The Moons of Roshar

[Jofwu he/him]

The map that Brandon tweeted in the Oathbringer dust jacket confirmed some suspicions about the size of Roshar. The bulk of the continent spans about 140 degrees longitude, meaning it wraps more than 1/3 of the way around the planet.

We know that Salas appears just after sunset on the Shattered Plains, and this got me thinking... When do the moons rise for people in the far West? The sun doesn't set in Shinovar for another 1/3 of a day after it does in the East. Wouldn't they be rising when it's still daytime?

Care to comment on this observation @PeterAhlstrom?

 

[raykoda16]

Okay, so some of the Math-fu one this topic got me inspired, so I used the mass of Roshar that @Leiyan got, and the fact that the value of the gravitational field is 0.7 times that on earth to derive the radius of Roshar (say that five times fast!).  Might not be too incredibly useful for the topic at hand, but it might be interesting.  

So, per Newton's Laws:

g = Gm/r^2

We can set g to be 0.7*g on earth, or 9.81 m/s^2,m to the mass of Roshar, or 2.1 * 10^24 kg, and G is the gravitational constant, or 6.674 *10^-11 Icanneverremembertheunits. 

rearrange for r,

r = sqrt(Gm/0.7g))

and we get a value of 4.49 * 10^6 m, or just under 4 and a half million meters in radius.  

That's about two-thirds of the radius of the earth, which seems reasonable.  

For all you dumb yanks, that's 2790 miles.

Please feel free to double check my work, I might have gotten something wrong. 

Also, that just might have been the nerdiest thing I've ever done.

Edited October 18, 2017 by raykoda16

[Jofwu he/him]

43 minutes ago, raykoda16 said:

Please feel free to double check my work, I might have gotten something wrong.

Aw, you didn't be to go through all that unfortunately. The math looks right, but I think the mass estimate is wrong. Where was that number from? This whole thread is pretty put of date. I don't think it got serious attention after WoR, and Arcanum Unbounded gave a few ore tidbits.

AU canonized the 0.7g gravity and told us Roshar is 0.9 the "standard" size. (i.e. Earth). So the radius is 5740km. From there we can use that equation to calculate the mass: m = 0.7g (5740km)² / G = 3.389×10²⁴ kg

So 70% surface gravity, 90% Earth size, 57% Earth mass. I think that comes to 78% Earth density, which is reasonable.

We can almost calculate the semi-major axes of the orbits, now that we know the mass of Roshar, by using the equation for the orbital period. Got to make a guess for the length of a day... I think there's a bit of ambiguity as to how long it is, but the error in assumptions ight be small enough not to really matter. Need to check.

And if someone really wants to go the extra mile, we might be able to use Peter's comments on how long they're in the sky to get a rough guess of their apsides (high and low points of the orbits). That'd be a bit trickier to do, but I think there may be enough for a respectable guess.

All of this thanks to a single number in AU.

I searched through WoR and there's a lot of good references I'm there that haven't been picked up as well. Particularly more insight on their "phases", sizes in the sky, and rise/set times. Though at this point perhaps it's best to wait for Oathbringer before doing a deep dive...

[raykoda16]

I got it from @Leiyan's post in the second page.  Can you permalink individual posts here? I'm kind of new.

Anyways, one minor nitpick is the figure of 0.9 cosmere standard size.  Does that refer to radius, or volume, or what? I don't have my copy of AU nearby, and The Coppermind isn't helpful.

Yeah, I noticed how old this thread is, but I just saw it after your necropost, and felt inspired.  All of this is honestly pretty beyond me.  I just found one little thing that I knew I could help out with.  

[Jofwu he/him]

7 minutes ago, raykoda16 said:

I got it from @Leiyan's post in the second page.  Can you permalink individual posts here? I'm kind of new.

Anyways, one minor nitpick is the figure of 0.9 cosmere standard size.  Does that refer to radius, or volume, or what? I don't have my copy of AU nearby, and The Coppermind isn't helpful.

Yeah, I noticed how old this thread is, but I just saw it after your necropost, and felt inspired.  All of this is honestly pretty beyond me.  I just found one little thing that I knew I could help out with.  

