our enjoyed relative safety from EM radiation and energetic particles.

[sweetolebob18 724]

Back in the 1970s I read a book called "Habitable Planets For Man" by Stephen Dole (IIRC).  One of the points was How long could day be?  Unfortunately, I lost my copy while moving & it seems to be out of print.  However, IIRC, it was 48 hours before the day/night temperature difference got to be too extreme to be tolerable.  One point the author made was that temperature differences are what powers storms. The longer the day, the more extreme the storms.

 

Another point was that plants don't need nearly as much light as the sun puts out.  Anything that is bright enough for us to see would have enough light for plants to grow.  As to length of year, streams depend on snow pack for water.  Too long a summer would kill the plants with drought.  Too short a summer & you get an Ice Age.

[truth is life 76]

Truth is Life: Thanks for the comment! Interesting information on the uniform temps on tidally locked worlds. I wonder if it might be a bit more delicate for worlds in the terrestrial goldilocks zone? Venus’ climate may be more uniform thanks to its thick atmosphere, but that mean surface temp is 462° C. Here on Earth, for example, the temperature changes significantly with the daylight terminus, even though we have a dizzying 24 hour day. I don’t think tidally locking onto our star would give us a more uniform temperature.

Oh no, Earth-like planets would probably not be terrifically uniform in their atmospheric temperatures (though ocean temperatures are another story, given sufficiently good communications between different parts of the world). Venus was simply an example of how other properties (in this, an extremely dense atmosphere that can efficiently transport heat) can overwhelm the day-night cycle length.

 

I can't cite the studies I saw, since they were presented as talks, but I did come across this rather succinct article, which concludes that a reasonable Earth-like tidally-locked exoplanet would have extensive areas of open sea and ice-free land, provided the continental configuration isn't completely ridiculous (like having a giant supercontinent filling the ENTIRE night hemisphere), and would be quite habitable, though chilly. There would be no need to rotate it faster to settle it.

 

As to the necessity of a magnetosphere, I’d be interested to see the breakdown of “short-term” and “cosmic scale” as you are using the terms. I have always read the ionosphere, magnetosphere, and plasmasphere presented as fairly important to our enjoyed relative safety from EM radiation and energetic particles.

The ionosphere is simply created by the impact of solar wind and cosmic particles into the atmosphere, so will self-form provided there is an atmosphere at all (Venus and Mars, despite lacking magnetic fields, both have ionospheres). As for the rest, all I can say is that the necessity of a magnetic field is a common and intuitive misconception that simply doesn't square with the data when you look into it.

 

As far as time-scales, "short-term" means anything up to millions of years, whereas "cosmic scale" means hundreds of millions to billions. Atmospheric erosion is an extremely slow process once you get past the lightest particles, so that it's mostly the amount of activity (or lack of activity) on the planet that's going to determine the atmospheric thickness.

Edited January 30, 2015 by truth is life

[sweetolebob18 724]

As to temperature variations on tidal locked planets.  Earth right now is (probably) in an extremely unusual state.  I've seen episodes of Nova which said there were large dinosaurs within 200-300 miles of the north pole & they didn't hibernate & the newly hatched were too small to migrate far.  This means that plants (probably) grew year round that close to the north pole.

 

Earth only has ice caps because there is a south polar continent & the Artic ocean is fairly isolated from the Pacific.  As best we can tell, 80%+ of the time, Earth had no polar ice caps.

 

On a tidal locked planet, the ocean acts as a heat sink.  +Evaporation is a cooling action &  condensation is a warming action.  Here in Phoenix, we get most of our rain about sunset.  This is when thunderstorms & tornadoes tend to start.  A tidal locked planet would probably have a storm belt about the sunset & dawn lines when the hot & cold air mixed.

 

For EQ, this might well be extreme enough to ground Pegasi.  +If this happens all the time, flying cities like Cloudsdale either won't be built or will have to keep moving fast enough to stay ahead of the storm line.  On Earth, this would be 1000 MPH at the equator (obviously impractical), but a tidal lock planet would be slower.  (On the moon, for example, it takes a month to rotate instead of a day)

[Comet Tail 808]

 That is quite a work. Comprehensive, detailed, also sadly hard to understand to someone with basic physics education, let alone any random user who happens to stumble upon this topic. There are quite a few terms and concepts introduced, and while they are properly explained, they still solidify the appearance of insurmountable wall of text.

This piece deserves far more attention than it is getting, however it's posted in place used mostly for discussion involving the show alone, without involving any scientific fields in it.  

 

 

What does raise questions is the assumption that Equestria's universe can be so directly compared to our own. After all, celestial bodies do not behave in the same way, with Equestrian's sun and moon shining their own light, an aura almost. Also the sheer precision and expertise that is required to maintain a system like that, especially if all the elements were moving, would be impossible to achieve, even for immortal demigods (which may be possible, however is still unlikely, especially considering not seeing what you are supposed to move).

 

 

Another problem is the idea of pre-magic Equestria. I do not believe that magic was an alien, or non existent element anywhere in this universe's timeline. It seems to be present everywhere, even if separate from forces commonly known to us. Each and every single aspect of Equestria's existence seems to be regulated by magic. It's not merely right conditions of the inhabited planet, but the sheer magical force itself keeping its citizens alive (which is shown in Twilight's Kingdom). Magic is used for literally everything, one way or another. That suggests a different perspective to this realm's inner workings. It is no secret that this show wasn't made as a complete, self compatible masterpiece. Most of the writer's probably don't know enough about physics and astrology to even consider the effect of shifting celestial bodies by two immortal mares, instead turning to ancient myth-like logic, requiring only a basic understanding of things around them, filling any gaps with simplistic yet imaginative magic.

 

 

But overall I think this is quite well put together, in depth and very informative perspective on Equestria's solar system. I look forward to more works like that. 

