Very nice, Bale! This is why I love my OSD guildmates.
Scientist. Student. Gamer.
Howdy all!
As a card carrying nerd and geek with a wide open Saturday on my hands, I decided to investigate the astrophysics of Elyria based on the available information!
As always, I may be wrong - If you spot any mistakes or just disagree with my methods, etc. I'm happy to be shown the right way!
Since we don't have all the data, I've had to make some basic assumptions to fill in some "gaps".
Physics on Elyria work the same as in our universe. This means various constants (like the universal gravitational constant) are the same. Similarly, various relationships hold true in the Elyrian Universe (such as Kepler's 3rd law).
Since there are humanoids on Elyria, I'm going to assume that they absolutely need to be in the habitable zone of the local energy source (star(s)).
There is no advanced tech that would mimic certain phenomena. As such, anything that is, must be explained in terms of natural phenomena.
Elyria is a spheriod and its orbit is almost perfectly circular (similar to Earth)
The assumption that Elyria is a spheroid and its rotation is constant (meaning it doesn't speed up or slow down on some rhythm) is reasonable since otherwise, the Day/Night cycle would depend on where on Elyria you happened to be. But since we assume that days are precisely 1/5th longer than nights are (3/5 : 2/5) anywhere on Elyria, this implies that the rotation of the planet is constant.
Similarly, the fact that all seasons last the same amount of time means that Elyria spends equal times in all 4 phases of its orbit.(Yes, I know that it's not your orbit that creates the seasons, but it does influence how long they last)
As pointed out by Ender below, in order to use the simplified version of Kepler's 3rd law we need to assume that the star(s) mass is equivalent to that of our own. This means that these numbers are an over estimate (since the Elyrian sun(s) are likely less massive).
I don't think these assumptions are too wild or unwarranted and as such, I feel that it's reasonable to move on.
A season in Elyria is 10 Elyrian days, which is approximately 24 Earth Hours.
There are 40 Elyrian days (96 Earth hours) in an Elyrian year.
There are 2.5 Earth hours per Elyrian day and night cycle.
Now, of all of these, the Day / Night asymmetry is the most problematic and the most influential. Because any given point on Elyria will experience light 3/5th of the day and night only 2/5th of the day coupled with the fact that Elyria is a spheroid, this means that we need to cover more than 50% of the planet with light.
Imagine a ball and a flashlight. Turn the flashlight on and point it at the ball. If the flashlight is far enough away, it will be able to bathe exactly half the ball in light (but no more).
However, this is not a proper solution for Elyria since rotation is constant, it's spherical, and the Day/Night cycle is asymmetric in favor of day. Without a really fancy solution, the only way to accomplish this is to ensure that more than 50% of the planet is lit at any given time. In fact, we need to make sure that 3/5ths of the planet is covered in light. This requires a second light source.
I just don't see any other way to capture this asymmetry, though if you have an idea, I'm all ears!
Also, note that the actual distance between both stars is dependent upon the size of Elyria. Since we don't have the info, we can't fix that distance (and there are good reasons not to assume Elyria is the size of Earth).
Now, we know that an Elyrian year is 40 Elyrian days long. As such, we can use Kepler's 3rd law to calculate the distance Elyria is from its local stars. Here we'll need to make a few more assumptions about the binary stars themselves. Since gravitational calculations are made based on "point" gravity sources, we can simplify by using the gravitational "center" of this binary system as a focal point for the orbit. I'm going to assume that both stars are the same size and, as we'll soon see, they have to be Very very small indeed. But, as noted by Ender, we must assume here that their combined mass is equivalent to that of our own sun in order to make the equations work. These are an over-estimation until more data becomes available :)
Since we lack information about Elyria's diameter or total mass, or really anything physical about it, we will not be able to use the more complete version of Kepler's 3rd law. Instead, we'll use p^2 = a^3. This is a wonderfully elegant equation that says that the orbital Period (in years) of an object is directly related to how far away that object is (in AUs - the distance between Earth and the Sun) from the main gravity source.
So we can do this as a fraction of the Earth - Sun relationship to get our answer:
1 Elyrian Year = 40 Earth Days
1 Elyrian Year ~= 0.11 Earth Years = P
So now we know P, let's get A.
A = 0.229577 AU.
0.229577 AU = 34,344,719.20 km ~= (21.3 million miles)
Now we have the distance from Elyria to it's host stars, but that's only half the calculation needed. We said that Elyria needs to orbit in a near perfect circle (similar to Earth which varies less than 3% between perihelion and aphelion). This means that the Radius of the orbit is 34,344,719 km which makes the diameter of the Elyrian orbit ~= 68,689,438 km.
In order to complete 1 orbit around its host stars, Elyria travels just shy of 215,794,233 km in 40 days. Compare that to Earth which covers approximately 940,000,000 km in 365 days. That means it's whizzing around at 62.4 km per second. As a comparison, Earth travels at approx. 30 km per sec. Pretty fast!