Welcome to the forums.

Yeah, the link to a specific post is shown in the little share button on the top right, or if you use the timestamp button on the top left.

And yeah, I've wondered about that size number as well. I think it's a safe assumption that she's referring to radius/diameter. That's a more directly useful number and it's easier to measure. But yes, it could be referring to volume. Hmm... We did just get a map of Roshar with longitude and latitude shown. Perhaps it would be possible to take some known distances and see what radius those would imply. The problem is we don't know how Rosharan units of measurement compare to our own... But they might help support one interpretation or the other. Something to look into...

This is all something I've been stewing over for a while. Just finally decided to say something about it.

[Vianki]

Sorry to not contribute anything useful- I just want to say this whole thread had been delightful and quintessentially useful. I want to paint Kaladin's first flight as a scene, but want to get the moons right. I ended up here. After reading this a few more times I think I might get close to a correct skyscape. Thank you all! 

[Jofwu he/him]

Felt like doing some more calculations...

Mass of Roshar was calculated here.

The length of a day is a little unclear. We know it's 20 hours and that the Rosharan year (500 20-hour days) is 1.1 Earth years. Is that 20 Earth hours in a day, giving a year of 1.14 Earth years? Or is that 1.1 number exact, giving 20 Rosharan hours = 19.3 Earth hours? Or neither? (both numbers are approximate) I'm going to assume the first, which feels most reasonable. (more on these numbers here)

So we'll say a 20 hour (72,000 sec) solar day. Sidereal day would be that times 499/500 = 71,856 sec. Figuring the orbital period of moons is a little tricky because of the way they precess. They are in sync with the solar day which is a bit more than sidereal, but they are in a retrograde orbit, so they make about 1/500th less than one full sidereal orbit each solar day. That gives us 71,712 seconds. Should be good enough.

Using the equation for orbital period, we can get their semi-major axes: a = (G*M*(T/(2*pi))^2)^(1/3) = 3.089×10^7 m.

Geosynchronous orbit altitude would be the same thing with T=72,000s, giving 3.097×10^7 m.

[ccstat he/him]

@jofwu I tried to work out the moonrise difference in Alethkar vs. Shinovar, and got far enough to confirm that yes, they definitely rise hours apart at different longitudes, but I couldn't get much more specific than that because the math is trickier than I gave it credit for, and I did something wrong in my calculations when I tried to move from the simplest case to comparing observations at different points on the continent with different angles to perigee. 

I started by trying to determine what eccentricity would be needed for the elliptical orbits so that the moons would cross the sky in "a couple to a few hours". We don't actually know how long the moons are in the sky or how their appearance in the sky relates to their perigee points, but @Leiyan describes the best guesses we have in this post. To recap (using 20-hour Rosharan time, as seen from Alethkar):

• Salas rises at sundown around 15:00, sets around 18:00
• An hour of darkness
• Nomon rises around 19:00, sets around 02:00 
• Mishim rises around 02:00 (when Nomon sets), and sets near sunrise around 05:00.
  (Note: We have no real info on when Mishim sets, but it's presumably close to sunrise, since the moon-less hour between Salas and Nomon is the darkest of the night.)

Kepler's laws tell us that an orbiting body sweeps through the area of its ellipse at a constant rate, so by comparing the areas of focal sectors of the ellipse, we get different amounts of time. The simplest case assumes that the moon crosses the sky at their fastest speed (i.e. they reach orbital perigee when directly above crossing the azimuth of the sky). This assumption cannot be true for the whole continent, but it's true somewhere so let's plug in the numbers. There is a simple formula for the area (pictured in blue) cutting the ellipse perpendicularly through one of the foci, and since [blue area / total area] = [time in sky / 20 hour day], we can change the eccentricity of the ellipse and see how that alters the amount of time from moonrise to moonset.

