The Celestial Conjecture 

Abstract: In this article, we explore a question as old as MLP itself, one that traces back to the very first episode: How does Celestia and Luna raise the sun and the moon? We attempted this question using evidences from MLP episodes along with some of the most fundamental laws in physics such as Einstein's theory of relativity. Working with the assumption that the Equestria sun has similar propeties as the our sun, we made the argument that the Equestria sun has similar size and positioned at a similar distance away from Earth as the moon. We further propose the three celestial bodies, Sun, Moon and Earth are not in orbits with each other but stationary relative to each other. Finally, we conclude that Celestia and Luna raises the Sun and the Moon with their magic in the most literal way by positioning them above the land of Equestria during day and night respectively. 

 Quantum Pony ¹

¹ Theoretical Pony Science, Pony Department

The Institute of Pony Studies 

SW8 3AZ  Equestria

 

Introduction: 

(contains extremely minor spoilers from S02E11: Hearth Warming eve)

 

Day and night in Equestria are brought magically by Celestia and Luna, and before that, by group of unicorns as shown in [1].  On the otherhand, in the world we are familiar with, magic is not required to bring forth day and night as it is achieved by the earth's orbit around the sun. Several questions are raised from this:  Does the Equestria solar system follow the same heliocentric (earth around the sun) model as our solar system or does it follow a geocentric model (with sun around earth). Interesting and detailed discussions of this can be found in [2]. But a more important question is the role of Luna and Celestia. Is the whole "Celestia raising the sun" simply a huge lie to keep them in power and ensure no pony would overthrow them as it would endanger equestria itself? It is therefore the purpose of this article to investigate just how does Celestia and Luna raise the sun and the moon. 

 

Some Physics prelude:

As stated in Axiom 2 of the previous entry, we will be assuming the laws of physics that works in our world works in Equestria universe as well. Although this does not mean there isn't new physics concepts in Equestria as well (which I am sure there are plenty). 

Luminosity:

To investigate the question laid out in Introduction, we need to know the role played by the sun in order to sustain life on earth. As outlined in [1], the Earth ponies needs the alteration of day and night provided by the unicorns in order to grow food. It can be computed using the surface temperature of the sun, its radius and distance from earth the amount of power (per unit area) we receive here on earth. In our universe, this adds up to about 1380Wm^-2 (where W is Watts, the unit of power). So the distance, d, the size, R, and the temperature, T, of the sun needs to be appropriate in order to provide that much power. Although the ponies may not need exactly 1380Wm^-2 we will strive for something at a similar order of magnitude. 

The equation for the luminosity L (defined as the power per unit area) is:

L = (some constant)  x  T ⁴  x  R ²  x  d ^-2

From this we can see the role played by inverse square law, basically, the closer the sun is to Earth, the greater the luminosity. So to have a large sun very far away is similar to having a small sun very near Earth (assuming they have the same surface tempreature T). 

Special Relativity:

Now we turn our attention to the next topic: Special Relativity. Special relativity, formulated by Einstein,  is one of the greatest achievements in the 20th century. It gives rise to what is arguably the most well know equation: E=mc² . But there is another consequence of special relativity, one that is even more important and controversial in the old days: Nothing can travel faster than the speed of light. This is arguably one of the most firmly established and tested law in physics and we must assume it to hold in the Equestria universe as well. Otherwise, we will not be able proceed at all with any form of physical theories after Newton, and assuming faster-than light travel causes a lot of problems with causality as well.  Hence, we propose the following: 

 

Theorem 1: Magic is a fundamental force of nature. 

Corollary: As any other fundamental forces of nature, Magic cannot travel faster than the speed of light (300,000km/s).

 

The Equestria Solar system:

Position of the Sun, Moon and Earth: 

In our universe, the moon is positioned d_moon=4x10⁸ m away from earth with a radius of R_moon=1.7x10⁶ m. On the otherhand, the sun is positioned d_sun=1.5x10¹¹ m away from earth with a radius of Rsun=7x10⁸ m. The position and size of the sun gives the correct luminosity to sustain life on earth. One interesting property is that the ratio Rsun / d_sun  is approximately equal to the ratio R_{moon / dmoon} . Infact, this is the reason why the moon and the sun looks the same size in the sky! The importance of this in our investigation will be obvious soon. 

In [3-4] there are several incidences where the sun is raised by Celestia. One of the most important thing to notice is that as Celestia raises the sun (the moment her unicorn shines bright with her magic), the sun immediately moves as well. But if the sun is at a distance 1.5x10¹¹ m we know it takes about 8 minutes for light to reach the earth. Hence, her action of immediately moving the sun (which if counting her magic reaching the sun and the light from the sun to reach us, should take 16 minutes) would violate Theorem 1 as stated above. To ensure special relativity and hence causality to hold, we need a sun much closer to earth for what happened in [3-4] to make sense. 

