Jofwu

The Moons of Roshar

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My interest is in their instability. Does this mean we're going to have a Majora's Mask situation here, or will one of the Moons going flying off into the Cosmere? What effect would that have on Roshar (I mean, the first scenario is pretty obvious, unless someone has either an ocarina, horn, guitar or drums handy). I'm also still trying to wrap my head about the moons story in-book, cause trying to separate symbolic imagery and actual fact is making my head hurt.

Agreed on the imagery significance although I can't particularly work out how. The moons orbits also aren't natural right?

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No, the moons aren't going anywhere. This has been talked about in the non-spoiler topic linked above, I think. And there are WoBs. When Peter says above that they are "unstable" he means on an astronomical scale. In millions of years they may be in different orbits, get tossed out from the planet, or come crashing into it. But on the timescale of the stories, they won't deviate in a notable way.

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Brilliant!  Well done on the clock theory!  I think others have made the connection between the 3 circles in the endpaper artwork and the 3 moons, but that it was a clock somehow eluded us.  Now that you mention it, it seems almost perfectly obvious, a circle with gem colors corresponding to numbers evenly spaced around the outside.  My brain just seemed to always glance over the fact that Jes/Sapphire (1) has always been near the 1 o'clock position on the double eye symbolism.  That Roshar has a 20 hour day just makes this feel ironclad.

Does this mean the little sub-circles inside the polestones on the Vedel Endpaper are quarter-hour time markers?  I always felt stumped what the point was of those tiny circles.

I'm eyeballing

0:45 Salas

3:00 Nomon (looks a little before 3:00 on the Vedel image, a little after 3:00 on the Jezrien belt buckle, so 3:00 seems close enough)

7:25 Mishim

Also, Salas needs to really blaze across the sky.  Szeth mentions the Shin believe in a "hateful hour", the darkest period of the night occurring between Salas setting and Nomon rising.  So, Salas would set around 2:00, giving us 2:00-3:00 as the hateful hour?

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Adding on to @ccstat's work, I think I've collected all references. (note: I've left out the mentions in Sigzil & Wit's stories, which are told in OB Chapters 35 and 67, and at least one other reference that wasn't useful at all) Some I added could probably use a bit more context, but I got the most important stuff. I searched for the moon names, "moon", and "sunset"/"sunrise". Not sure if there are other terms that might catch something...

MISC

Spoiler

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!”

OB Chapter 67 - Shallan - Kholinar

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“You say that, my dear man,” it proclaimed, “but everyone thinks they know the moons. How could they not? We live beneath their gaze each night. We’ve known them longer than our friends, our wives, our children. And yet . . . and yet . . .”

[...] (It was a night when the moons were large, and these—everyone knows—are nights when the moons pay special attention to the actions of mortals.) 

 

SALAS

Spoiler

WoK Chapter 2 - Kaladin - Unclaimed Hills

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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.

WoR Chapter 15 - Shallan - Frostlands

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Darkness was fully upon them, the first moon having yet to rise. As she walked, her feet didn’t hurt nearly as much as they had. Was the knobweed sap doing that much good?

[Bluth reports sighting bandits and they pack up and leave]

The first moon began to rise, making it lighter than Shallan would have liked.

WoR Chapter 20 - Shallan - Frostlands

Quote

The sun was a smoldering ember on the horizon, sinking toward oblivion, as Shallan and her little caravan neared the source of the smoke in front of them. [They climb the last hill on, spy, and speak with Tyn.]

[...] Two forces, then. Bandits ahead and behind. Shallan found herself sweating in the cold air as the sun finally vanished beneath the western horizon.

[...] She met his eyes in the near darkness, and he stopped. [She convinces Bluth to turn around and recruits the bandits.]

[...] Salas, the first moon, made a violet disc in the center of a cluster of bright white stars. The screams and yells of fighting continued. 

Edgedancer Chapter 7 - Lift - Yeddaw

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[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

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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.

WoR Chapter 67 - Dalinar - Shattered Plains

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The feast basin was made up of a series of Soulcast islands beside the Pinnacle complex. [...] The water glowed. Spheres, and a lot of them, must have been dumped into the water to give it that ethereal cast. Purple, to match the moon that was just rising, violet and frail on the horizon.

[...] He frowned as they passed a shalebark outcropping where a gardener was working late, carefully filing away and humming to himself. The sun had set; Salas had just risen in the east.