Equation inside spoiler:

Spoiler

Assume an ellipse with semi-major axis a=1 and ellipticity e.
The semi-minor axis can be calculated as b=sqrt(1-e^2).
The the equation at this site then simplifies to Area(blue)=b*arccos(e)-e*b^2 ; and Area(total) = b*pi

The more complex equations angles other than the perpendicular can be found here, here, and here. I didn't feel confident in any of those approaches, so wasn't surprised when I got nonsensical numbers out the other side.

When you do this, you get the following transit times (in hours):

• e=0.49 t=4.0
• e=0.54 t=3.5
• e=0.58 t=3.0 (value used for ellipse pictured above)
• e=0.64 t=2.5
• e=0.69 t=2.0

Note that these are minimum times for the actual case. If perigee does not occur directly above the observer, the moon will take longer to cross the sky. This also means that not only will the relative timing to sunset and sunrise differ across the continent, but also the relative timing of each moon's appearance. (i.e. Nomon-rise and Mishim-set may not coincide for observers elsewhere on the continent--they likely appear in the sky together in many places, though it is possible that some places experience a short span of time with both moons below the horizon.)

If we take the value that gives 3 hours in the sky (e=0.58) and use jofwu's measure of the semi-major axis (a=3.09x10^7 m), that gives us a distance at perigee of 1.3x10^7 m and a distance at moonrise/set of 2.05x10^7 m. That means that the moon will be nearly 60% further away when it rises and sets, and appear proportionally smaller. For the eccentricities above, that difference will is between 50% and 70%, and represents the lower bound of apparent size change, since a moon that (e.g.) rises at perigee will be an even greater distance away when setting.

The math is a lot trickier if we want to determine when the moon rises or sets for other places on the continent, and/or if we stop assuming that perigee occurs in the middle of its transit. I'm not sure I'm ready to tackle that myself. If you've taken calculus more recently than than I have, you may want to check out the links in the spoiler box above.

 

 

By the way:

12 hours ago, jofwu said:

Or is that 1.1 number exact, giving 20 Rosharan hours = 19.3 Earth hours?

I believe this interpretation is correct. We've been told repeatedly that the 1.1 figure is exact, and it makes more sense to me that they would use even divisions of time for Rosharan hours than that they would hold to Earth hours in the text, especially since the difference is so minor (for those who haven't clicked through to jofwu's reddit link, this would make a Roshar hour 2 minutes, 11 seconds shorter than an Earth hour). Either way, the 3.5% difference should be well within the error of our other assumptions so I doubt it matters much which version you choose.

Edited October 27, 2017 by ccstat

[ccstat he/him]

Took another look at the moon visibility question. This feels obvious to actually say, but it took me a stupidly long time to draw it out and convince myself of the geometry so I'll post my conclusions in hopes that they're useful to someone else.

Without doing any math yet, the concept can be explained very simply: the continent takes up less than half the planet, so there is some portion of the sky that is visible to observers on the east and west coasts (and everyone in between). When a moon passes through this strip of sky, it will be visible to everyone on the continent. Since the moons are moving across the sky quickly, they will rise much earlier (local time) for people in the west than for people in the east. Now let's use some actual numbers to figure out how much earlier.

According to the new map from OB, roshar spans 77 "Rosharan degrees" of longitude out of a total of 200. (Converting to Earth units, that's ~140 degrees.) A big chunk of that comes from including Aimia where nobody human goes, so let's confine ourselves to comparing the shattered plains to Shinovar. Those are about 60 Rosharan degrees apart (110 Earth degrees). Since the Rosharan day is 20 hours long, each "time zone" spans 10 Rosharan degrees, meaning that there is a 6 hour difference in local time between the shattered plains and eastern Shinovar. The two locations share about 70 (Earth) degrees of sky, so if the moons will take three hours to cross the sky then they will rise in Shinovar close to an hour before they set on the plains. 

