#large posts

[asksciencepony]

Non-Sequitur: Winter Wrap-Up

Apologies on not continuing the current thread on gravity spells. Through course of conversation, another interesting topic has come up that I feel compelled to write on: artificially induced seasons.

I recommend taking a look at it, over here: http://mlpforums.com/topic/117318-tidal-locking-equestrian-orbital-mechanics/

Sky Soldja has reviewed the topic I initially covered with an impressive level of depth and rigor. It's definitely worth a look!

Anyways, these artificially-induced seasons are responsible for possibly the best/most catchy song of the series, and have always been one of the things that has interested me... But how can they work?

Part 1: Earth's Seasons

It's not quite common knowledge, so I'll review how seasons work on Earth, in real life.

A common misconception is that seasons are caused because the Earth gets closer to the sun. This simply isn't the case. Although all orbits are, in fact, ellipses, for most planets they are extremely close to a circle and only very slightly elliptical - so much so that it makes very little difference. Illustrated below is Earth's orbit, to scale.

Although technically an ellipse - it is very nearly a circle. Perhaps it's also worth mentioning that the Earth is closest to the sun in December.

Before we continue, let's review a little something:

If we shine a certain amount of light "I" onto two surfaces, A1 and A2, which will get hotter?

Answer: A1 will reach a higher temperature. Although both receive the same amount of energy, A1 is spread over a smaller area, so there's more energy per area, thus a hotter surface.

What causes the seasons is the fact that the Earth is tilted a little in how it spins. This means that one hemisphere (A hemisphere is half of the Earth above or below the equator) gets more sunlight, and gets it more directly, than the other. 

Carefully study this illustration:

The sun being at a steeper angle means it'll heat the ground less, just like we just established above. In this illustration, for example, it is summer in the northern hemisphere, and winter the southern hemisphere (So, June).

And as the Earth goes around the sun, the way it's leaning doesn't change. Because of this, the seasons change:

So, now that we've established that, what could cause the seasons on Equus?

Part 2: Seasons on Equus

So, the theory that I formed has seasons working differently. Instead of happening because of axial tilt like on Earth, the axial tilt of Equus would be very small, and seasons would happen due to a much more elliptical orbit.

  Unlike Earth's orbit, this one is far more elliptical, so that the difference in heat from the parent star is much more significant.

So first, let's look at heat, and some maths.

The hotter something is, the more heat it lets off by thermal radiation. The more solar radiation falls on the planet, the hotter it gets. The first factor cools the planet off, and the second warms it up, until it reaches an equilibrium.

dQ/dt simple means "change in Q" (Q is often used to represent internal/heat energy). eq.1 shows how a surface radiates heat by the fourth power of the temperature (in kelvins), multiplied by some numbers that I've just condensed into a single coefficient for our purposes, here: K1.

eq.2 Shows how the energy something receives is directly proportional to how much energy falls on it, once again multiplied by some unimportant coefficient K2. 

When these two are in equilibrium, they equal eachother, thus the rest of eq. 2.

This leads to eq.3: equilibrium is achieved when the energy flowing out is the same as the energy flowing in.

Now, eq.4, we realize that Temperature, as a function of time, will eventually come to equilibrium at some value, K4. Since we're not interested in anything but the system at equilibrium (on a weeks sort of time scale), we can simply regard the temperature and energy as a function of time as being some constant. So, when we integrate with respect to dt, we find that really we're just multiplying the whole thing by some constant, K4, leading us to eq.5.

This line of math leads us to something very useful:

An energy curve. We find that the system will reach equilibrium where dQ/dT = 0, or in the bottom of the curve. If the planet heats up, it will radiate more energy than it is receiving from the sun, and cool down back to the bottom of this "bowl". If it cools off, it will start receiving more energy from the sun than it's radiating off, and it will heat up, falling back into the bottom of the "bowl".

Now, let's take something a little extra into account...

While these factors by themselves push the system to an energy bowl, other variables lead to a bump:

At the top of the little bump (marked with the dotted line) is a balancing point. From there, melting snow will lead to a runaway system: snow and clouds reflect heat. If they disappear, less heat is reflected, and the planet heats up more, melting even more snow until the system comes to equilibrium at point C. On the other hand, if extra snow forms, more heat will be reflected, and thus more snow will form and reflect more heat, so the world will cool off, coming to equilibrium at point B.

Now, here's where things get interesting. My first thought, was that when the ponies pile up snow, they reveal less-reflective Earth. When they crack and melt ice, they reveal water, which absorbs more heat. These things would lead to the planet warming, and thus a fall to C. But there's one problem...

You'd have to alter a significant fraction of the planet's entire surface. Planets are big. Very, very, very, freakishly big. Like, really, you don't quite get how big they really are. The concept of manually moving enough snow to make a difference is not just staggering, it is impossible.

This is where the elliptical orbit comes in... It can lend a helping hoof to push things along. When the planet gets closer to the parent star, the original curve will skew. The little bump, however, won't, because water still melts and freezes at the same point. The result, is the graph now looks like this:

As you can see, it's skewed towards higher temperatures. This is Equus closer to its star. During the winter, the world was sitting at point B: the colder, winter side of the bump. Now, however, the more intense radiation from the nearer star is giving a helping push, and now the ponies need only clear a much smaller amount of snow and clouds, to push the temperature back up over the hump, and into summer: point D.