[...] Outside, past the small rivers—they now glowed blue, the spheres having been changed to match the second moon—the king’s carriage rolled away.

OB Chapter 18 - Shallan - Urithiru

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With him humming happily, she crossed her room and stepped out onto the balcony. The first moon had risen, violet and proud Salas. She was the least bright of the moons, which meant it was mostly dark out.

WoR Chapters 42 & 43 - Shallan - Shattered Plains

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What time was it? A clock on the wall read half past first night bell. It was just first moon, right after dark. [Shallan agrees to meet the Ghostbloods]

[Spanreed conversation. There's one break in the conversation that lasts an unclear amount of time. Seems not much.]

I’ll draw you a map. Have your apprentice arrive at Salas’s moonheight. Good luck.

A sketch followed, indicating the location. Salas’s moonheight? She’d have twenty-five minutes, and she didn’t know the camp at all. 

[After the meeting with the Ghostbloods]

She fished in the other pocket for the pencil she’d instinctively put there and tried to draw while walking. Impossible. Salas had almost set, and it was too dark.

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

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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

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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]

OB Chapter 78 - Shallan - Kholinar

Quote

First moon was up by the time they reached the steps to the Oathgate platform.

[...] She pulled her coat tight, then picked her way across the street full of crawling people. No bonfire lit her way, only the moon overhead and the light of the jewelry the people wore.

[...] She stepped between the buildings and entered a moonlit square, colored violet from Salas above. [just before leaving the Revel]

OB Chapter 4 - Dalinar - Urithiru (NOTE: Peter has shared that the mention of the moon's appearance at this time of day (mid-morning) is a mistake)

Spoiler

The Everstorm appeared in the distance[...] He saw it by the light of the first moon above, and by the intermittent flashes of the storm beneath.

 

MOONLESS HOUR

Spoiler

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

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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

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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

Spoiler

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

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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.

WoR Chapter 22 - Kaladin - Shattered Plains

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Eventually, the storm passed, and Kaladin opened the window to a black sky, a few phantom clouds shining with Nomon’s light. The storm had started a few hours into the night, but nobody could sleep during a storm. He hated when a highstorm came so late; he often felt exhausted the next day.

WoR Chapter 52 - Shallan/Kaladin - Shattered Plains

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“It’s not even second moon yet, sir,” Shallan said in what she hoped was a boyish voice. [Shallan arriving in Amaram's camp]

[...] He eventually came to a stop hanging in midair. The second moon had risen, bathing the Plains in light far below.

[...] Finally, he stopped in place. Amaram would be there, just ahead, inside Sadeas’s camp somewhere. It was late, Nomon inching toward its zenith.

OB Chapter 74 - Shallan - Kholinar

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The friendly light of spheres, and with it a sound that seemed impossible. Laughter?

She chased it, hungry, until she reached a gathering of people singing beneath Nomon’s azure gaze. They’d overturned boxes, gathering in a ring, while one man led the boisterous songs.

WoK Chapter 23 Kaladin Shattered Plains

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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.

MISHIM

Spoiler

OB Chapter 17 - Kaladin - northwest Alethkar

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As the sun set, long shadows stretched across Kaladin, plunging the camp into darkness again. It seemed that the group moved at night.

[...] he parshman grunted, then looked to the girl at his side, who tugged on his arm and pointed. He gave her a whispered response, and she ran on tiptoes toward a patch of flowering rockbuds, visible by the light of the first moon.

[lots of marching, including two stops for water breaks]

By Mishim’s pale green light, he decided this girl was not as timid as he had assumed. She was nervous, but she met his eyes with hers.

OB Chapter 67 - Shallan - Kholinar

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Wit tossed something into the brazier, producing a bright green puff of smoke the color of Mishim, the third and slowest of the moons.

OB Chapter 76 - Dalinar - Rathalas (11 years ago)

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The last moon was close to setting. Not long until morning. 

 

 

 

A few thoughts and observations...

First concerning their clock... Palona lists mealtimes in WoR "at second bell, noon, and tenth bell." In WoR 42 Shallan mentions "first night bell" as being around sunset. This makes me think "first [day] bell" is sunrise (6 am) and first night bell is sunset (6pm). If you count up ten hours I feel like that means they're eating dinner too early though, as tenth bell would be roughly equivalent to 4:50 pm. It's possible there's some overlap. (e.g. 10th bell = xth afternoon bell = first night bell) I think maaaaybe it's possible that it takes nearly an hour for the sun to set at their latitude (and maybe Roshar's atmosphere plays into it taking longer to go dark?). I'm terrible at visualizing/calculating how astronomical movement looks in the sky. Maybe someone else can chime in. :) In any case, it does make me feel like we're working with a 10-hour clock that's got an am/pm based on sunrise/sunset.