In order to keep Elyria within the habitable zone (meaning water can exist as a liquid on the surface), we have to make the Elyrian stars smaller. Much smaller. For the sake of simplicity, let's use the Earth - Sun as a model.
The Earth is 1AU from the Sun, and the sun has an equatorial radius of 696,342 km
Elyria is 0.23AU from its host stars, which means that they need to have a radius of 160,159 km BUT there are 2 stars, not just 1, and they orbit each other (basic physics). So let's allow for the radius of their orbit to be 160,159 km and just split the difference. This would make each star's radius at Most 72,071 km [(160,159 / 2) * 0.9 <-- allows for some distance between them]. Now, I COULD use what we know about the required angles of light to allow for 3/5 : 2/5 day/night cycle to calculate how far these stars need to be from each other, and thus further constrain their size (and then be able to calculate their orbital speeds) but since we don't know Elyria's diameter, I'll just leave it for now.
Some of you may be a bit peeved (and rightly so) that I sort of ignored the fact that smaller stars produce less luminosity thus affecting the "habitable zone" (meaning it needs to be closer to the energy source) which would then affect its orbital period, etc. Fair enough! Here' we go!
This is a Hertzsprung-Russell Diagram Showing Masses and Luminosities of Main Sequence Stars.
note the log scale of temp
What we derive from this (and a bit of maths) is the following:
We know that the total orbital radius of our binary stars is ~ 0.23 the size of our Sun's, which means that both stars together put out around 1/1,000th of the luminosity of our Sun (on the positive side, these stars will survive on the order of Trillions of years rather than the mere Billions our Sun will!)
Which makes the total luminosity of our binary stars just 0.04 solar units.
This all means you need to be much closer to the binary stars to get the same effect. Now, it might seem like the maths don't work out (they do) but we also need to keep in mind that Light follows an inverse square law which means that it "fans out" as below.
This means that the closer you are to the source, the more of it you get. (this is true of sound as well - closer you are to the speaker, the louder it is, which is why your earbuds can be so "silent" and still sound really loud when close to your ear!). Tying this back to the Habitable zone, we're almost there. First, we need to know how "hot" the stars are. Again, for the sake of simplicity, I'm going to use the Combined temp of both stars.
A quick glance at the chart above shows us that our combined binaries fall somewhere between Cygni A and Bernard's Star. This puts us around 10^-2 solar luminosity units, and around 4,000 kelvin. Using this fancy maths we see that the habitable zone falls between 0.205 and 0.389 AU (plugging in 4000 for Teff K, and 0.04 for luminosity). Luckily, with a distance of 0.23 AU we're golden(locks)! Oh, and the light shining down on Elyria would be Reddish Orange.
I think we've reached something like the limits of what we can squeeze out of the data on hand. I hope you enjoyed reading this as much as I enjoyed writing it!
Again, any comments, observations, disagreements and general thoughts are always appreciated!
Don't forget to pack your sunscreen!
Cheers
Edited for numerical accuracy!
Scientist. Student. Gamer.
I could say that it's just a game, and that we can ignore physics like this, but I really like reading stuff like what you put down. Bravo!
I may be wrong, I'm not very good at this, but if you use AU and Kepler's 3rd law to calculate the distance between Elyria and its sun, you put Elyria in our solar system. Or, more specifically, you assume that Elyria's sun has the exact same mass as ours, which is a pretty significant assumption (and I don't see it in the list of assumptions). Our sun is very small, actually.
Again, I may be wrong, it doesn't matter, I learned a few things today and I thank you for that.
My only questions now after reading that well organized wall of text and images, to the Developers is;
Based on Balerathon analysis will Elyria have two suns?
Will the color of the current suns rays be changed so the world has a more Reddish Orange?
Hey Ender, that's a great observation! In fact, in order to be fully "converted" we'd have to use Kepler's more general equation. But since we don't have any data on the mass of Elyria (the star we could approximate it based on available data), we wouldn't be able to plug it all in.
So absolutely, mass equivalence was an implicit assumption in using the simple equation. I've edited that bit in and add that the numbers should be taken as a rough estimate based on the above :D
Love it!
Scientist. Student. Gamer.
Thanks for this. Loved it!
It brought up a thought. Will we have a moon or two? If yes, will there be a tide?
You sir, are a legend. Pure and simple. As for Elyrian mass, perhaps young Caspian will be turning to you for some assistance in the correct calculations?
A small question to consider though, would atmospheric refraction not explain the discrepancy between hours of light and hours of darkness? A single, larger sun, would light the planet for one half of the rotational cycle, if you add in the extra time that the refraction could cause (depending on atmospheric composition), you can have the remaining 1/10th of the day length being in daylight fully explained.
Hey Frithgar,
Thanks :) That's a great question! Here's what I think:
I think that atmospheric refraction Could lead to the planet being lit for longer, but probably not that much longer. When considering the 2 light source solution, I decided that it's likely the case that anywhere you are on Elyria, the game would look as though you were in normal sunlight and that light would "fade" at a constant-ish rate. This means it's probably not refraction.