Then, Equus rides out to its furthest point from the sun...

Note, naturally, the planet will cool by itself down to point C. But it's still not quite enough to cool it back down to a snowy, planet-wide winter. They do a little summer wrap-up; obscure the planet under heat-reflecting clouds, let it cool off so it overcomes the little bump, and falls back to winter at point A.

Well, that's the qualitative argument. My guess is, the planet will have to be extremely fine-tuned for this to work, but seeing as its artificially controlled by two semi-immortal semi-dieties, I wouldn't complain about that.

In summary, the artificially induced seasons are actually somewhat plausible, and considering Celestia and Luna's power, very much doable. But why not just make the seasons come naturally? Perhaps they simply thought it best for social reasons to give the ponies of Equestria something to work together on every year, to encourage community, cooperation, and hard work - as well as add something to spice life up. In any case, I for one, welcome our alicorn overlords and stand behind their decisions, and at the very least it led to a most wonderful and joyous song and wonderful yearly fun, fulfilling, team effort.

Thanks for reading! Feel free to comment, like, and message. I'll see ya'll next time.

[asksciencepony]

Gravity! (Pt2)

Alrighty! My somewhat late part 2. Let's dive right into this, shall we? (Don't worry - it should be deep enough to be safe for diving)

But first, a reply to something I got from the last post:

Ooookaay. I got that as a question, but it's not really a question, is it?

I was already getting off on tangents, so I didn't really explain this part with probably as much depth as I should've.

The problem with getting most of your gravitational force from the sun, is that it interferes with your ability to orbit the Earth. Two objects in orbit generally have a hard time staying next to eachother (that is, in all but carefully controlled conditions, they have a tendency to drift apart).

If you took an object in orbit at height A, then moved it up to height B without changing its velocity, then its orbit would grow larger because gravity at that distance is weaker than it was at A. Refer back to the graph of orbital velocities in the previous post: Near the Earth's surface, it takes 7.8 km/s (roughly 5 miles/second) to stay in orbit. But up at 20,000 km, that would be too fast: so you'd "miss" the Earth by too much and end up in much larger, longer orbit than you would near the Earth's surface.

In this elliptical orbit, much like on a swing, as you get higher up, you'd slow down, so you'd spend the vast majority of the orbit going much slower than 7.8 km/s.

So the orbit would be bigger, and you'd be going slower. The end result is it takes you much, much longer to complete an orbit.

And so, if you were in orbit next to another object that is lower than you, you would fall behind it; drifting away as it sped on ahead in a much faster orbit.

Now, typically, when Earth's gravity dominates, for general approximations you can ignore the gravity of other bodies because their effects are small. But if you move too far away from Earth, then you can't do that anymore: the orbital effects of both of you being in orbit around the sun will try to drive you apart.

That's very problematic if you've only packed enough supplies for two weeks, and find yourself unable to ever reach Earth again. Now, sure, you can get back to Earth with a rocket engine, but typically the requirements for such maneuvers aren't quite so nice, and still takes a very long time to get back to Earth. These things make it a much less attractive option than just going up into an elliptical orbit with your levitation spell.

Pt2: Gravity on a Space Station

Put quite simply, the whole reason you're going up into orbit is largely for weightlessness. The International Space Station, Skylab - these places are laboratories. There's a few key features that make them so useful that you'd rather pay an experiment's weight in gold to launch it up there than to just use some lab on Earth:

1. The Vacuum of space 2. Cosmic radiation (of all kinds - certain types of astronomy that are largely blocked by Earth's atmosphere like X-ray, for example) 3. Weightlessness

That's really a reason that NASA, or any other agency, has never really put in the resources to make artificial-gravity environments with spinning wheels or modules by using centrifugal force.

Half the reason you're going there in the first place is for the weightless environment.

Note: There's no reason to make an entire enormous wheel, though...

Robert Zubrin - a leading advocate of colonization of Mars and aerospace engineer - has proposed putting a cable in-between the Mars habitat module and the used upper stage of the rocket that launched it to Mars, then spinning them around their common center of mass.

What about long-duration spaceflights where we WANT artificial gravity (say, on a trip to Mars or the outer planets)? Well, if we refer back to the clip, her horn is glowing the entire time. The spell is an active one, and we saw in that same episode what happened to Cadence when she had to continuously power a spell.

True, that depends on how much energy it takes (a point we'll return to), and an answer could be to just cast it for a few hours each day.

However, this assumes that magic can be done at all in deep space (see: "Here Comes The Sun - Theory 3: Magic (Symmetry-Breaking) Field"), and a user-cast spell may not be as reliable and predictable as say, simply stringing a cable across the module and spinning it.

Though admittedly, it's not really a closed case.

But, back to space stations and science, maybe you could cast a gravity spell on some parts of the station and not others, retaining a microgravity lab? Or just on thet inhabitants of the station but not the station itself? But that ties in with the next problem:

Let's say we cast a gravity spell on the whole station... Well, then the whole station would just free-fall, and you'd be free-falling inside of it, so you'd still be weightless inside. Much like how in orbit, it's still under some-odd 96% of Earth's gravity, but the astronauts are weightless.

Now let's say we only cast a gravity spell on the inhabitants. Well, then we got another problem:

Let's say we have seven passengers; the mane 6 and Spike, and the station masses at some-odd, oh let's say 70 tons. An average mass for a human being might be some-odd 80 kilos (see my post on pony sizes), for 1g of gravity, this is a ~784-Newton force. On a 70 ton station, that's enough force that your feet pushing into the floor of the station will push it at 0.0784 m/s^2. Sure, that's only 1/100th of a g, but this means that over the course of 24 hours, you (and your six buddies) will have pushed the station up to a speed of ~6,770 m/s! (~15,150 mph).

Now, before we go getting all excited about; "well, this would actually serve as an excellent fuel-less engine!," I actually have to object that this is clearly a violation of my favorite laws: conservation of momentum and energy.

In trying to understand how something happens, we respect nature's laws and use them as tools to tell us how things work, so sorry to spoil the fun of reactionless drives based on gravity spells - since it's all fiction anyways, you can do what you please with the idea - but here I'd prefer to be "realistic," ie, respect nature's laws as we know them.

So, this actually leads right into part 3 - "The Energy of the Spell," or "How does it work?"

See ya next time!

[asksciencepony]

Gravity! (Pt1)

First off It's taken me a while to settle down and start this, partly because it's quite a daunting task (creating a physics-y explanation of magic). I've constantly been wanting perfection, and that really doesn't help the overwhelming feeling.

But alas, no first attempt is ever perfect, and for my peer review I have an entire peer group of 1 (if you'd like to join in discussion on speculating on MLP science - please message me! Preferrably giving me a Skype name). So, disclaimer; anything I state, here, developing theories on how magic works, may be - and probably will be - corrected, or contradicted with later updates.

So now, I'll be diving right into some magic! (with, as promised, an answer to someone's question. NOTE: If you don't ask anonymously, your question will be given priority)

First a little nitpicky thing: I think by "solid rocket fuel" you mean "physical rocket propellant," because there's a lot of technical terms with precise meanings here, and a "solid rocket" is a specific kind of rocket that has, well, solid fuel. More typically, Launch Vehicles that can make it to Earth orbit usually have a stage or two of liquid rockets, powered by liquid propellants and fuels.

(Propellants: stuff you put in that makes the rocket go. Fuel: The material from which energy is taken. "Propellants" in rocket engines that use chemical combustion typically involve a fuel and oxidizer)

But, nitpickiness aside, this was actually one of my thoughts on Harry Potter. A levitation spell can be an effective way to overcome gravity... And harness potentially unlimited energy.

1: Using Gravity spells to Get to Orbit.

I've probably mentioned this before - but the astronauts on the space station are actually under 96% of Earth's gravity. The reason they're weightless (floating about), though, is because they're free-falling along with the space station.

Let's say I have a ball, and I drop it on a plate. Now, I pick it up again, and toss it to the side. It falls towards the floor (and thus in the direction of the plate on the floor), but misses it because I threw it sideways. Now, replace the "ball" with anything in orbit: a spaceship, a satellite, a space station - and the "plate" with Earth. That's how they stay up there.

But they're going so fast sideways, that they're missing the entire Earth.

This is an orbit. Planets do this over the sun, moons do this over their planets, and spaceships do this over whatever it is they're orbiting.

However, one thing common knowledge says about gravity actually IS true: it gets weaker as you go further away. The exact equation is

Where M1 is the mass of the object experiencing the force, and M2 is the mass of the other astronomical body, and r is your distance to the object's center.

And this leads to something very useful, using Newton's F=MA and cancelling M1 from both sides:

where u = GM (often called the "Standard Gravitational Parameter).

Next, centrifugal force. Anyone who's spun a yo-yo or used a sling (David and Goliath style) knows what this is.

The blue arrow is the string pulling on the Yo-yo, and the green arrow is the direction the Yo-yo is going. The red arrow represents centrifugal force. It happens simply because the Yo-yo wants to keep going forward in a straight line (inertia - along the green line) but it's being pulled in a circle (by the blue arrow - the string).

So, the simplest way to explain it, is that as this thing spins, it will want to fly outwards - that's centrifugal force. It's really just inertia, but it's useful sometimes to think of it as a force, as I'm about to describe:

Another, alternative way of viewing an orbit, is a balance of centrifugal and gravitational force. In some ways, it's physically identical to the Yo-yo spinning on a string, where gravity is the string:

The exact equation for this force is:

Now, where are we going with this? Levitation can, in fact, lead to you putting things right into orbit, because the speed required to be in an orbit changes with your distance from the center of the body, thusly:

For Earth, this gives us this:

(graph is only approximate)

Now, the trick is, that Earth spins. Sitting on the surface, everything is going a good 463 m/s (997 mph) relative to the center of the Earth, so you just levitate the object and let it hover up until it's going at orbital velocity for its altitude and speed.

To get a circular orbit, with the formulas we've derived, you need a height of almost 2 million kilometers! That's five times farther from Earth than the moon!

(To scale)

The major problem with this, is you wouldn't be in a very good orbit around Earth - you'd experience most of your gravity from the sun. You'd effectively be in an orbit alongside the Earth around the sun, rather than in orbit around Earth - and that can be problematic. Furthermore, it would take you a very long time to go that distance, even falling the whole way (because gravity would get weaker as you fell).