Also geography, for the record... the Reshi Isles get up to the equator, but most of Roshar is well into the southern hemisphere. I calculated that the more southern areas get down to nearly 60 degrees south. I believe the Shattered Plains would be around 35-40 degrees south.

The mentions of Salas in WoR 42/43 are very detailed. "half past first night bell" = "first moon" = "just after sunset" Then she mentions Salas will reach it's height in the sky in 25 minutes, which is half a Rosharan hour (got a WoP somewhere that they've got 50-minute hours). It's not 100% clear how much time passes between this and the statement that it's "just first moon". Reading the passage, I'm inclined to think no more than 5 minutes pass. She does step away from the spanreed briefly, but doesn't do very much while she waits. If we can assume the time from rise to moonheight is roughly half of the moon's duration in the sky, this suggests Salas is only up for a little over an hour. I think that fits with the info that the moon is nearly set shortly after her meeting with the Ghostbloods. If the meeting started at moonheight and lasted half an hour, the moon would be nearly setting. (and it doesn't seem to take that long) BUT this doesn't fit with Kaladin's TWoK 2 comment that Salas is still up two hours after it rose. We could say that Shallan stepped away from her spanreed longer. Maybe I'm missing something odd (about their latitude?) and the time from rise to moonheight isn't the same as moonheight to set? However, these sorts of details tend to get revised as the story goes. And we've still got to fit the moonless hour in. I think I'm inclined to assume the TWoK timing was retconed... But the faster Salas moves through the sky the more problematic we're going to get with what time it's supposed to appear to other parts of Roshar... So I'm really torn on how to interpret this.

During Wit's story, Shallan refers to Mishim as the "slowest of the three moons" which I think is pretty notable. It does seem to be a statement of fact rather than part of the story. This doesn't fit super well with the timing suggested in the Herald artwork... But those could easily be a case of artistic license. We definitely ought to take Shallan's statement as fact above artistic imagery inside of in-world artwork.

Wasn't planning to reconcile these observations when I started this, but I think maybe the best way to do so would be to assume (1) Salas is up longer than the WoR passage suggests and (2) Nomon rises a bit later than shown in the artwork. Without those assumptions... Salas is up for one hour. Then the hateful hour. Then you've got about 7 hours left for Nomon and Mishim before the sun starts lightening the sky, with Nomon seeming to take most of it.  With those assumptions, Salas is up for perhaps 2.5 hours. Plus an hour of no moon. Nomon rises about 4 hours after sunset (an hour or so before midnight, which matches several comments that it rises late. We've got 6 hours to work with before the sun begins to come up, so let's say Nomon is another 2.5 and then Mishim takes 3.5. Maybe a bit less difference between those two.

Still have the issue of the moons rising too early in the west though.

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Could Shallan referring to Mishim as the "slowest" of the moons merely refer to the fact that it's the last one to appear in the night sky?

Or is she and Roshar much more astronomically advanced than we give them credit, and knows that Mishim has the closest orbit and the slowest transverse speed?

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26 minutes ago, Subvisual Haze said:

Could Shallan referring to Mishim as the "slowest" of the moons merely refer to the fact that it's the last one to appear in the night sky?

Or is she and Roshar much more astronomically advanced than we give them credit, and knows that Mishim has the closest orbit and the slowest transverse speed?

That's a very good question.

I absolutely think they're smart enough to understand the relative speeds of the moons. Rosharan's are pretty scientifically minded. Equating them to a typical medieval-fantasy tech level is a big mistake. But regardless, you don't need to understand orbital mechanics to see and track how they move. If you've got a clock, you can measure how long it takes them to cross the sky.

That said, I think it's very reasonable to suspect that Shallan is merely speaking poetically in that line. Especially given the context.