Also, Refraction has its limitations. For starters, certain wavelengths of light are more and less likely to create a noticeable effect. More interestingly Refraction is just "bending" light. So in order for refraction to play this role, the refraction angle would have to be wildly steep.
Let's consider the scenario:
Firstly, we need to agree that the light we "care" about here is on the very edge of the planet (the black lines in the images above) since all the lines in between are going to hit the planet anyways.
So, a ray zipping along from the star (the black line) enters the Elyrian atmosphere where it is refracted. In order to not just "stay" in the atmosphere longer, it would need to be refracted (or redirected) basically more than 90 degrees such that it would then hit the surface of Elyria. There's likely a lot of wiggle room (pardon the pun) here, but that's a general idea. In order for enough light to be "reclaimed" we're talking a serious refraction (that would require some exotic atmospheric compositions).
So either Elyria has some special super refractors that redirect the majority of light back towards Elyria, or something else even weirder is going on.
I sort of counted this option as the "really fancy" solution because I think it, on its own, isn't enough to get the effect you would expect to see in-game.
Hope that helped!
EDIT:
With regards to the 2 sun thing, we have to keep in mind that they are Reaally really close to one another and so they orbit each other noticeably very fast but again, we have no data. I'd have to do the math, but it's probably the case that we'd either be able to see them spinning quickly, or that they'd look like a blur from our point of view. If that's the case, personally, I'd rather just see 1 star and "know" that it's two :)
Scientist. Student. Gamer.
Just going to throw this out there.
Game engine lighting doesn't work like RL light does. It isn't nearly as hard as you think to make two light sources and have a part of a sphere be in darkness. The Issue I think that will be the problem is that I don't believe that the whole planet will even be used. If I remember correctly Caspian said today in the live stream that the game world would be about the size of the United States. I, of course, do not know how big the world will be in the end and whether or not it will have similar geography as earth. I would guess that the world will be "flat" not to say that they can't do things to make it seem not flat. but the terrain mesh will be a flat sheet that is molded to look as they wish Elyria to look. Lighting is will be very different from RL situations.
The sky will be either a Sphere or a Cube that has a texture. Sphere will most likely get an HDR texture, while the cube will have a 6 sided texture that gives the Illusion that it is a round surface.
I have a Game Design Degree, which is why I know about this stuff. I don't know about all game engines. I have used CryEngine and have an understanding of the lighting system. It shouldn't be to difficult to figure out.
They will do a rough setup of the lighting and see have well it works. After that they will do some tweaks to get the lighting to feel right. Game lighting is basically like buying the perfect lightbulb from the store.
Like I said in my previous post though. This is an awesome thread and I am glad I had the chance to read it. It got me all excited. lol
Thanks for taking the time, Balerathon!
This is awesome. But, I also must remind everyone that the universe that Elyria is in may not(does not) follow the same laws of physics as the universe that the earth is in. So, its easily argued that a world with a 2.5 hour day, and a 40 day year can exist without any special needs. Its also possible that the world is not a sphere, but more disc shaped and has an irregular rate of rotation. All the math in the world wont help us with the physics of Elyria, because Elyria exists outside our physics.
PS: Im pursuing an advanced degree in physics so I did enjoy this post a lot. :)
Great points MugenZero and Deffcon.
There is no question that the game world will follow its own rules. Making an asymmetric day/night cycle for a game is just changing a few values.
It would be impractical to actually model our universe for the game heh. I would not expect any of this stuff to actually translate into the game, just a thought experiment :)
Thanks for the kind words!
Scientist. Student. Gamer.
Thank you for the detailed answer there, I enjoyed it!
Two points now, first the spinning suns, I don't have time to investigate the physics, but if we're assuming the world of Elyria to follow our own universes basic laws, is it even possible for 2 stars of the size you're suggesting to spin so fast that from that close distance (the planet surface), they'd be blurred into one large orb? Surely they'd adopt a more gentle rotation that could be seen from the earth, maybe with some interesting sunsets thrown in.
Point two, my question about refraction was indeed based on the atmosphere of the planet being somewhat more exotic than that of Earth!
Thank you again for the interesting and detailed answer!
Hey Frithgar,
So, in order to calculate how fast they'd actually be orbiting each other, let's make some assumptions:
We can use the following equation for binary stars to plug it all in since we know M1 and M2 which will equal to 1!
P^2 = A^3/M1+M2
Again, P is in Years, A is in AUs, and Ms are solar masses.
P = Wanted A = 160000/149600000 = 0.0010695 AUs M1 = 0.5 M2 = 0.5
P^2 = A^3 / M1+M2
P^2 = 0.0010695^3 / 0.5+0.5
P^2 = 1.22339*10^-9 / 1
P = 0.000034977 Years = 18.38 minutes.
So we finally find that if you stared at 1 spot in the sky, every 9 minutes you'd see a different star in that position. That's pretty fast but not "blurry" fast. :)
We'd also need to take into account how bright it is from our PoV on Elyria to tell if we could discriminate 2 globes.
Scientist. Student. Gamer.