 

Why is moon-glow a problem?

 

 

Admittedly, the night-side of the moon seems to be reflecting light as well, but I should point out that it will reflect both starlight and reflected light from Earth. If OP's analysis on the apparent retrograde motion of the moon is anything to go by, it seems that the moon could be in a much lower orbit and much smaller; in which case it would reflect a lot more light from Earth than ours does.

 

Also, this is purely visual. I'm not sure the animation is a good source for measuring relative apparent magnitudes. Considering how large ponies' eyes are, I'd almost expect them to be sensitive enough to see the night side of the moon rather well

 

Furthermore, it's very possible that life on Equestria made adaptations to magic. One example I can produce as to how quickly life can adapt is Movile Cave, Romania.^[Link] Life there is based on chemosynthesis rather than photosynthesis, and has adapted to oxygen levels less than half that of open air, and thrives off of methane and hydrogen sulfide. Similarly, once magic was introduced to Equestria, it's very believable that life there began to adapt in such a way to take advantage of the newly-introduced resources, then outpopulate non-adaptive life through natural selection, resulting in a biome that has become dependent upon magic.

 

 

I like to keep science and magical talking ponies separate, not to say I don't indulge in a little application of learning myself, from time to time. Sadly, as I am only at AS Physics level currently, I'm taking a little while to work my mind through all of this. 

 

Overall, the only workable comparison we currently have is our own, when it comes to the celestial bodies and the universe in general, but, due to what we've seen from the show, and a little assumption, I think it can be safely said there are large similarities, though also large differences. I have to say, I am a fan of the geocentric plan of the Equestrian universe (GODPONIES, 'nuff said.)

 

Just wondering if anyone's ever even thought about the conversion rate of magic (Of the various sorts) to more standard measures of energy and power...

 

 

 

 

These concepts both interest me hugely. The biological sciences of Equestria I have my own theories on, I eagerly await. Especially the idea of a Natural Selection process in a land governed by super-powered, eternal, generally benevolent princess.

 

It's late and I feel I ramble. Consider this work mentally pinned, and I shall research unto full understanding, at least, what I can reach before the end of the holidays.

 

I could list the reasons I'm both disgusted and horrified by the geocentric model, but not the least of which is that it largely precludes any significant space travel, and limits the habitable confines of the universe to be extremely small, indeed, more or less precluding the rich vastness of the universe as we know it. The wonder of the vastness of the universe is, in my opinion, one of the very things that make life worth living. A universe confined to a single world is truly a horrifying prospect to me, to say the least.

 

[...]

After these and many other effects have emerged and stabilized, two last pieces of the puzzle remain, neither of which is assigned a patron alicorn in the show like Celestia and Luna. The first of these is planetary tilt. At full planetary tidal lock, there would be no rotational tilt, no angle separating the planes of planetary rotation and revolution. But tilt is required for seasonal procession, and Equestria definitely has seasons. The final element of a restored living planet is of course biological life. How the various life forms were created or restored must remain purely in the realm of head cannon, however. All we know is that on Equestria all of ponykind, and perhaps other sentient species are active participants in the march of time. Seasons, weather and the life cycles of other forms of life are enabled and guided by mortal hooves.

 

[...]

 

Fantastic read. Though I must ask, it sounded like your description of pre-magical Equestria has the moon sitting at Lagrange Point L1? Or I suppose it could work anywhere, in general. It seems to me though, that a lunar orbital period as long as a year would put the moon at such a distance that orbital effects of each body's orbit around the star would drive the two worlds apart. Admittedly, I don't have much of a quantitative argument, but qualitatively I believe that would be very far outside Earth's SOI.

 

Oh, and I've quoted this particular paragraph because it seems to me to hint very strongly that there's a connection, which seems to stand out to me. If the princesses put the world into a rotation with negligable axial tilt, then that would explain why seasons must be done manually. A short burst of activity to somehow create a thick cloud layer to reflect much of the sun's light, cooling the surface, allowing for snow and a runaway process of increased albedo, and thus cooled surface, could create an artificial winter. When it comes time to end it, they need only decrease the amount of area that reflective objects (clouds, snow) cover and thus decrease their worlds' albedo, causing a runaway warming effect to melt the rest of the snow.

 

Thinking on this further; the amount of horsepower required for this would be staggering - essentially completely impossible for a world like Equus (Equestria's planet). An idea that comes to mind is perhaps that there are regular seasons - but that their effects are minute enough to not overpower the runaway effects...

 

Actually, as I've been typing out, I've decided to make my own post about this. It'll be coming shortly.

 

EDIT:

 

Here it is as the latest post at the moment: http://asksciencepony.tumblr.com/

Permalink: http://asksciencepony.tumblr.com/post/109959398800/non-sequitur-winter-wrap-up

Edited February 3, 2015 by Comet Tail

[Buck Testa 5,503]

 

Apologies for the missing equations, I am trying to figure out how to post the actual document itself.

 

 

 

 

 

 

 

 

 

My Little Planet: Entropy is Tragic

Volume One:

 

The Celestial Mechanics of Equestria

 

 

Introduction

I was first introduced to the pony show by a couple of friends of mine who had three little boys and a girl; the whole family loved the show. Now, this was early 2013 so I am a bit of a latecomer to the… um, herd. My own daughter loved the show (and books, and toys), and I shamelessly used her as an excuse to watch it as well. At first, I resisted participating in the fandom, but now that I’ve written an Equestrian orbital physics paper, I guess there’s no turning back.

I will start off this (very informal, plain-language) paper by briefly addressing a glaring issue from the show that caused me great mental distress, then explore the original pre-magic state of the Equestrian planetary arrangement, and wrap up by describing the magical process that changed everything and made life on our characters’ home planet possible. But first, a few side notes.

 

Welcome to the "herd." Its always nice to see intellectual tyes talk about cartoon physics, its my favorite pass time actually. 