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Since you've done such great work compiling textual sources on our moons, I would recommend adding the Roshar Solar System image from Ars Arcanum.  I've snipped out the little part with Roshar and its moons:

Spoiler

5a79ba954a502_RosharMoonsfromArsArcanum.PNG.8e5fa3a82fb490266ca2407bc2e4ee72.PNG

I don't think this image is designed to be perfectly mathematically to scale, but I think in the rough sense the positioning of the orbits matches a lot of what you've deduced.  I'll refrain from drawing any conclusions since I have to look up Keplar's laws to reminds myself about elliptical orbital speeds every time :P 

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Great work collecting those quotes, @Jofwu. I'm inclined to agree with you that the speed of Salas was retconned (or just in error in that first scene) from several hours to a bit over one hour, but as you mentioned that makes moonrise in western Roshar even more problematic than it already was. 

Here are the seals from the Vev and Jes endpages, and the moons behind Ishar (clearly a more fanciful rendition that won't help with timing):

Spoiler

Moons_vev.JPG.8c2ede46173973c5d5e07acf7a122633.JPG

moons_jes.JPG.d3183f77d81131d1def80740c2d31fdc.JPG

moons_ishi.JPG.55da92e2a2a661e30f41821ef91acb18.JPG

From the spacing, I'm not entirely convinced that the position corresponds (accurately) with each moon's appearance. I would have expected Nomon to be further from Salas to account for the moonless hour. I'll need to look at it a bit more closely, together with the textual references.

23 hours ago, Subvisual Haze said:

I would recommend adding the Roshar Solar System image from Ars Arcanum.  I've snipped out the little part with Roshar and its moons:

  Hide contents

5a79ba954a502_RosharMoonsfromArsArcanum.PNG.8e5fa3a82fb490266ca2407bc2e4ee72.PNG

I don't think this image is designed to be perfectly mathematically to scale, but I think in the rough sense the positioning of the orbits matches a lot of what you've deduced.  I'll refrain from drawing any conclusions since I have to look up Keplar's laws to reminds myself about elliptical orbital speeds every time :P 

Since all three moons have a period of one day and are visible near periapsis, a more elliptical orbit will mean a faster transit of the sky, while a less elliptical orbit will mean a longer time spent in the sky. It does appear from the AU chart that Mishim has the most circular of the three orbits--so it being slowest to cross the sky makes sense. 

It is worth pointing out that along with different moonrise times relative to sundown, the amount of time a moon spends in the sky will change based on how far east or west the observer stands. Moons travel fastest at periapsis, and slow down considerably away from that point. Without knowing where periapsis falls for each moon we can only apply it as a fudge factor, but in general moons should rise slower than they set in Alethkar, and conversely set slower than they rise in Shinovar.

On 2/5/2018 at 11:42 PM, Jofwu said:

Without those assumptions... Salas is up for one hour. Then the hateful hour. Then you've got about 7 hours left for Nomon and Mishim before the sun starts lightening the sky, with Nomon seeming to take most of it.  With those assumptions, Salas is up for perhaps 2.5 hours. Plus an hour of no moon. Nomon rises about 4 hours after sunset (an hour or so before midnight, which matches several comments that it rises late. We've got 6 hours to work with before the sun begins to come up, so let's say Nomon is another 2.5 and then Mishim takes 3.5. Maybe a bit less difference between those two.

I agree that Salas needs to take more than an hour, but 2.5 seems long. I'm inclined to put it around 1.5, which means Nomon would rise ~2 hours before midnight. Say Nomon takes 3 hours, and Mishim takes 3.5, setting about half an hour before dawn. Just spit-balling at the moment--again, I'll have to look at it a bit more closely.

On 2/5/2018 at 11:42 PM, Jofwu said:

First concerning their clock... Palona lists mealtimes in WoR "at second bell, noon, and tenth bell." [...] I feel like that means they're eating dinner too early though, as tenth bell would be roughly equivalent to 4:50 pm. [...] In any case, it does make me feel like we're working with a 10-hour clock that's got an am/pm based on sunrise/sunset.

Also geography, for the record... the Reshi Isles get up to the equator, but most of Roshar is well into the southern hemisphere. I calculated that the more southern areas get down to nearly 60 degrees south. I believe the Shattered Plains would be around 35-40 degrees south.

Good catch on the clock system. I don't think there's any need to mess around with overlap from day bells and night bells. Yes, dinner an hour before sunset seems early, but I suspect that's a lighteyes/nobles thing. The highprinces seem to have feasts every few days that last well into the night. I'm guessing "dinner" is a light meal for them and they eat again while entertaining or being entertained in the evenings. A working class family would probably order their time differently.