From [5], we can directly compare the size of the sun and the moon in the sky and it shows they are approximately equal, similar to our universe. So we have two conditions to meet: 

Condition 1: The sun must be near enough to almost immediately react to Celestia's magic 

Condition 2: Its luminosity must be such that it can sustain life on earth and appear as the same size as the moon. 

Miraculously, both of these conditions can be met!

 

Proposition 1: The sun is just as bright as ours but has the same size of the moon and placed at approximately the same distance away from the earth as the moon.

This is near enough for Celestia's magic to cause an immediate reaction of the sun (with about a 2.5 second delay) and bright enough (~1380Wm^-2) to support life on earth. Hence explaining the scenes in [3-4] as well as not violating special relativity. Of course, we can place a slightly larger sun slightly further away as well and still meet Condition 2, however, we need it as close as possible in order for Condition 1 to hold. Furthermore, due to the possiblity of an eclipse, the lower boundary on the distance is that it still needs to be further away than the moon. 

 

The actual movements of the Sun, Moon and Earth:

When two celestial objects such as the sun and earth comes near each other, they will be caught in each others' gravitational pull. As a result, they orbit around each other, with the heavier body appear more still and the lighter one appear to move around it. This is how planets orbits the stars and moons orbits planets in our solar system. However, one of the reason this works is that out of all the fundamental forces, only gravity is significant in this situation. Equestria on the otherhand, has another significant force which is Magic. The ability of Celestia and Luna to move the sun and the moon shows this long range force is significant enough to combat gravity. Hence, it wouldn't be a surprise that the even though planets might orbit around each other before the time of ponies, when the unicorns came they stopped the orbit with their magic. As a result, one can make an educated guess that the sun, moon and earth are stationary relative to each other. 

Now lets get into some more detail. There are times in [5-6] where there is no one to perform the duties of raising the sun and the moon. If we consider the above theory that unicorn magic is the force that repels the gravitational attraction of the three celestial objects, wouldn't they collide into each other during its absence? The answer is yes. However, due to their distance apart, it would take a significant amount of time for this to occur such that in the time frame of [5-6] there wouldn't be a significant difference in their positions in the sky. This can be computed using Kepler's laws and the result is about 5 days. For more information see [7]. 

With these features established, the act of Celestia and Luna raising the sun and the moon is exactly what it is. They used their magic to position the sun and moon above equestria to create day and light. At night, the sun would be rotated to the otherside of earth and similarly for the moon during the day. 

 

Questions yet to be addressed: 

The propositions above solves some of the questions but also raised some more questions. For a star to be the same size of our moon is unheard of in our universe and seems even more difficult for it to be just as bright as our sun (since it needs to be at a certain size to sustain the fusion reactions in its core). Furthermore, the mean density of the moon is lower than that of the sun, hence for them to be the same size, the moon would probably have been heavier thus contradicting the comments made by Celestia in [8]. However, the above calculations maintains that the sun merely have to be approximately the size and distance of the moon. We can place it slightly further away, with a larger volume and lower surface temperature and still allows the same luminosity to sustain life on earth and keeping laws of relativity intact. Although the exact computations needs to be worked out. There are also questions about whether the Earth is flat or spherical. My personal view point is for Earth to be spherical and such arguments were already made in [9]. However, a flat earth Equestria would not significantly hurt the arguments above as gravity still works the same way. Celestia simply needs to take the sun to the 'backside' of earth. See [10] for a visualization of this process in a different universe. 

 

Conclusion:

The position of the sun can be chosen to be approximately the same distance away from earth and with the same size as the moon. This allows a luminosity that can sustain life on earth as well as not violating the laws of relativity when Celestia uses magic to move it. Furthermore, the sun, moon and earth are stationary relative to each other instead of being in orbit. As a result, Celestia and Luna raises and lower the sun and the moon by using their magic to resposition them above the sky of Equestria and thus bringing forth day and night. 

Future work can include doing some more computations so that the numbers adds up and considering other effects that a smaller and closer sun could do to Equestria. 

 

Acknolwedgements:

Quantum Pony is grateful of all the insightful and stimulating discussions in mlpforum and fimfiction. Quantum Pony is supported by the Equestria Potato Grant. 

 

References:

[1] Williams, M et al. (2011) S02E11 MLP:FIM 

[2] Batbrony et al (2013) The Solar System of MLP: Ptolemaic or Copernican? mlpforum

[3] McCarthy, M et al. (2013) S04E02 MLP:FIM

[4] McCarthy, M et al. (2014) S04E26 MLP:FIM

[5] McCarthy, M et al. (2013) S04E01 MLP:FIM

[6] Haber, J et al (2016) S06E25 MLP:FIM 

[7] Scileander et al (2017)  If you were to fall the the distance that the Moon is from Earth, how long would you fall? 

[8] Lewis, J et al (2017) S07E10 MLP:FIM  

[9] Ponitten et al (2016) A theory that could prove that Celestia doesn't raise the Sun after all, mlpforum

[10] Summit Entertainment (2016) Gods of Egypt