 

 

Perspective and Giants’ Shoulders

Science is not the only thing which fascinates me, about the show or in general. But there is a sprawling megapolis of pony fandom out there already analyzing every last drop out of this show in terms of characterization, narrative, world-building and theming. There may come a day when I can scrape together enough original thought on those subjects to add something worthwhile to the ponysphere, but for now this is where I think I can best contribute. I do really enjoy story-crafting, however, and I haven’t been this into a story since The Lion King.

I have read exactly one other work on the physics of the ponyverse, so it gets cited right up front. Check out “How Celestia and Luna "Raise" the Sun and Moon” by Comet Tail on the MLPForum[1]. Comet Tail and I approach the idea of Equestrian orbital mechanics from two different directions, I focus on tidal locking and Comet Tail on retrograde and erratic orbits, a concept I really enjoyed.

Last side note: I don’t consider any of this to be head canon. I think there is a difference between the extrapolation of concepts which the canon story directly implies—and even the analysis of those implications—versus real head canon, which implies the introduction of at least some new material into the story, characters, or world. Now don’t get me wrong, I likes me some head canons. I’m just going to limit the content of this paper to those things I consider direct extrapolation from the show’s story material, and straightforward analysis of that, and save the head canon for another edition.

 

 

The Curious Case of the Backward Moon

For all my enjoyment of the story, characters and world of Equestria, and even the scientific and philosophical implications of the world, I probably would never have committed any serious effort to exploring the subject of this paper if not for one blatant violation of sensible orbital mechanics which drove me crazy. And drove me to research.

I know that feel bro

From the first moment I heard that Celestia raises and lowers the sun and Luna the moon, what my brain heard was that Celestia rotates the planet and Luna revolves the moon. Not everyone made this assumption and there are plenty of geocentric model fans out there in the ponysphere, but that is what happened in my head. This assumption stood unchallenged until the ending of the season four two-part premier, where during the Summer Sun Celebration, Princess Luna lowers the moon for all to see, and then Princess Celestia raises the sun in the same part of the sky. It was as if the moon and sun had simply swapped places with each other, with no explanation. This happens a few other times in the show, but always as a cartoony effect easily dismissed as just a fun way to move the story (also, because Discord). But in S04 E02 it is a conscious act draped in a formal ceremony. So, the sun and the moon move across the sky in opposite directions? What does that even mean? After some thought, I decided that this was either the single best geocentric argument in the whole show, or a special event that isn’t representative of a normal day in Equestria.

Most of the time, a planet and moon both revolve and rotate in the same direction as the rotation of the star around which they orbit, all either clockwise or counterclockwise depending on if this is being viewed from the system’s ‘north’ or ‘south’. This is called prograde motion; when a body rotates or orbits in the opposite direction it is called retrograde motion. While retrograde orbit moons are present even in our own solar system, this phenomenon would not begin to explain a moon that appears to travel in the opposite direction across the sky as does the parent star from the viewpoint of the planet’s surface. This called apparent retrograde, and it is very different.

Regardless of direction, a spinning body tends to rotate significantly faster than anything orbiting it revolves. Take our own planet and moon for example. Earth ‘spins’ or rotates in exactly one day (that is the definition of a day, after all). The moon orbits Earth in about 29.5 of these days, so either way it revolves, prograde or retrograde, it will still appear to travel east-to-west across the sky, because that’s how everything that slow appears to move due to planetary rotation. So what would have to be going on for a west-to-east moving… anything?

Anything orbiting retrograde in respect to the direction of rotation of the orbited body will always appear to travel east-to-west, and anything orbiting at all at a lower angular velocity (fewer degrees per unit of time) will also appear to travel east-to-west. Only something orbiting in the prograde direction with a greater angular velocity than the rotation of the orbited body will appear to travel west-to-east.

 

O.O...So you're saying (I think) anything that is revolving around the planet opposite to the planets rotation is going to appear to move from east to west in the sky. Same goes for anything orbiting at an angle (how that works I have no clue). Only something revolving around the planet, in the same direction as the planet is rotating, faster than the planet can spin would appear to move west to east. Okay I think I'm following now. 

 

Around Earth, only artificial satellites do this. One simple reason for this is escape velocity. The further away you get from a gravity source, the less linear velocity (rate of motion through space) is required to escape its gravity well. A prograde orbiting body at geosynchronous-plus angular velocity at a distance (orbital radius) typical of moons would simply fly away into space. Or, more likely, into the nearest star.

 

o.o...wat... so basically if a satellite strayed to the distance of a typical moon...Okay so what you are saying is there the "escape velocity" is needed to keep the satellite rotating around the planet as supposed to just shooting off into space. If the object which is moving around the planet faster than the planet is spinning already has less than the required "escape velocity" variable its going to leave the planet, and the biggest culprit of this is straying to far from the planet and its pull holding it in place. Good googly moogly the jargon is strong in this one. 

 

    

Here’s an example. The equation for escape velocity (which is a misnomer, it should just be ‘escape speed’, because any direction that doesn’t cause a collision will result in escape) is:

 

Where  G is the Universal Gravitational Constant of 6.67 x 10^-11 m³ kg^-1 s^-2 

            M is the mass of the body being escaped in kilograms and

            r is the radius, or distance separating the two, measured center-to-center in meters.

The average distance from the center of Earth to the moon is 384,399 km. At this radius, the moon’s orbit traces an ellipse 2.415250 x 10⁹ m in circumference (2πr), or about 1.5 million miles. At exactly geosynchronous orbit, or an angular velocity of 15° per hour (360° per 24 hours), this works out to be a tangential (linear) velocity of 27,954 m/s ((2.348949 x 10⁹ meters traversed) / (86,400 seconds in one day)), which is over 62,000 mph.