The mechanics of the elliptical orbits will mess up the actual rise and set times, but for a ballpark let's pretend that the moons cross the sky similarly in both places. In Alethkar the approximate moon schedule (in 20-hour Rosharan time) is: 

• Salas rises at sundown around 15:00, sets around 18:00
• An hour of darkness
• Nomon rises around 19:00, sets around 02:00 
• Mishim rises around 02:00 (when Nomon sets), and sets near sunrise around 05:00

Using our conclusions from above, that would mean that the Shinovar schedule looks something like this:

• Salas rises at 11:00 and sets around 14:00
• Nomon rises around sunset at 15:00, sets around 18:00 
• Mishim rises around 18:00 (when Nomon sets), and sets around 02:00
• Darkness until sunrise at 05:00

In actuality, those times will be shifted later because the moons will slow down after crossing their point of periapsis, but it definitely gets us close. It also means that Szeth's reference to the "hateful hour" of darkness between Salas and Nomon doesn't make sense for the Shin people since their moonless hour would occur around dusk not in the middle of the night.

Conclusion: The moons should rise substantially earlier in the western part of Roshar. But we may have to ignore that and suspend disbelief a bit. It looks like Brandon may not have seen or paid attention to those calculations, and the moons' behavior is potentially being treated the same across the continent. On my next OB read I'll try to pick out references to the moons and see how they are described (if at all) from other locations.

[Jofwu he/him]

@ccstat Yep, this is my concern. It struck me when Dalinar mentions Salas during [Oathbringer spoilers]. I pointed it out to Peter, and I believe he said that would be a mistake as [Oathbringer spoilers] happens in the early morning. Would have to dig up the PM. In any case, the timing just didn't seem to match well with the time Salas rises in the east.

Elliptical orbits make it more complicated and introduce lots of unknowns. Plus there's the fact that Roshar spans well below the equator. Could be error in all this... But I feel like the problem you can see in these numbers isn't going to go away easily. Peter seems to think it will work out, but hasn't done the math. I suspect Brandon set up an impossible moon situation and we'll just have to roll with it, but we'll see.

We definitely need to scroll through sometime and compile a list of EVERY reference to the moons. I think there's a good list for TWoK earlier in this topic, but I don't think that was done for WoR, Edgedancer, or Oathbringer.

Edited February 5, 2018 by Jofwu
removed portions with minor Oathbringer spoilers

[ccstat he/him]

On 2/2/2018 at 5:21 PM, Jofwu said:

I suspect Brandon set up an impossible moon situation and we'll just have to roll with it, but we'll see.

That's my impression after starting your suggested quote compilation. I only have WoK and Edgedancer on ebook right now, but I'll get WoR and OB from my library to search for references. Here is every mention of the moons from the two I have, organized chronologically though a given night. I tried to include the location of the observation and any available time markers.

Spoiler

 

Misc

WoK Chapter 21 - Kaladin - Shattered Plains

Quote

 

Rock snorted. “We are bridgemen. We die. Is how this thing works. You might as well promise to make the moons catch each other!”

 

Salas

WoK Chapter 2 - Kaladin - Unclaimed Hills

Quote

 

The sun set in the west, but the wagons kept rolling. Violet Salas peeked over the horizon to the east, seeming hesitant at first, as if making sure the sun had vanished. It was a clear night, and the stars shivered high above. Taln’s Scar— a swath of deep red stars that stood out vibrantly from the twinkling white ones— was high in the sky this season.

[…] Two hours past First Moon, Tvlakv finally called a halt.

[…]The landscape was dark. Salas was the smallest and dimmest of the moons, and while her violet coloring had inspired countless poets, she didn’t do much to help you see your hand in front of your face.

 

Edgedancer Chapter 7 - Lift - Yeddaw)

Quote

[At shift change for the guard post]

As Lift had guessed, now that it was getting dark, the streets were clearing. Maybe there would be an upswing in activity once the first moon got high enough, but for now there wasn’t enough light.

WoK Chapter 37 - Young Kal - Hearthstone

Quote

 

The door swung closed. Kal set down the tubers and charged through the streets of Hearthstone, passing men chopping wood, women throwing out dishwater, and a group of grandfathers sitting on steps and looking at the sunset.

[at least one hour passes while Kal and Lirin meet Roshone]

The carriage turned, and the violet light of Salas illuminated Lirin’s face.