If the continent extends only to 60 degrees south then latitude won't gain us more than 20 minutes of leeway on sunrise/set. From what I found online, it's only when you approach 80 degrees or so that things really start to shift around. A more refractive atmosphere could extend daylight a bit, but I'm not sure that would actually make much difference. They seem to have fairly accurate and consistent clocks, which makes me think that their hours are well defined and wouldn't alter the bell system much.

On 2/5/2018 at 11:32 PM, Subvisual Haze said:

Does this mean the little sub-circles inside the polestones on the Vedel Endpaper are quarter-hour time markers?  I always felt stumped what the point was of those tiny circles.

I think those are just the surges associated with the polestone essences, rendered artistically as "2 each" rather than "2 each with adjacent essences sharing one".

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1 hour ago, ccstat said:

It is worth pointing out that along with different moonrise times relative to sundown, the amount of time a moon spends in the sky will change based on how far east or west the observer stands. Moons travel fastest at periapsis, and slow down considerably away from that point. Without knowing where periapsis falls for each moon we can only apply it as a fudge factor, but in general moons should rise slower than they set in Alethkar, and conversely set slower than they rise in Shinovar.

That's a good point.

They're in awfully low orbits (to get the 20-hour period), so the speed doesn't vary by large factors. I've calculated a semi-major axis of 5.27R. For the sake of getting a feel for this, if the moon drops to a periapsis altitude of 1R it reaches a maximum of twice the mean orbital velocity. Then apoapsis velocity would be about half the average. (The upper bound, moon grazing the planet surface, only gets up to 3x vs 1/3x) Not a massive difference, but certainly noticeable.

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15 hours ago, Jofwu said:

They're in awfully low orbits (to get the 20-hour period), so the speed doesn't vary by large factors. I've calculated a semi-major axis of 5.27R. 

Either I've misunderstood you or there is a math error here. Never mind, it was my error. Your numbers are correct. I misread your semi-major axis from the other thread as km rather than m. (For the record, in kilometers your numbers from the previous thread are radius=5740 km and semi-major axis=30,890 km). I can confirm that with the eccentricity we settled on in the previous thread, the moons should approach well within 1R at closest approach. That makes sense but wow, that's a close orbit.

In light of this, it turns out that my visibility calculations from before are way off. I ignored displacement across the planet, and the effective horizon; it was negligible when I thought the orbit was 1000 times bigger than it actually is, but now it definitely has to be factored in. At first glance it will help substantially. The shared visibility between Alethkar and Shinovar is completely eliminated, even for a circular orbit. We need to recalculate the eccentricity in light of this, and the visibility times. I'm working on the calculations now, and will post when they are ready.

===EDIT=== 

Calculations: (NOTE--I've made an error here. See my next post for corrections.)

Okay, here are the numbers. They are better in some ways, but the increased detail reveals some more complication that I'm not entirely sure what to do with. The first upside is that the moons are close enough that they are never visible to the entire continent at once, no matter how eccentric the orbit. Depending on the details, moonrise in Shinovar is up to an hour after moonset in Alethkar.

The complication is that the moons spend very different amounts of time in the sky depending on the observer's location. Using the fairly eccentric orbit from the first thread (which actually brings the moon to an altitude of ~0.5R), an observer directly below periapsis would see the moon cross the sky in 2 hours. Assuming that happens in the center of the continent, an observer at either coast would have 4.8 hours between moonrise and moonset. 

With a less eccentric orbit the times only get longer. We can make the orbits more eccentric, but then the moons are passing ridiculously close to the surface of the planet. If we go super extreme and let a moon get within 0.2R (~1000km), then the same periapsis observer sees it rise and set in 1 hour, while the coastal observer gets 3 hours of moon time.

For comparison, note that with a circular orbit the moons would still be close enough (1.6R) that they would rise and set in 7.5 hours; this would be true everywhere on the planet.

On a separate note, the distance of the moon from a given observer (and therefore its apparent size) changes a lot as it travels across the sky. Even if the orbit was circular, the moons are close enough that they would grow by 50% from moonrise to moonheight. If we take the same orbit as before (the one that reaches 0.5R over central Roshar), our central Rosharan would see the moon more than double in size, while a coastal observer would see it more than triple. So far nobody in-world has remarked on this except for Wit's "It was a night when the moons were large" comment, which doesn't quite convey the same idea.