 

 

X.X *brain.exe has stopped responding, would you like to send an error message?*

 

The escape velocity at that same radius from Earth, a mass of 5.97219 x 10²⁴ kg, is 1,439 m/s, or about 3,200 mph. So just to maintain position in the sky, the moon would have to exceed its planetary escape velocity by over 19 times. To actually move from west to east, it would need to go faster still. While the home planet and moon of Equestria do not need to be exact copies of Earth and its moon for the story world to work, the magnitude of impossibility involved here leads me to the conclusion that the show writers never intended to imply that Luna (or Celestia, for the millennium prior to episode 1) causes the moon to cross the sky in a west-to-east direction, even with telekinetic magic. Yet this is exactly what seems to occur in the season 4 premier, part two.

My conclusion is that due to the chaos unleashed by the Plunder Seed vines’ entrapment of Celestia and Luna and their attack on the Tree of Harmony, the planet and moon of Equestria were left in very unusual positions relative to each other and their star. After all, directly after Celestia and Luna’s abduction, both the sun and moon were left hanging together in the sky, causing panic among the populace, and justifiably so. In this scenario Luna simply backed the moon down from its crazy position towards something more normal, followed by Celestia’s moving the planet back to its regularly scheduled rotation. Even this scenario involves Luna temporarily revolving the moon prograde at an insane velocity without shooting it across space like a severed tether ball, but temporary is better than routine. Either this, or the ponyverse really is geocentric.

 

 

Okay we are heading into the land of the written word again. I don't think the Moon (or sun for that matter) are nearly as massive as our irl counterparts. I suppose I would fall into the geocentric theoriests in that the sun rotates around the pony's world and not the other way around, and that it isn't much larger than their own moon. Now don't expect me to pull out pages of math because that is NOT my strong suit, but there is evidence to support that they are indeed BOTH satellites. Chief of them being the Season 4 finale where Twilight gets temporary control over the celestial bodies. If Our sun and moon had did what their sun and moon did, then it would of been Armageddon on earth, I only need a basic grasp of physics to call that one out. If I'm right it also mean their sun is much cooler than ours as well, cause I'm pretty sure a real star of any size revolving around a planet would scorch its atmosphere and surface. 

 

Also, the writers probably just didn’t care, and my daughter wasn’t bothered in the slightest. And then I gave Hasbro some money for a toy for her, so I guess they win.

A very real and very practical answer lol. 

Formless and Void

The show’s world building has on more than one occasion implied that without magic, life on Equestria[2] would be difficult or completely impossible. I’ve already mentioned how extremely powerful magic is required to properly rotate the planet and revolve the moon. Both of these things are crucial for planetary life to thrive. The mortal and even non-magical residents of Equestria also seem to have a part to play, as evidenced by such episodes as Winter Wrap-up, Hearth’s Warming Eve and Hurricane Fluttershy. Magic or else considerable effort is necessary or at least really helpful in seasonal procession, cloud creation, and even animal migration and hibernation. To describe what Equestria might have been like prior to the influence of magic, I need to explain two concepts: entropy and tidal locking.

Entropy is essentially disorder, with a certain sense of inevitability. When a system is highly organized and complex, it is said to have very low entropy. A brass watch is complex and organized, so it has low entropy, while that same amount of brass melted and re-solidified as a nugget has higher entropy, because it is simple and disorganized. The second law of thermodynamics teaches us that the overall entropy of a system always increases when left to spontaneous (naturally occurring) forces. By investing organized effort, a system can undergo a local and/or temporary decrease in entropy (increase in order), but only at the cost of enough expended useful energy that the overall effect of a larger system is an increase in entropy.

I follow 

The same holds true at the scale of a planet or star system; entropy increases over time. Rotations slow down, satellites either escape or fall into their planets or stars, and ultimately, the star itself dies in one of a number of ways. Of course, the law of entropy does not take into account magic, but more on that in a moment.

The second concept, tidal locking is a result of tidal bulging and braking, the subject of some discussion in the piece by Comet Tail which I referenced earlier. As a moon rotates and revolves it tends to flatten a bit due to the gravity of its planet (provided its planes of rotation and revolution are sufficiently aligned). Like any other macroscopic physical object, moons do not have uniform density, so different longitudinal cross-sections will present more or less mass than its average density would present, so this flattening is likewise not uniform. The cross-section that is flattened the most is referred to as the major axis, or simply the ‘bulge’.

Once a tidal bulge emerges, it begins to alter the angular velocity of the rotating moon. As the rotation swings the major axis closer and closer into alignment with the planet’s gravitational pull, the angular velocity increases slightly, in a way falling into place. As the inertia of the moon’s rotation then begins to pull the major axis out of alignment, the angular velocity decreases, now fighting gravitational drag. This effect is referred to as ‘tidal braking’.

The cumulative effect of repeated tidal braking is that the moon favors its major axis more and more, which in turn increases the severity of the bulge more and more. Eventually, the planet’s pull on the major axis is actually stronger than the force of rotational inertia, and the moon slips into a rotation period equal to its revolution period, thereby ‘tidally locking’ onto its planet. In this arrangement the same hemisphere of the moon is permanently facing the planet as in the case of our own moon.

 

So there has been this gravitational tug of war between the moon and earth and the moon settled into a position where its axis was aligned with the planets, and this causes the moon to have the same hemisphere showing towards the planet at all times. 

 

Before a moon has tidally locked to its planet (or a planet to its star), it is possible to roughly[3] approximate the time until it does so with the formula:

 

Where  w is the rotation rate (in radians per second) of the satellite

            a is the average of the perigee and apogee of the satellite’s orbit (in meters)

            I is the satellite’s moment of inertia (in square meter kilograms), which can be estimated as (0.4)(m_s)(R²)

            Q is the dissipation function of the satellite (no units), which can be estimated as 100

            G is the Universal Gravitational Constant

            m_p is the mass of the orbited body (in kilograms)

            k₂ is the tidal Love number of the satellite (no units), which can be estimated as much less than 1 (typically around 0.1 for a mostly solid satellite)

R is the average radius of the satellite (in meters) and

m_s (from the description of I) is the mass of the satellite (in kilograms).

Examples of tidal locking are all over our solar system. Earth, Mars, Jupiter, Saturn, Uranus and Neptune all have moons tidally locked to them, and Pluto and its satellite Charon are tidally locked to each other.

What does this have to do with Equestria? Well, hopefully it’s clear that these two concepts are related. Tidal bulging, braking and locking are all examples of the unstoppable march of entropy on a lunar and planetary scale. As time goes on, orbital mechanics slip from complex arrangements into straightforward ones, which are sadly ineffective at supporting life. A tidally locked moon is not unusual, but an otherwise M-class planet tidally locked to its star would be completely uninhabitable, a blistering super-desert on the sun-ward hemisphere and frozen perpetual night on the other.

Yay I got that one right.

This is the cataclysm that Celestia and Luna guard their subjects from, absolute extinction across the entire planet.

 

 

Let There be Magic

There isn’t too much detail I can offer as to exactly how the alicorns would have gone about decreasing entropy and resetting the required rotations and revolutions without getting into head canon territory, which I pledged not to do in this volume. But here’s what I have:

According to what I perceive the story has told us about its world, this was the original, no-magic state of the Equestrian solar system. A planet locked onto its star, unable to rotate beyond its revolution around the star, unable to support life. A moon not only locked onto its planet Earth-style, but also tidally ‘pinned’ in place between the planet and the star, its revolution in sync with the planet’s revolution. This moon would appear to hover directly above the planet’s surface at exactly the sun-ward pole, casting an unmoving solar eclipse shadow on the surface of the planet’s desert side, creating a small area of shade, assuming a roughly Earth-like size-and-distance arrangement. Solar magic is required to rotate the planet any faster than its one day per year rate, and lunar magic to revolve the moon any faster than its one month per year rate.

It seems most likely that once the alicorns (whoever they were and wherever they came from) decided to revive Equestria’s ability to sustain life (for whatever reasons), they would have first begun to accelerate the rotation of the planet, as this is absolutely necessary and the change requiring the most energy. But there’s a problem. The moon is locked on to the planet’s tidal bulge axis too strongly. As the alicorns accelerate the rotation of the planet, the moon tries to match angular velocity to maintain its position relative to the planet’s surface. But the star’s gravity pulls it back, threatening to tear the satellite apart. So the alicorns would then have to exert magical force to slow down the moon’s revolution as the planet continued to spin faster and faster. The moon’s orbit would still be accelerating (from one per year to the order of 10¹), just not as rapidly or as high as the acceleration of the planet’s rotation (from one per year to the order of 10²).

With the planet now rotating hundreds of times per revolution and the moon now revolving tens of times in the same time period, key changes begin to happen. The hemisphere-spanning super glacier begins to melt, evaporate, and partially refreeze in a daily cycle, causing intense flooding and erosion. The desert cools and gigantic storm fronts race around the globe as the planet’s rotation and cycles of heating and cooling the atmosphere rapidly change temperature and pressure. The revolving moon now pushes and pulls the emerging liquid water in a tidal bulging sequence of its own, beginning to delineate land from sea.

Assuming the planet has the internal structure of one at all capable of sustaining familiar life, the now spinning core begins to assert a discernable geomagnetic field and trap energetic particles into its magnetosphere and plasmasphere. This provides an increasingly strong shield against dangerous particles and electromagnetic radiation from space, restoring some habitability to the planet.

After these and many other effects have emerged and stabilized, two last pieces of the puzzle remain, neither of which is assigned a patron alicorn in the show like Celestia and Luna. The first of these is planetary tilt. At full planetary tidal lock, there would be no rotational tilt, no angle separating the planes of planetary rotation and revolution. But tilt is required for seasonal procession, and Equestria definitely has seasons. The final element of a restored living planet is of course biological life. How the various life forms were created or restored must remain purely in the realm of head cannon, however. All we know is that on Equestria all of ponykind, and perhaps other sentient species are active participants in the march of time. Seasons, weather and the life cycles of other forms of life are enabled and guided by mortal hooves.

 

Well, there you have it. I hope you’ve enjoyed my paper and that whatever amount of time you just spent reading it was not wasted. I would (probably) enjoy your comments and questions.

 

 

 

Next:    Devolution, Natural Selection and Immortality

Soon:   Talent, Choice and Cute Marks of Destiny

Later:   Twilight and the Divine Harmony

 

 

About the Author

The author is currently serving as a Senior Scientific and Technical Analyst at the National Air and Space Intelligence Center in Dayton, Ohio. He holds a Bachelor of Arts in Business Administration from Malone University in Canton, Ohio as well as Associate of Applied Sciences degrees in Intelligence Studies & Technology and in Scientific Applications Technology. He and his wife live in the Dayton area with their daughter, who loves the ponies, especially as toys gathered around a play tea set.

[1] http://mlpforums.com/topic/27530-how-celestia-and-luna-raise-the-sun-and-moon/

[2] For the rest of this paper, rather than invent a name for the planet, I will refer to both the realm ruled by Celestia as well as the actual planet which hosts that realm as “Equestria”. Which is meant should remain clear in context.

[3] No, really, it’s pretty rough: http://en.wikipedia.org/wiki/Tidally_locked#Timescale

 

 

I really enjoyed this, despite having to draw on my knowledge of root words and cracking out the trusty dictionary on a number of occasions. In my opinion it actually strengthens the case for a geocentric model of how the pony solar system works, and my own theory that the celestial bodies that revolve around the planet are actually artificial (as you say, only artificial satellites behave in this way specifically to maintain orbit without breaking the escape velocity barrier).

 

I am also extremely interested in your upcoming topic about twilights cutie mark of destiny, I have a rather extensive theory on cutie marks myself and how they tie into the structure of pony society and even how a pony perceives themselves. 

 

Looking forward to other posts from you!

Edited February 4, 2015 by Buck Testa

[John Locke N7 52]

I hope you don't mind if I read this over many long poops 0.0

[Comet Tail 808]

I really enjoyed this, despite having to draw on my knowledge of root words and cracking out the trusty dictionary on a number of occasions. In my opinion it actually strengthens the case for a geocentric model of how the pony solar system works, and my own theory that the celestial bodies that revolve around the planet are actually artificial (as you say, only artificial satellites behave in this way specifically to maintain orbit without breaking the escape velocity barrier).

 

I am also extremely interested in your upcoming topic about twilights cutie mark of destiny, I have a rather extensive theory on cutie marks myself and how they tie into the structure of pony society and even how a pony perceives themselves. 

 

Looking forward to other posts from you!

 

That's really not what he was saying... Whether artificial or natural, any object orbiting another will behave the same way, with the exception that a very large mass will behave very, very slightly differently (I'm talking a mass the size of the moon or so causing a slight wobble in the parent body's orbit as the two orbit the common center of mass) - but for all intents and purposes - pretty much the same. From what I got, it looked like he described a system where the planet would become tidally locked with the sun, and Celestia prevents that from happening, keeping their world habitable, whilst Luna keeps the moon's orbit from decaying due to tidal braking.

Edited February 4, 2015 by Comet Tail

[Buck Testa 5,503]

 

 

That's really not what he was saying...

 

Whether artificial or natural, any object orbiting another will behave the same way, with the exception that a very large mass will behave very, very slightly differently (I'm talking a mass the size of the moon or so causing a slight wobble in the parent body's orbit as the two orbit the common center of mass) - but for all intents and purposes - pretty much the same. From what I got, it looked like he described a system where the planet would become tidally locked with the sun, and Celestia prevents that from happening, keeping their world habitable, whilst Luna keeps the moon's orbit from decaying due to tidal braking.

 

 

You misunderstand me. I didn't say that is what he said, I said it gives credence to the geocentric theory by virtue of the fact that the situation Equestria has with its satellites are so foreign and counter intuitive to our own understandings of physics (or that was my intent anyway). 

 

His theory is brilliant don't get me wrong, I have a very difficult time wrapping my brain around some of his concepts, and maybe I missed something (as I very well could of). 

[sweetolebob18 724]

As to life on tidally locked worlds.  The day & night temp differences on the moon is close to 500 degrees F.  I remember there were some old time SF stories about life on worlds like that, with a habitable belt on the dawn/dusk line.  (Usually down in canyons/valleys).  The problem is if the world isn't perfectly locked, the temp swings are too extreme (the moon wobbles a bit, for example, & we see about 60% of it).

 

But, I firmly believe EQ fits the old Geocentric model.  The Moon & Sun are both relatively small (I recall Aristotle believed the sun was a red hot ball of rock about 40 miles in diameter) + IMO, EQ is flat.  It is the simplest explanation for what happened in Princess Twilight.

 

As to satellites, I recall reading that Deimos is near synchronous orbit & thus hangs in the Martian sky, going through the phases twice & Phobos rises & sets 2 or 3 times a night.  (Of course, from Mars' surface they are both magnitude 5 & barely visible)

[Buck Testa 5,503]

Turns out I was right about the Equestian moon being pretty small in comparison to our own

 

That thing is a tiny little pebble in comparison to our earth's moon, its actually smaller than I had guessed it to be. There is no way something like this even comes close to having the same gravitational effects as our moon. Its floating not from gravity but from some other force, else it would of crashed into the ground being so close to the planet, not being held in place via a lasso. If Our own moon were to get this close we would all be dead. 

 

Now the question of how they see such a tiny thing from space comes to mind... 

[truth is life 76]

And yet it has a breathable atmosphere...

 

My answer is, "it's magic, you really should just relax".

[Comet Tail 808]

Turns out I was right about the Equestian moon being pretty small in comparison to our own

 

That thing is a tiny little pebble in comparison to our earth's moon, its actually smaller than I had guessed it to be. There is no way something like this even comes close to having the same gravitational effects as our moon. Its floating not from gravity but from some other force, else it would of crashed into the ground being so close to the planet, not being held in place via a lasso. If Our own moon were to get this close we would all be dead. 

 

Now the question of how they see such a tiny thing from space comes to mind... 

 

Hah, they drew the rope going out in an Apollo-type trajectory (orbits Earth, then shoots out to Moon coming in on the moon from the opposite side than the side of the Earth that it came from).

 

Anyways, yeah, you kinda have to disregard the comic's moon for anything to work physics-wise, and just stick with the show.

[Buck Testa 5,503]

Hah, they drew the rope going out in an Apollo-type trajectory (orbits Earth, then shoots out to Moon coming in on the moon from the opposite side than the side of the Earth that it came from).

 

Anyways, yeah, you kinda have to disregard the comic's moon for anything to work physics-wise, and just stick with the show.

But the comics are secondary canon though. Although the stories are different, the facts that are in them apply in the show as well as long as they do not contradict each other. This was said in this way so both the show and the comics were free to do what they want without worrying about breaking canon, but I think something as substantial as a MOON would be the same in both versions. So yes, this counts. You can disregard it and only accept the show, they certainly left that option, but if we accept Hasbro's terms then this is canon and this means either that universe could be operating on entirely different laws of physics, or the Moon is only rotating around the planet and not flying away is because of magic and magic alone.

 

I wonder though is that lasso related to THIS lasso?

 

[Aidan OGain 112]

Simply amazing. I'm blown away like the rushing hot winds at the terminator of a tidally locked planet.