 

WoK Chapter 19 - Dalinar - Starfalls vision (past era, location unclear)

Quote

Dalinar spun, pushing the girl behind him. His side hit a stack of sacks filled with grain as he edged away. The barn fell silent. Salas’s violet light shone in the sky outside, but the small moon wasn’t bright enough to illuminate the barn’s interior, and the creature had moved into a shadowed recess. He couldn’t see much of it.

WoK Chapter 57 Kaladin Shattered Plains

Quote

 

By the time night drew close, the light had long since stopped streaming from Kaladin’s body.

[He walks to the chasms, hears the wandersail story from Hoid]

The cremlings had retreated to their cracks and burrows, but many of the plants still continued to let their fronds float in the cool wind. When he passed, the grass pulled back in, looking like the fur of some black beast in the night, lit by Salas.

[He returns to the barracks, where Bridge 4 is having their nightly stew]

 

Moonless Hour

WoK Interlude 6 - Szeth - Bornwater, in Bavland

Quote

He reached the wall and pressed himself against it. It was the time between the first two moons, the darkest period of night. The hateful hour, his people called it, for it was one of the only times when the gods did not watch men.

WoK Interlude 3 Szeth Ironsway, in Bavland

Quote

 

The street was dark outside.

[…]Szeth looked over his shoulder, wishing that the Second Sister— known as Nomon to these Easterners— had risen to give a little more light.

 

WoK Chapter 40 Kaladin Shattered Plains

Quote

 

A few hours later, Kaladin sat on a chunk of wood beside Bridge Four’s nightly fire.

[…] It was the time between moons, and so he was lit mostly by the firelight; there was a spray of stars in the sky above. Several of those moved about, the tiny pinpricks of light chasing after one another, zipping around like distant, glowing insects. Starspren. They were rare.

 

Nomon

WoK Chapter 8 - Shallan - Kharbranth

Quote

 

She was surprised to discover how dim it was outside.

[…] The roadway down to the docks was not nearly as busy as it had been earlier, but there were still a surprisingly large number of people about. The street was lit by oil lanterns— spheres would just have ended up in someone’s pouch— but many of the people about carried sphere lanterns, casting a rainbow of colored light on the roadway.

[…] “Kharbranth is a major port, young miss,” [Yalb] said with a laugh. “Stores stay open late. Just wait here.”

[she shops for books]

Nomon— the middle moon— had begun to rise, bathing the city in pale blue light. Staying up this late had been a rare privilege for her in her father’s house, but these city people around them barely seemed to notice the late hour.

 

WoK Chapter 73 - Kaladin - Shattered Plains

Quote

 

Nomon, the middle moon, began to rise. Bright and pale blue, bathing the horizon in light.

[Kal talks to Syl briefly]

Footsteps came from behind. Syl turned. “It’s him.”

The moon had just risen. Dalinar Kholin, it appeared, was a punctual man.

[…] Dalinar reached out, taking his hand, shaking it by the light of the rising sapphire moon.

[…] Kaladin smiled, leaning back, looking upward toward the dark sky and the large sapphire moon. Then he closed his eyes, listening.

 

WoK Chapter 23 Kaladin Shattered Plains

Quote

 

That night, Kaladin, Teft, and Rock walked the makeshift streets of Sadeas’s warcamp. Nomon— the middle moon— shone with his pale, blue-white light.

[...] A lone boy sat upon a pen post, staring up at the moon.

[they collect the reeds and return to the chasms]

Kaladin hesitated; Nomon was bright, but it was still night. “You don’t have any spheres, do you?”

[they milk the reeds]

Nomon was setting in the west, and the small green disk of Mishim— the final moon— was rising in the east.

 

 

 

[theuntaintedchild he/him]

On ‎10‎/‎18‎/‎2017 at 6:12 PM, raykoda16 said:

For all you dumb yanks, that's 2790 miles.

I'd be offended if I didn't agree with you.

 

[Jofwu he/him]

I had some Oathbringer-related stuff I've been meaning to share, and if we're going to gather Oathbringer moon references, I figure we need a topic in the spoiler board. So I made this: