Equestrian Cosmology and Supernatural Physics

Prefix

In order to uncover how powerful a My Little Pony: Friendship is Magic unicorn is, we must first reveal the astronomical and cosmetically involved aspects of the providence Equestria. It is prospectively smaller than Earth, perhaps the size of Mars. The lower gravity would explain how pegasi can fly with such small wings. It would also allow for more fantastic architecture (the type we see demonstrated in Canterlot). Due to its small size, the planet would have quickly run out of geothermal heat. It would rely almost entirely on the sun for warmth.

Being a geologically dead planet, Equestria's tectonic plates would have 'frozen' in place, forever fused together. The solidifying of the planet's core would make it less susceptible to tidal forces. Smaller tides would mean that global weather patterns would be dampened, vindicating why the pegasi need to manage the weather. Therefore, with the core of the planet dead, it would be lacking a magnetic field. This means that Equestria could not have a sun like Earth's, as the solar wind would slowly strip away all of Equestria's atmospheric water. A significantly smaller star would not have as much coronal mass ejections and would be safer for Equestria. However, this would mean the star would also need to be closer to make up for the lower output.

The sun would likely be below the threshold for self-sustained fusion. If forced to do such a thing, it might sputter and burn for a few hundred years, but never ignite into a true celestial fusion furnace. Thus, magic is needed to sustain the sun. Given this understanding, if Celestia died, this would not mark the sun's destruction, but rather its regression to a black dwarf. It would be possible to reignite the corpse of Celestia's 'fake' sun.

Facts

-The apparent brightness of Earth’s sun is the same as that as the sun controlled by Celestia.

-The apparent size of Earth’s sun is the same as the sun controlled by Celestia.

-The blackbody curve of Earth’s sun is the same as the sun controlled by Celestia.

-Therefore, Equestria’s need for pegasi to maintain weather is due to the planet being geologically dead. This has caused it

to have a mostly stagnate climate (with places like the Everfree forest being the exception because of various factors (mountain ranges, bodies of water, etc...).

-Celestia’s sun was not a true star. Assuming Equestria is geologically dead would mean that it has no protection from coronal mass ejections (unless the moon has a magnetic field).

-Celestia’s sun requires a constant flux of energy to maintain. It is not simply ‘running’ of a preexisting well of energy. This rules out class F white dwarfs. This means Celestia needs to constantly feed the sun energy. This also means her sun needs to be relatively small (so that gravitational pressure is not causing fusion).

-The fact that Celestia’s cutie mark is a sun leads me to believe maintaining the sun is her special talent. I will assume her efficiency is 100%, i.e., all of the energy she pours into her sun is converted to luminous output.

-Celestia would put her sun in a position as to minimize the burden it would place upon her.

Because the geothermal energy fluxes of Earth, it is several orders of magnitude lower than the solar energy flux, which for the purpose of energy calculations we do not need to worry about if Equestria is geologically active. Any discrepancies that exist could be accounted for by higher levels of greenhouse gas (perhaps also helping to explain the lift generation of pegasi).

Physics Application

For simplicity, ESun will mean Earth’s sun. CSun will mean Celestia’s sun.

The brightness multiplied by 4pi times the distance squared will give us the luminosity (or energy output). We will assume that the brightness of Esun and Csun are equal so we can find the luminosity as a function of solar distance. To reduce the required energy to run the sun, we will be assuming that Celestia keeps it close to the planet. I am assuming a Low Earth Orbit (or in this case, Low Equestria Orbit) of 2000km.

This states that the power output (Luminosity) of the CSun needs to be 210 Petawatts (thereabouts).  I will put this in perspective a bit, but we can now use the Stefan-Boltzmann law to find the size of her sun.

The Stefan–Boltzmann law, states that the total energy radiated per unit surface area of a black body per unit time (also known as the black-body irradiation, or emissive power), is directly proportional to the fourth power of the black body's thermodynamic temperature.  Thus at 100 K the energy flux density is 5.67 W/m2, at 1000 K 56,700 W/m2. Convert it, and the distance is 9.4km.

This is only about twice the size of Manhattan (quite small), only about 0.5% the size of our moon. This puts it on par with Neutron Stars in terms of size. I should also mention that at Low Equestrian Orbit it is significantly closer than the moon. We now have a good understanding of what the sun might be like. I would assume its mass is only large enough to hold it together against the outwards energy flux (I haven’t done those calculations yet, and it may well turn out it will need to be massless).

To put the energy output into perspective:

121 Petawatts is how many joules of energy per second the sun is emitting. Not all of it reaches Equestria; some just goes out into space.

Humanity is used on average 16 Terawatts of power (or 16 Terajoules) of energy a second during 2010. This is 1300 times less than our value of 210 Petawatts.

Things Celestia could accomplish by redirecting the energy she sends to the sun for one second:

Power a hurricane for 16 minutes.

Cause a 60 megaton explosion (the largest hydrogen bomb ever detonated was 50 megatons, most are much smaller than that. She can do this once every second).

Launch three billion kilograms to the moon (about six billion pounds).

Since her special talent is the sun, not sending things to the moon, causing hurricanes, or blowing things up, she is probably less efficient at those things. However, even assuming 1% efficiency at non-solar activities, it is still very impressive.

Twilight Sparkle in Season 1:

Based on the Ursa Minor’s size, and assuming its density is the same as a pony, the Ursa Minor weighs around 100,000 kilos. Add this weight to the water tower she was also levitating, and you get 2,185,000 kilos.  Assuming she was near her limit, this puts Twilight`s peak output at around 3 megawatts (assuming that her apparent struggle is not an issue of finesse, or control). I suspect the average power output of a skilled unicorn (like Trixie) is closer to fifty kilowatts, and your average unicorn is capable of 1/2 that.

Chapter Summary:

-Princess Celestia was capable of creating a 60 megaton explosion every second (a 60 megaton explosion can send the Hawaiian Islands into fallout). A 1 megaton explosion is 80 times as powerful as the atomic bomb dropped on Hiroshima.

-In episode 6, Twilight Sparkle could create a 0.0000108 megaton explosion.

Author`s Note-

Please comment or PM me about any errors you see, grammar or scientific. Expect Chapter 2- The Fundamental Nature of Magic- tomorrow!