 

I can't wait for your next articles!

[SkySoldja 7]

And we're back! At some point I'm going to wrap these preceding comments into a sort of Q&A follow up, but for now I really wanted to get the second volume posted. This volume is more in the fields of biology, fundamental force physics, natural selection, and even a bit of immortality philosophy, if you can believe that.

 

 

 

 

 

 

My Little Planet: Entropy is Tragic

Volume Two:

 

Devolution, Natural Selection, and Immortality

 

 

 

 

Introduction

I hope no one minds the shift from last volume’s focus on celestial orbital mechanics to this volume’s genetic biology and fundamental force physics. And, yes, immortality. What do those three have in common? Magical talking ponies, of course.

In this volume I start by examining how many elements there are in Equestria, and then talk about natural selection and entropy. Finally, I roll those discussions into the Grand Unified Field theory and top it off with the formula for immortality. For the aforementioned magical ponies, of course, not for you and me. Sorry. Another time.

 

The Quintessential Classics

How many elements are there? Well, 118 last time I checked. However, the world building of Equestria utilizes so many themes from classical mythology[1], including life forms with clear “elemental” themes[2], I feel it fair to examine the older meaning of the term. The most explicitly described elements in Equestria are, of course, those of harmony. Five of what I would call “constituent elements”: loyalty, laughter, generosity, honesty and kindness and then one element of a different nature, more of a “dynamic” or “synergistic” element, of magic.

But to take an even slightly scientific approach to the subject, we cannot simply throw out the periodic table with its metals, metalloids and non-metals. What I propose is that we treat the classic elements, which clearly have functionality in Equestria, as bundles of chemical elements, compounds and even processes which interact intra-elementally as a discernable component, but can still be further divided into true elements. “Air” could be thought of as a functioning bundle of atmospheric gases and the ideal gas laws, “Earth” as a bundle of mineral compounds and microbiological… things (sorry, soil science is not my calling), “Fire” would basically be the combustion process, and “Water” would be H₂O, fluid dynamics and probably tidal gravity effects. I’m sure with more time and more collaborators, we could put together better lists for the bundles, but you get the idea.

So how many elements are there in Equestria? After all, different cultures and philosophies answered this in differing ways. I see the show’s world building suggesting a five element, “quintessential” model, with “Magic” taking the fifth spot in addition to the classic four detailed above, standing in for ether in Aristotle’s fivefold model. Magic as an elemental bundle is easy, as harmony is large scale friendship and friendship is magic, and we have already discussed laughter, loyalty, etc. The best example of this model in the show is the dominant sentient species itself. Earth ponies are associated with earth, the pegasi with air, and the unicorns with magic. I seem to recall seeing that the comics and previous ‘gens’ of the show feature a race associated with water, and as to fire ponies, I’ll have to leave that up to head canon for now. And alicorns? Keep reading.

 

Natural Selection and the Shrinking Genotype

There is a difference between natural selection and counter-entropic biological evolution—or if you prefer, two separate aspects of the natural selection/evolution process which is commonly seen as unified. In order to discuss the two as separate from one another, I would describe natural selection as the process by which a certain branch of life comes to most often produce those traits available in its genetic arsenal best suited to survive and thrive in its environment. Counter-entropic biological evolution, on the other hand, would be the process by which said genetic traits are added into that branch’s arsenal in the first place. Not everyone sees a distinction; I may be in the minority on this point. I mention all this because I’m only going to discuss the first: natural selection, or the survival of the fittest.

Go to a certain dusty brain shelf if you will and recall with me the difference between the phenotype and the genotype. No? Well, basically, the genotype is the entire genetic arsenal. Every trait that a specimen possesses and has the potential to pass on, dominant or recessive, whether or not the trait is actually present in the specimen’s makeup, is written in the genotype. But there are only so many genetic ‘slots’ which can be occupied by any one specimen’s configuration of traits, and that is the phenotype. This is why it is possible for full siblings to actually look quite different from each other occasionally. Each one represents a particular genetic snapshot (phenotype) of the pool of possibilities provided by their parents (the genotype).

Over time and generations, entropy (see volume one) plays its part and genetic information is lost or corrupted. Also, when a trait make its way into a specimen’s phenotype and proves unhelpful, it is lost by the natural selection process (i.e., the specimen is not competitive, and fails in one way or another before it can procreate much or at all). These two process have two notable results. First, the branch of life is left with only the most competitive genetic traits. Second, the branch of life has fewer overall traits as time goes on. Of course, all other branches of life are experiencing the same effect.

This gets at one reason I see a difference between natural selection and counter-entropic evolution; natural selection is not even absolute improvement, it is relative improvement. It is effective damage control, not counter-entropy but managed and mitigated entropy or devolution. Losing genetic information over time is inevitable, but through natural selection the best information can be held onto the longest.

 

 

Entropy, Harmony and the Elements Thereof

So, back to the ponies. For while in our world we are constrained by laws of thermodynamics and entropy, not so in Equestria. Entropy may still set the ground rules but harmony, as magic, comes along and changes the rules. The elemental hierarchy which I see the show presenting to us reminds me a lot of the diversification of the superforce.

According to the theory, at the first instant of the big bang, there was but one cosmic force, which then quickly diversified into the four fundamental forces with which we are familiar. First was gravity, in many ways the most different of the four, which separated from the original superforce at 10^-43 of one second (one tenth of one micro-pico-pico-picosecond), leaving the unified gauge forces (non-gravitational forces). Next came the strong nuclear force at around the 10^-36 second mark (one pico-pico-picosecond) or 10 million times the elapsed time the first force took to diversify. This left the electroweak force. Finally, after 10^-12 second (one picosecond), which was one billion quadrillion times the elapsed time of the second diversification and ten quadrillion quadrillion times that of the first, the weak nuclear force gained distinction, leaving only the electromagnetic force, which continues as a unified force to this day.