But, there's an easier solution. You could capture into an elliptical orbit. Now, the math for all this is even more complicated, so I won't show you all my steps (for more info, see "Vis Viva equation" - I set the apoapsis height to my current height, substitued semi-major axis for apoapsis+periapsis/2, and solved for apoapsis height using quadratic formula, with periapsis at 250 km altitude). But suffice it to say, your final orbit would look something like this, if you released as early as possible:

This should only take a few hours to complete.

So there are my thoughts on getting to orbit with gravity spells. Pretty nifty, eh? best part is, getting around is very easy at that point.

You'd still need a spaceship, of course, but instead of needing to be able to change its speed by some-odd 11,000 meters/second to get there, you'd only need to change your speed by some-odd 1,200 m/s to go into a circular orbit at 153,000 km, or about 3,000 m/s to go into a circular orbit at 250 km altitude. Roughly speaking, this means going to space would be about something as easy as taking an airplane flight.

My next 2 updates will be a continuation on this, parts 2 and 3: "Putting Gravity on a Space Station," and "The Energy of the Spell."

Sources:

Twilight Sparkle vector

Pinkie on her back, with a balloon

Pinkie having a ball

Pinkie on the Moon, and Earth

[asksciencepony]

Here Comes The Sun - Theory 3: Magic (Symmetry-Breaking) Field

Now, Magic Field Theory. This one is my personal favorite/headcanon.

Frames of reference.

Let's say you have two spaceships way out in space, zipping towards eachother, the Enterprise and the Dawn.

The Dawn's crew thinks that their ship is holding still, and the Enterprise is rushing towards them.

The Enterprise's crew thinks that they're holding still and the Dawn is rushing towards them.

You, in-between the two, think they're both moving towards eachother.

Who's right?

Turns out, everyone is. Who is moving to who is completely relative. There is no such thing as holding "absolutely still."

Whether you're "stationary," or in a closed room hurtling through space at some fantastic speed makes absolutely no difference to any experiments you conduct in your room. It's the same as if you're holding still. For example, if you were riding in a jet and all the windows were closed, you would have no way of gauging your speed. Everything would be just the same as if the plane were parked on the ground and the floor had a vibrator with some engine noises playing; or if you were actually flying.

This is something known as a symmetry. Symmetry means "same."

(A better, but less relevant example of this concept of symmetry would be a sphere; you can rotate a sphere any way you like, and it's perfectly the same. A cube has less symmetry. You can rotate it along 3 axes by 90* increments in any way you like, and it'll be exactly the same. But rotate it by something other than 90*, and a corner will be where it used to be flat, so it has less symmetry than a sphere)

The symmetry of different frames of reference is known as "General Covariance."

Now let's talk about a "broken symmetry." In the fundamental laws of nature, all frames are created equal. Whether you're in that jet or on the ground makes no difference to your experiments. Whether you're on the Enterprise or the Dawn; it's just the same. But, some local environmental factors can change that; they don't change the laws of physics, they just change how things work locally.

Normally, for example, if you release a ball, it'll just float there. But here on Earth, it falls because of gravity.

Normally, in a classroom, a ball falls straight down because of gravity. But if I'm sitting in an open-cockpit biplane and let go of a ball; it's going to zip backwards because of the air rushing by. The air creates a special frame of reference; within Earth's atmosphere, because of aerodynamic drag, that "General Covariance" symmetry is broken, in a sense.

The Earth's gravity, the air; these are symmetry-breaking things.

In what is currently my favorite theory, magic is a fifth fundamental force (There are four fundamental forces that we know of: The Electromagnetic force (responsible for just about everything you can think of, from the force of a hammer to pressure under water, because it holds molecules together), The Gravitational force, the Weak Nuclear force (responsible for some particle decays), and the Strong Nuclear force (holds the nuclei of atoms together)).

Equus has a large field of magic around it.

The magic field has three key properties;

1. Like an electromagnetic field, differences in it can be used to make magical effects happen. If you're not in this field, you cannot use magic. The stronger this field is, the stronger your magic will be.

2. The field gets smoothly weaker the further you are from the source. In Low Equus Orbit (LEO), your magic would only be a little weaker. But out on the moon, a great magician will be struggling to lift a feather against the Moon's miniscule gravity.

3. The field breaks General Covariance. Like a kind of space goo, it will drag on things down moving through it. Thus, it will slow Equu's spin.

In much the same way that a ball spinning in water will be slowed down by the water it is immersed in, Equus' spin will slowly lose speed because of this magic field it is immersed in. It will also drag on the moon's orbit, making Luna's job necessary.

Once again, each year at the Summer Sun Celebration, Celestia has a magic surge and makes up for the speed that Equus' has lost in its spin over the past year. And every time Luna does her thing, she's giving the moon a boost in its orbit.

There's a tremendous amount of room for formulating the details of the theory, but those are its general precepts.

The thing I love most about this theory is this idea of a magic field, of magic being a fifth fundamental force, and that it allows an Earth-like solar system. In fact, as illustrated, Equus could be Earth with this theory. We don't even need any other planets doing something with their orbits.

Finally, it's cool because, well, it's not impossible. I mean, in the geocentric theory, we don't even exist. In the "unstable orbits" theory, by itself, magic should be everywhere in the universe. In THIS theory, however, magic only exists in certain places that have active magic fields. How is it generated? Why have we never observed it? I dunno, but it's kinda cool because it's not impossible. I'm not saying Equestria is real or anything like that, but it's not impossible and that by itself is pretty cool for writing fanfics, imo, since the whole point of fiction is things that aren't real, and of accurate science fiction, "things that aren't real but aren't impossible."

Well, that's it for now. I'll keep my eyes peeled for any details in canon that could point to details in the formulation of this theory. At the moment, I'd like to begin by paralleling it to magnetic fields and perhaps using some analogy of differences in charge allowing a current and such. Problem with that is, I'm a completely illiterate idiot when it comes to electromagnetism. Like, for all this ridiculous amount of knowledge I have of general relativity, orbital mechanics, aerospace engineering, general physics, etc., I have this blaring gap of knowledge in electromagnetism, so I'll have some things to read about before starting to get into the details of this theory, but it's promising and exciting.

Feel free to message, ask and fan-mail me anything! I'd love to discuss these theories, and I'll even post any interesting/big modifications. Next up, I aim to answer someone's question, here. Thanks for reading!

[asksciencepony]

Here Comes The Sun - Theory 2: Unstable Orbits

Stability.

Set down a stool, and it sits there quiet happily. Try to balance a pencil on its tip, though, and you'll find the task is pretty much impossible (unless you stab it in the ground - but that's not the point).

A stool sitting on its legs quiet happily is a stable system. The pencil, on the other hoof, is an unstable system.

The second theory on how Celestia and Luna "Raise" the sun and moon, is that Equus is in an unstable solar system.

To really understand what this means, we first need to explore the concept of stability. It's quiet a bit more involved than you think. Let's take a look.

Let's start with another example. Get a big beach ball, and set a big heavy weight on it (doing this in your head works, too :P ). That's going to fall over, right? Just like balancing a pencil on its tip, balancing a, say, 40 kg (~90 lb ) weight on a beach ball is pretty much impossible.

But now, instead of a big heavy weight, let's put Pinkie Pie on top! If she's a healthy adult mare, she should weigh a lot more than that weight...

(Click images for source!)

Fig. 1

Source

...Yet she can stay on top, despite it being an unstable system, because of her balance. When she starts to fall a little one way, within a tiny fraction of a second, she counteracts it by moving a little to keep herself balanced and on top. She keeps herself very near a balancing point.

Note, though, that the further she falls from her balancing point, the more force she has to apply to keep herself up.

Fig. 2

Source

If you look carefully, she's off balance a bit. She's probably about to topple off to our left. However, if you push her to the right, oh, with say just a dozen or so pounds of force, then she'll go back to her balancing point.

Now finally, if she goes even further... (Pretend she's still touching the ball :P )

Fig. 3

Source

Here she's in quite a predicament. In order to get her back to her balancing point, you'll have to apply a lot of force! Back in figure 1, she only had to make the tiniest of little thoughtless nudges to keep herself balanced. In figure 2, it'd take a good push to get her back into balance. And in this figure 3, you'd really have to throw her back on the ball to get her back to her balancing point.

Orbits have a behavior that is a lot like a weight on a balancing ball.

Just like a weight set on a ball will want to topple over onto the floor, a planet in an unstable orbit will, over just a few dozen years, shift into a stable orbit.

The theory, then, is this: Equus (the planet our ponies live on) is in an unstable orbit.

Sometimes, planets can cruise around in interstellar space without orbiting any star. These are known as rogue planets. The theory is that at some point, a rogue planet, or perhaps even a small star, swung by the solar system Equus is in and knocked the whole thing out of whack with its gravity. What resulted, is that a large Jupiter-like gas giant (let's call it Zues) was knocked into a highly elliptical orbit.

Not drawn to scale, this is an illustration to get an idea of what this would look like:

Fig. 4

The red path would be Zues' orbit, and the blue circle is Equus' orbit.

This orbit is unstable. The gravity of Zues will try to throw Equus into a different orbit. This means one of a few things could happen:

1. Equus is thrown into a stable, but highly elliptical orbit, one where the amount of heat the planet gets would vary so much that life on Equus would struggle to survive, crops would fail, mass starvations, droughts, storms, dust storms, etc. would ensue.

2. Equus is thrown either out of the system, or onto a trajectory that will take it too far away from its sun to sustain life, even if its still in an orbit.

3. Equus is thrown into the sun, or into an orbit with a perihelion (closest point to the sun) that's so close that all life is burned.

This situation is exactly the same as the weight sitting on the ball, in the sense that this system is unstable. Where the weight will inevitably fall to the floor, Equus will inevitably be thrown into one of those situations by Zues.

However, what Celestia does, is every year, at the Summer Sun Celebration, she has a controlled magic surge.

Fig. 5 (Magic Surge)

Using this magic surge, just like Pinkie can give tiny little pushes to keep herself balanced on the ball in Figure 1, Celestia nudges Equus back on-trajectory. As long as she does this every year, then it doesn't take too much to keep Equus on track, though some years the planetary alignment may be that she needs to do it an extra time at some other point in the year.

So, simply put, keeping Equus in a livable orbit is like Pinkie balancing on the ball, and Celestia is the one who uses her magic to keep the balance. Remove Celestia from the equation, and Equus topples into an unsurvivable orbit, just like the weight on the beach ball topples to the ground.

Thus, Celestia is the reason the sun rises every day. If she didn't do her work, then in just a few years, you would see your last sunrise and the day/night cycle would be way out of whack, if you were close enough to the sun to have anything you'd call a "day" to begin with.

(Also, as some have pointed out - eternal night isn't too bad for starvation; oh no, you wouldn't worry about starving, you'd freeze to death long before that was an issue XP )

Now... What about Luna?

To explain how Luna keeps the Moon going, we first need to cover something called "Tidal Braking"

First off, the tides happen because of the Moon and Sun's gravity.

Fig. 6

The Moon orbits the Earth, but a lesser-known fact is that the Earth orbits the moon a little bit, too (they both orbit a common Center of Mass). As a result of this, there's a little bit of centrifugal force on the Earth. In the Earth's center, this centrifugal force balances perfectly with the Moon's gravity (that's what an orbit is - balancing centrifugal forces and gravity). But at its surface, it doesn't. The result, is a net tidal force ("net" meaning when you add all the factors together).

Fig. 7

That create these tides.

Now, tides do an interesting thing... Take a look.

Fig. 8

As illustrated, the tidal bulge pulls on the Moon, pulling it ahead in its orbit. Energy from the Earth's spin goes into the Moon's orbit.

However, if the Moon were to orbit the other way, the opposite direction from the planet's spin, then the planet's spin would pull energy out of the Moon's orbit, and the moon would be slowed down in its orbit, which would cause its orbit to decay.

In this theory, that's where Luna comes in. Every so often, she has to push the moon along in its orbit a little to make up for speed that it has lost to Equus' tides.

Now, say Equus' moon is in a highly elliptical orbit...

Fig. 9

At this point, every nudge is a critical one. Luna would be best off nudging the moon up at apogee (furthest point from Earth/Equus) and perigee (closest point to Earth/Equus), so twice a month. If the moon's perigee fell below a certain altitude, then the moon would be torn apart by Equus's gravity due to tidal forces.

In order to make the perigee go higher, she'd be best off giving the moon a little push at apogee (as anyone who's played some Kerbal Space Program would know! :D ).

However, if Luna only pushed it at apogee, then over a huge span of time, as the Moon is slowly dragged in its orbit, its apogee would come down, too, since Luna would only be pushing its perigee up. Eventually it'd level off into a circular orbit and slowly decay.

So to keep that from happening, and because it's easier to keep an elliptical orbit up, Luna should give the moon a little nudge at perigee and apogee, and thus keep it in orbit.

So because of her, the moon rises. If she didn't do her job, then the moon wouldn't rise.

...It would be torn apart by tidal forces and crash to Equus in pieces.

Also, I should note, that all this pushing and stuff is going to mean that their moon might have a hot, liquid core, so it would have a magnetic field, and perhaps even active geology and volcanism, which would be super really awesome and cool :3

This was my favorite theory for a long time. I wrote a large post about it here. However, recently I've come up with a new favorite theory... That'll be my next update. For now, thanks for reading! :D

EDIT: Oh, and I'm sorry I haven't answered anypony's questions yet on an ASK blog! Right after I finish these posts on How Celestia and Luna Raise the sun and moon, I'll answer some questions, m'kay?! :D

[asksciencepony]

Here Comes The Sun - Theory 1: Geocentric Model

How do Celestia and Luna "Raise" the sun and moon?

There's a number of possible explanations, the most direct, is also, to me - a Physics-Astronomy major - the most appalling. A Geocentric system (where Equus is in the center of the universe and everything spins around it) simply... Doesn't comply with too many laws of physics. It's absolutely appalling.

THEORY 1: THE GEOCENTRIC MODEL

A compromise might be that there are no planets in Equus' system. Just the Sun and Moon, and Celestia and Luna, respectively, keep them in their orbits.

First, I need to explain how an orbit works:

Gravity doesn't just go to zero in space. In fact, up at the International Space Station, they feel 94% of Earth's gravity. It just gets weaker and weaker as you get further from the planet, but never reaches zero (though it does get so tiny that it's virtually nonexistent - but never zero).

The reason, then, that the astronauts float around in space is because they're free-falling. They don't fall back to Earth because they're in an orbit.

An orbit works like this: Imagine we have an enormous tower, and a cannon. The tower is so tall, it goes way above Earth's atmosphere, so we don't have to worry about that. Now let's see what happens when we shoot cannonballs at faster and faster speeds...

(This is "Newton's Cannon")

Cannonball A will just fall and hit the ground.

Cannonball B will go further, because we launch it faster. It goes especially far because of Earth's curve, though: if the Earth was flat, it'd hit the ground at the same up/down distance in the picture as cannonball A did, but because Earth curves down, it falls further before hitting the ground.

Then, with Cannonball C, something magical happens. When you go a certain speed (V = Sqrt(GM/r)), you go so fast, that you miss the entire Earth. For just above Earth's atmosphere, in Low Earth Orbit, this speed is absolutely fantastic - 17,500 mph, or 5 miles per second (7.8 km/s, 28,000 km/h) - only a small portion of a rocket's launch is getting above the atmosphere - most of it is getting up to that tremendous speed.

Cannonball D is if you go a bit faster, and E is if you go fast enough to escape Earth's gravity altogether.

The reason I've gone over this is to point out something important: The lower you are in your orbit, the faster you'll go. If you drop something, it'll be going faster when it's about to hit the ground, obviously, than otherwise. Likewise, the lower something is in its orbit, the faster it'll be going.

Add on top of this the fact that at a higher orbit, it has to travel a bigger circle to complete one full orbit, and you'll find that something goes a lot slower the higher it is.

The Space Station circles the earth about once every ninety minutes. The Moon, once every 27 days.

So, how is this relevant?

There's a certain speed associated with orbiting at any height. That's the important thing to take from that. If you're going lower, you're going to complete an orbit faster because you feel gravity more strongly and you're travelling in a smaller circle.

At Space Station altitude (350-450 km or so) it's 90 minutes. At the Moon's altitude, it's 27 days.

If Celestia put a small, artificial sun in orbit that she keeps burning with her own magic, then she'd have to put it at the right distance to keep Equus warm, but not too hot (It'd also need to be high enough to be seen from most of Equus: Earth has a radius of 6,370 km - about 4,000 miles, it'd need to be at least half that high in altitude). But if Celestia put it in an orbit and just leaves it there, then how could she be said to be the one responsible for the sunrise and sunset?

You could either say A) She's the reason the sun burns, or B), the sun isn't in an orbit; it could need to go the wrong speed for an orbit at that height in order to give the day its proper length. If this is the case, then Celestia would have to actively work to keep it up. This is that thing I said about every height having a certain speed; the speed needed for an orbit may not be right to give the right day length for the height that Celestia's sun needs to be at. In that case, she'd need to keep it up by constantly putting a force on it.

As for Luna's role... That just doesn't make much sense, really, unless you consider the Lunar cycles to be extremely important...

All-in-all, though, it's largely a matter of flavor. I just don't like this headcanon. I suppose they could just want to keep the Moon in a certain orbit for... Whatever reasons, but this also makes it so ponies would struggle to ever come to an understanding of gravity, and makes it so space exploration just doesn't pan out very well with the moon and sun being the only astral bodies, and the sun not even being a natural star at that.

Personally, I prefer a whole solar system and more natural orbits, and some more interesting intracacies about magic...

I have a second theory that I'll be posting soon, and a third theory that I'll be using in a fanfic I'm working on. Stay tuned for more!

(PS, perhaps the closest to show canon would simply be that the sky is a sky bubble and the sun and moon aren't actual distant bodies... But I find the idea of a tiny universe like that too horrible to contemplate, so, yeah. Unless it's like, some kind of epic artificial sky or something and there IS space behind it, like a Dyson sphere, but around a planet and to create an artificial sky, instead of around a star...)

[asksciencepony]

Pony Size pt.2

So, this isn't the first time I've addressed the subject of "Exactly how 'Little' are 'My Little Ponies'?"

Here's the first shot: http://eagle1division.deviantart.com/art/My-Little-Pony-How-Little-311034846

Also on my tumblr page here, if you scroll down a little.

But I've decided to re-visit this in light of some interesting other articles I've found. Namely, this one: http://derpibooru.org/395227?scope=scpefcef5e23482ae321b60bd4602159619a58a71d60

A quick search also brings up this: http://i.stack.imgur.com/EuepU.png

And this: http://www.funnyjunk.com/channel/ponytime/Just+how+big+are+the+ponies/poBvGcb/

What is wholly remarkable, here, is that every one of these measurements coincide within just a few inches of eachother.

3'9" - Butterfly measurement 3'6" - 8' Candy Cane measurement 3'4" - "Apple Theory" 3'2" - using doorframe and Angel

The median value is 3'5.5", with a spread of only +/-3.5"!!!

None of the methods were perfect, so we can expect that kind of range - in fact, I would've personally expected even more scatter than that. That error is absolutely remarkably small. Using four completely different methods, we've arrived within an astonishingly small range! I'd say, bravo! This is really well done, considering it's a cartoon.

There is, however, one little fluke...

The big gem Spike had in "Secret of My Excess" was claimed to be 50 karats by Rarity, which, with it's size, would mean ponies are only about an inch tall.

http://earthenpony.deviantart.com/art/New-Size-Scale-for-Ponies-398073917

So, with this included, we get this:

3'9" - Butterfly measurement 3'6" - 8' Candy Cane measurement 3'4" - "Apple Theory" 3'2" - using doorframe and Angel 1-3" - 20 Carat Gem

It really looks like the "20 Carat" measurement is just a complete scatter. In fact, there are even some interesting observations that directly indicate that ponies are at least a good few inches tall. This has to do with materials science.

Materials science, simply put, makes it impossible for a creature to simply be shrunk or enlarged a huge amount and not have that creature's blood fail to flow enough, due to viscosity, or have it collapse under it's own weight, respectively.

So, seeing as ponies are mammals, and water acts normally (doesn't congeal into enormous blobs, or even small hoof-sized blobs. Think of the water blobs from: "A Bug's Life" or "Antz") that limits them to being at least a few inches tall, and smaller than real horses (real horses would die if they laid down for too long - that thing I said about "collapsing under their own weight," means they can't hold a lot of poses for long).

For example, if ponies were only an inch tall, then water droplets like this

would be at least as large as their snout, if not their hoof or even up to their knees. Water simply wouldn't act the same way. If they were even a few inches tall, then when Rarity or any other pony gets their mane wet (Rarity first comes to mind because of "Look Before You Sleep"), we'd see beads of water droplets form. Not from extremely oily hair, but from water's viscosity being much stronger at smaller scales, like how it's so strong it makes this water droplet dwarf this ant.

Now, a little analysis on each method that I find rather convincing for the ~3'6" size:

3'9" - Butterfly measurement

Butterflies can be larger or smaller, true, or drawn at not-quite-the-right scale. But this does provide a rough idea of scale, and generally speaking, they won't be drawn at a size drastically off, and materials science limits their deviance from the size of terrestrial butterflies.

So this measurement will have at least a roughly 25% accuracy (if butterflies were twice as large, and drawn twice as large, or half as large, and drawn half as large), very conservatively. This means anywhere from 15' to 11.25", though the upper size limit lies very roughly around 5', since anything around that size could not lie down or jump as we see our ponies do.

(I will concede that Butterflies could vary by more than half or twice their size, but if we allow an even larger range, than the inaccuracy of this measurement makes it almost completely worthless. So this particular measurement is with the added assumption: *If the Butterflies are within a range of half to twice as large as their terrestrial counterparts (that is to say, the ones we know of in our world))

3'4" - "Apple Theory"

This falls victim to the same exact issues as the Butterfly measurement, only apples could theoretically vary in size by an even larger amount. So, simply put, this offers a height only if you assume Equestria's apples are the same size as Earth's. With that assumption down, and assuming that the artists wouldn't depict the apples as being only half or twice as big, but will be more precise than that, this gives us a good 50% accuracy, for 1'8" to 6'8".

3'6" - 8' Candy Cane measurement

This, up until the Angel EQG measurement, was my favorite. "8 foot" is a solid answer that completely gets rid of the "apples/butterflies could be larger or smaller" problem. We'll ignore the "how do you measure a candy cane's height; do you measure around the nook?" objection. I find that plain silly. The height of the object is the distance from it's base to it's top, quite simply, and she stated it was an "8-foot candy cane," and generally speaking, when you refer to a tall, narrow object by a single-dimensional distance, you're referring to its height.

In general, you refer to things by their greatest dimension. For example, a 20-foot boat, 11-foot snake, 30-foot alligator (why not?), or 11.5-foot pole. I need not specify; "20-foot long boat," or "11-foot long snake" (though 11' dia would be very impressive) or "11.5-foot long" pole. It's a simple taken: we measure things by their greatest dimension.

So, taken it's 8-foot tall, this places ponies at 3'6," with, I'd say, roughly a 75% accuracy. You could mistakenly call a 6' or 10'8" object as being 8', but outside of that, you'd probably at least call it 7' or 9'. If that's accepted, then our accuracy here gives a range of 2'7.5" to 4'8."

3'2" - using doorframe and Angel

Now this is my absolute favorite! We know for a solid fact, we have a standard, and standard doorframes are either that exact height, or close to it. Using that, we get the height of the humanized ponies. Then we have angel, an object that is the same in Equestria and humanized world. So we have an implied size for Angel, and thus an implied size for Fluttershy, and all the mane 6 are roughly the same size.

The only possible error here is if the doorframes are non-US standard, and errors of mere pixels in measurement. The former would only throw us off, at most, a few inches, or whereabouts 10%, and the latter is so small it's not worth describing. But if we must, I'd attribute it to no more than 5%. 15% Cumulative error, or 85% accuracy. This produces the spectacularly small range of 2'8.3" to 3'8.7"

Now, this one. I think by this point, you can understand my disdain for this one.

1-3" - 20 Carat Gem

It was a good go, it really was. This works excellently if we assume that ponies "Carats" are the same as ours. However, given the vast amount of rather well-established data that contradict this (namely, every single other measurement requiring at least 10", and the ones of solid nature, the 8-foot candy cane and doorframe, give at least 2'7"), I think we're forced to conclude that what ponies call a "carat," isn't the same as what we do.

Carat, as a unit of mass, as is used when measuring gems, stems from the Carob seed (s). So this unit of measurement falls under the same problem that "Apple Theory" does. Namely, while materials science puts some loose limits on the size range of animals, it puts practically no size limitations on trees and other plant-based life, not to mention our measure of "Carat" has come from such a winding history, and in a world where a fist sized diamond would cost many fortunes. Meanwhile, in Equestria, a fist-sized diamond seems to be the equivalent of only a good few bucks. If their world wasn't like this in antiquity (think; three tribes before formation of Equestria, journeying to a new land, finds that the new land is rich in naturally occurring pure gems), then it would make sense that their history of such measures would be radically departed from ours.

In any case and in summary, there's a huge number of very strong indications that are ponies are somewhere very near to 3'5.5," and the fact that 4 different methods all converge on this answer to within +/- 2.5", despite each individual method having a much, much larger range, is an extremely strong indicator that this, is, in fact, the correct height of our ponies.