CONCLUSIONS:

  1. These moons are practically grazing the surface of the planet in order to get across the sky in under 2 hours.
  2. There is no way that everyone on Roshar experiences the same moon schedule. Those living near periapsis are likely to see a moon for less than half the time compared to distant observers.
  3. We don't need to be quite as concerned about the time zone issue, since the moons can't be seen by the whole continent at once.**
  4. The apparent size of these moons is going to vary dramatically as they cross the sky. 

**Edit2--Clarification on why the time zone concerns are less die: Before, it seemed like the moons would rise in Shinovar at least an hour before they set in Alethkar, which put Salas rising around 2pm local time.  Now they rise in Shinovar up to an hour after setting in Alethkar, which buys us an extra 2 hours and Salas now rises just an hour before sundown local time and probably stays in the sky for an hour or two after sundown, making the Shin experience of Salas much more similar to what we've seen from Salas in the east.

Edited by ccstat
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Is Nomon in a geosynchronous elliptical orbit above Urithiru with its perigee at midnight and its apogee at noon?  From the clock image it appears to peak in the night sky right around midnight.  The map of the Roshar system also gives a relatively simple orbital shape to Nomon with its perigee appearing exactly on the far side of Roshar relative to the sun. 

edit: no, wait, duh the moons are spinning the opposite direction.  But I do think passing over Urithiru at noon and midnight would make sense in an artificially designed solar system.

Edited by Subvisual Haze
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Okay, this is embarrassing. I just caught a dumb mistake in my calculations from yesterday. (I somehow doubled Roshar's radius when I graphed it out.)

Correction:

Now the example orbit is not quite as close: 2R at closest approach (rather than 0.5R). This means it rises in Shinovar just after setting in Alethkar. (So we've gained a buffer of one hour, not two, in our time zone considerations.)

The increased distance also means that the change in apparent size, while still substantial, is less dramatic. Nothing is going to triple in size, though it can still come close for some locations. Approximately doubling in size won't be uncommon.

The visibility times don't change drastically from what I posted before. Add half an hour for coastal observers, three quarters of an hour for central observers.

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I've been thinking that really big moons close to the planet are going to make HUGE tidal bores, especially if the orbits are slightly eccentric. With regard to lunar instability moons below geostationary orbit lose momentum (and altitude) and increase the planetary spin rate until they impact reach the Roche limit (which shreds them and makes a gorgeous ring system) or the planet rotation increases and tidally locks the moon. Moons above geostationary (like ours) increase their altitude by sapping momentum from the planetary rotation until the rotation slows enough for tidal locking or the moon is ejected (our moon is receding at about 1 in per year and will escape in about a billion years). There are also inter moon gravitational interactions that may or may not be stable.

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On 2/8/2018 at 10:18 AM, physicskid said:

I've been thinking that really big moons close to the planet are going to make HUGE tidal bores

Since the moons are small, I have in mind that they won't be affecting tides very much. I don't have a good enough grasp of the relevant factors to say for sure though. 

I thought to check how small the moons actually are. Peter has said that Phobos (11 km across) is the right ballpark, so let's start there.

Our own moon has an angular size of about half a degree in the sky. Assuming a closest approach of 2R, a Phobos-sized moon would reach a maximum angular size of 0.05 degrees. To appear as large as our moon, a body would need to be more like 100km across. Phobos weighs 10^16 kg, so 100 km moon of similar composition would be ~10^18 kg. In comparison to Roshar's mass of 3x10^24 kg that is still very small, but it might be big enough at these distances to cause tidal effects? I'm not sure.

[EDIT: I used this online calculator to figure out tidal forces. Plugging in the numbers for Roshar and this hypothetical 100 km moon, it says that the average tidal force would be 3% of our moon's. Tidal force decreases with the cube of the distance, though, so at periapsis it would be significantly more than that. Using the orbit I've been dealing with (eccentricity=0.45) the tidal force at periapsis would be 20% of our moon's. If you increase the eccentricity to 0.68, periapsis gets you the same tidal force as our moon. I still don't know enough about tides to understand what that varying force (arising from the eccentric orbit) would do. I'm inclined to think that because the moons orbit with a period of exactly one day that there would be resonant effects and the tides would be larger than you might expect from only e.g. 20% of the force.]

(Incidentally, seen from Mars Phobos has an angular size of 0.1 degrees, and orbits a bit less than 2 Martian radii from the surface.)

I think it's reasonable to have the moons (at periapsis) appear between 10% and 100% the size of ours in the sky, so we can probably conclude that all three moons are somewhere in the range of 10-100 km across, (they can tend to the smaller end if we go with a more elliptical orbit). 