In MLP:FiM, we see two distinct but overlapping element schemes. First we see that laughter, loyalty, generosity, honesty and kindness synergistically give rise to magic, which are altogether the elements of harmony. We also see the quintessential model of the natural elements (or elemental bundles) which both describes the configuration of the natural world and the main branches of equine life: earth, air, water, fire and magic. Magic here serves as the point of overlap between the two schemes, as it is one-fifth of the makeup of the natural world complete with its own phenotypical tribe of the dominant sentient race as well as the dynamic interaction of the other harmony sub-elements; so that magic stands as both part of harmony and as equal to friendship, illustrating harmony as large-scale pervasive friendship.

If these forces were to have begun as a unified force which gradually diversified, I would imagine it to have begun as a single unified harmony (synonyms, actually) which first diversified into a harmony branch and a magic branch. The magic branch would have further branched into the full set of five natural elements still including magic, while the harmony branch would have diversified into the full set of six harmonic elements, which would include the magic/leadership element. This arrangement would preserve the idea of magic as a pivotal point of overlap between the two elemental schemes.

 

Diversity and Recombination

As a species undergoes generation after generation of entropy mitigated by natural selection, it becomes specially adapted to its environment, both in terms of actual climate and its place among its prey, predators and rivals. One interesting category of this effect is the ecotype, in which two or more geographically separated populations of the same species become unsuited for each other’s environment before the point where they would become unable to interbreed. While we see this to some degree in our own species, humans (and MLP ponies) have a distinct advantage over this tendency to become ill-suited to environments outside our own. We can actually impose our conscious will onto our environments, whether this be altering the environment or else creating artificial comfortable environments within less friendly ones.

The ponies of Equestria takes this a step or two even further; they take part in driving critical aspects of their climate itself from a local scale to the planetary (for more on this topic see Volume One of this series, titled The Celestial Mechanics of Equestria). This environmental taming provides a unique opportunity to effect some measure of repair to the slowly but surely decaying genotype: as the various ecotypes develop the ability to artificially thrive in each other’s environments, cross-breeding can then re-inject fresh genetic possibilities which had been previously lost in any one ecotype’s history. While this could easily result in a phenotype which would be at a disadvantage in the environment of either parent ecotype, again, in the case of a more dominant species capable of environmental taming, this is not a problem.

But wait. We’ve only encountered one clear case of cross-tribe pony breeding, that of the Cake family. Both Mr. and Mrs. Cake are earth ponies, one having a pegasus ancestor and the other a unicorn ancestor. This ancestry makes possible their twin foals, Pound Cake the pegasus and Pumpkin Cake the unicorn. So while inter-tribal breeding is clearly not problematic, it would still seem to produce only offspring of one distinct form or another. While the show never explicitly rules out hybrid forms, I don’t see the storytelling presenting such as a real occurrence. This hearkens back to the idea of the natural elements being functional clusters or bundles, which while not truly elemental do still have concrete functionality as a cohesive collection.

From the world story I see from the show I theorize that alicorns are not only a separate and higher form of the diverse species, but also a parent genotype from which the various element-themed tribes quickly emerged and diversified. I would also theorize that over the course of the Mane Six bearing their associated Elements of Harmony that their natural elemental natures (earth, air and magic) intersected with their harmonic elements (honesty, loyalty etc.) which resulted in Twilight being able to complete the superspell at the end of season three which repaired her own genotypic specialization by reintroducing the pegasus air element and presumably the earth pony earth element as well as a second measure of the unicorn magic element into her being.

This sets forth the two major requirements for immortality in the MLP story world. The first of these is a philosophical enlightenment of the harmonic elements; that is, an internalized mastery of loyalty, laughter, honesty, generosity and kindness, as well as the developed ability to coordinate and synthesize these five elements through leadership, an ability which stands as a sixth harmonic element all its own. This first requirement seems to be a prerequisite for the second, which is a genotypic recombination of the alicorn descendant tribes, through a process which magically piggybacks on the intersection of the harmonic elements. This process expands the subject’s phenotypic capacity to a complexity capable of manifesting much more of the newly available genotype, thus creating an alicorn who fully embodies their primal concept, and in so doing, becomes effectively immortal.

This theory does leave a few loose ends, however. First, it implies that there is some part of this process which Twilight yet lacks, for she is certainly not on the same level as Celestia and Luna. Perhaps this is tied to the fact that not all five natural elements were present at the moment of her elemental intersection superspell, and that she would have to somehow track down a water pony and fire pony to assume two of the four harmonic elements not borne by herself or Rarity, the only unicorn element bearer other than the spell’s subject. Second is the closely related fact that Cadence would then seem to be lacking even more of the immortality process than Twilight, for she never even experienced a harmonic element intersection event and may very well not understand all of the magical friendship concepts as well as Twilight.

Finally, it leaves completely untouched the concept of cutie marks and their role in the superspell which ended season three and created the Alicorn Princess Twilight Sparkle which we know and love today. This subject is so big and complex it deserves its own volume in this series. So stay tuned!

 

Next:    Talent, Choice and Cute Marks of Destiny

Soon:   Twilight and the Divine Harmony

 

About the Author

The author is currently serving as a Senior Scientific and Technical Analyst at the National Air and Space Intelligence Center in Dayton, Ohio. He holds a Bachelor of Arts in Business Administration from Malone University in Canton, Ohio as well as Associate of Applied Sciences degrees in Intelligence Studies & Technology and in Scientific Applications Technology. He and his wife live in the Dayton area with their daughters, who love the ponies, especially as puzzles and as toys gathered around a play tea set.

[1] Unicorns, pegasi, dragons, phoenixes, a hydra, a minotaur, a chimera, a centaur…ish thing (Tirek? What was he?), Cerberus, Tartarus, etc.

[2] Equines associated with earth, air, and magic