We had a discussion on Discord yesterday where I was reminded that Roshar is still rotating relative to the moons' orbits, a factor that was omitted from my previous visibility time considerations. This has two major effects. The first is that the moons cross the sky twice, once during the day and once at night. With the eccentricity we are considering for the orbits, the moons at their smallest will be 20-25% of their maximum size. (That is, if Nomon at periapsis looks as big as our moon with an angular size of 0.5 degrees, then at apoapsis during the day it should look about one fifth as large with an angular size of 0.1 degrees.)

The second effect is that the visibility times are shortened a bit compared to what I calculated. The correction for Roshar's rotation will have the biggest effect when the moons are moving slowly (especially during the day) and the smallest effect when they are moving quickly (for observers in central Roshar). Consequently, the visibility times for central and coastal Roshar will even out a little bit from the disparity calculated before. Unfortunately, this also exacerbates the time zone issue.

Regarding the complete absence of daytime moon sightings by our characters, there is no way that people haven't noticed but I find it reasonable to suggest they don't care much. One suggestion on how to make the daytime moon appearances less prominent was to give the orbits a sharp inclination. I calculated the highest position in the sky for a day and night moon at various inclinations, when observed from either the equator or from a latitude of 45 degrees South (hopefully the chart formatting will work here). Angles given indicate degrees above the horizon, so 90=zenith, 0=at horizon. I've rounded off to the nearest 5 degrees, so we don't get too distracted by details.

Inclination of Orbit Observer at equator Observer at 45 S
Night Day Night Day
0 90 90 30 40
10 75 75 45 30
25 60 60 60 10
45 30 40 90 below horizon

The upshot is that an inclined orbit won't make any difference for people near the equator, but further south (where most of our cities are) it could matter a lot. The inclination needs to be at least 20 degrees before it has a real impact, though.

 

Edited by ccstat
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I'm just gonna throw something else in the mix:

Are the moons spherical or irregularly formed? According to this thread I found on the question, icy objects need to be about 400 km in diameter while rocky objects need to be about 600 km in diameter. We haven't seen any comments on this, but it seems unlikely to me that they would be round, though we do of course know they were placed there by either Adonalsium or a Shard.

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As for size all I know is that people describe the moonlight as an illumination source. That means that its a lot bigger than Phobos which is just a shiny speck from the Martian surface.

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3 minutes ago, physicskid said:

As for size all I know is that people describe the moonlight as an illumination source. That means that its a lot bigger than Phobos which is just a shiny speck from the Martian surface.

No idea about illumination, but Phobos is visible with the naked eye as a 1/3 size moon.

https://www.nasa.gov/mission_pages/MRO/multimedia/20071127-caption.html

Phobos and Deimos are about 21 and 12 kilometers (13.0 and 7.5 miles) in diameter and orbit Mars with periods of 7 hours, 39.2 minutes and 1 day, 6 hours, 17.9 minutes respectively. Because Phobos orbits Mars in a shorter time than Mars' 24 hour, 37.4-minute rotational period, to an observer on Mars' surface it would appear to rise in the west and set in the east. From Mars' surface, Phobos appears about one-third the diameter of the Moon from Earth, whereas Deimos appears as a bright star. 

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I think they are described (at least once) as discs, and I'm pretty sure Brandon imagines them as spherical. Ah! Ishar's artwork comes in handy. :D They are depicted as spheres there. It doesn't matter whether that's realistic or not, as we know they didn't end up as Roshar's moons naturally anyways.

Tidal forces would definitely cause their orbits to degrade, but I think we can wave that away as a long (looooooooooong) term concern. Peter frequently states that they are unstable anyways, on astronomical scales, so I don't think that's something we need to be concerned about. And thanks to @ccstat's great work, it doesn't sound like Rosharan's need to worry about crazy tsunamis.

I don't think we need to be too picky about the sizes. The orbits seem loosely defined enough that we can play with that to make them look right. Or we can play with their density if we want them to look bigger or smaller for the same mass. I'm not sure how specific Peter intended his comment to be. I felt it was more of a statement about the general order of magnitude. That is, that they're simply very small compared to Earth's moon. Brandon apparently intends for Nomon to appear larger in the sky than our moon (source), but he also points out that this isn't set in stone.

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well, I went and got a picture of Phobos from the Martian surface taken by the Spirit rover. It does look a little bigger than the speck I thought it was but is still don't think something this size is going to cast shadows.

phobos_deimos_from_mars_300.jpg

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We might be taking the concept of the "hateful hour" too literally.  I think it's a symbolic term more than anything, we probably shouldn't interpret it as needing to last a full hour, the actual time between Salas setting and Nomon rising could potentially be quite small.  There also might be important east-west variance.  The actual references pulled to this time frame are pretty sparse.  Kaladin mentions it once without giving a timeframe, and only Szeth names it.  Perhaps the time is quite short in the east, but closer to an actual hour out west in Shinovar?  Either way, I think reducing this "hour" would help a lot in making our moon schedule fit.

Salas also seems to have a very eccentric orbit (just from eyeballing the Solar System map).  It's closest point (perigee) is near the horizon on one side of the planet, thus we would expect it to move fastest near this point, and slower on the other side when further from the planet.  Net result: Salas' rise and fall in the night sky would not be uniform in speed, one would be faster than the other.  I think to make our moon times "fit", Salas rises to its peak rather slowly, then sets much quicker.  Kaladin even makes a reference to Salas seeming "hesitant" when first rising - "Violet Salas peeked over the horizon to the east, seeming hesitant at first, as if making sure the sun had vanished".

Add together a shorter hateful hour and a quicker setting of Salas after peak and I think we can make our data fit the clock.

Regarding the eccentricity of the moon orbits: Nomon alone seems to have a very symmetrical elliptical orbit in the Solar System map.  In fact, I wouldn't be surprised if it's calibrated to peak over Urithiru at local midnight perigee and noon apogee (normally not visible during the day, but maybe alluded to in the beautiful endpaper artwork of Ishi standing under a solar eclipse).  Salas and Mishim both seem to have eccentric orbits with perigees occurring near the opposite horizons of Roshar.  I would guess Salas' perigee is near the dawn/sunrise horizon, while Mishim's is near the dusk/sunset horizon.

edit: better add that solar map or this post doesn't make any sense.  Also: these moon positions are occurring at/near (Urithiru?) dawn!  Salas and Nomon are already on the day-side of Roshar, and Mishim (3rd moon) is on the horizon.  The lunar orbits are clockwise in this picture.

5a79ba954a502_RosharMoonsfromArsArcanum.PNG.8e5fa3a82fb490266ca2407bc2e4ee72.PNG

Edited by Subvisual Haze
pics plz
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A lot of good points @Subvisual Haze, though I'm hesitant to rely too much on the details of that system chart. It doesn't strike me as a particularly technical document. I do like your analysis of the orbit eccentricities and orientations, and it that makes a lot of sense. I particularly like your idea that Salas' "hesitance" is related to its slower velocity at moonrise. I'll have to take a closer look at how different periapsis points would influence the relative timing of the moons. For now, I think you are definitely on to something.

Changing the length of the moonless "hour" may help the timing some, but for me the main problem is that east-west variation. In accounting for the breadth of the continent, and therefore the different time zones, it still appears that in Shinovar the hateful hour ought to occur in mid-afternoon, rather than after sunset when it could actually be dark. 

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I found another tidbit reinforcing our original guesses of Salas' rising and setting.  When Kaladin and Shallan are tromping through the bottom of the Shattered Plains, they discuss the timing of the next Highstorm:

Quote

"Tomorrow night," she said softly. "Just after first moonset."

The next day Kaladin notes:

Quote

The sun passed through the crack overhead, vanishing from sight.  Already past noon.  They had seven hours until the highstorm..."

It's 5 Roshar hours from noon to sunset.  So this seems to reinforce that Salas does actually set by 2nd night hour (or shortly after).  Maybe there is in fact nearly an hour between Salas setting at 2nd night bell and Nomon rising around the 3rd.

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10 hours ago, Subvisual Haze said:

So this seems to reinforce that Salas does actually set by 2nd night hour (or shortly after).  Maybe there is in fact nearly an hour between Salas setting at 2nd night bell and Nomon rising around the 3rd.

Good catch!

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Goofy observation that might tie into further moon/clock connections: Cusicesh always appears in the city of Kasitor at "Seven Forty Six in the Morning".  It might be a total coincidence, but roughly between 7th and 8th bell on the clock (assuming 100 minutes in a bell) matches up quite well with the green circle, which we assume to represent the green moon Mishim.  Is this a totally random coincidence, or does the timing of Cusicesh's appearance connect to the position of Mishim relative to Roshar?

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