Physics of the Taldain System

[RShara]

Question about the physics of the Taldain system.  It was complicated enough with one sun, one tidally locked planet, and one moon that always rotates around the light/dark terminus.  How does a binary system work with this?

From what I understand, the L1 point (aka the barycenter) between the two stars is extremely unstable.  Any kind of jiggle to the rotations or gravity of the system and the planet spins off into space or crashes into one of the stars.  Judging from the sketch of the system, we have the two suns in a near-circular orbit (very difficult).  And Taldain in the gravitational center of the binary system, with a rotational period that exactly matches the orbits of the stars?

And that still doesn't explain the orbit of the moon, which should stay the same no matter which direction the planet itself is facing.

It seems to be an extreme balancing act.  I suppose Investiture could account for it, but I kinda hate to see this hand-waved away as "magic," since from what I understand of Brandon, he tries to keep as close to actual physics as possible (red/blue shifts not withstanding ). 

Does anyone smarter than me have a good explanation?

[Khyrindor]

Keep in mind that the orbits might not necessarily be to scale. That's my input for now.

[Weltall]

I imagine it's possible you could get a planet into the L1 position between two stars, but not keep it there because that's an unstable point. Thus, the best I can offer is 'A Shard Did It'. Or since most worlds appear to have been tinkered with pre-Shattering in various ways, 'Adonalsium Did It'. Dunno, maybe he/it got bored with doing things the 'proper' way and decided to have some fun, knowing it would make astronomers thousands of years later tie themselves in knots trying to figure it out.

[RShara]

18 minutes ago, Khyrindor said:

Keep in mind that the orbits might not necessarily be to scale. That's my input for now.

Well, the scale doesn't really  matter in this scenario.  It's kinda a given that the orbits AREN'T to scale, actually, given the sizes involved.  The orbits would have to be near circular for the planet to be tidally locked to both suns, though.  Otherwise, at least one of the suns would "move" as the planet turned to stay tidally locked to the other, if they were elliptical orbits.

 

12 minutes ago, Weltall said:

I imagine it's possible you could get a planet into the L1 position between two stars, but not keep it there because that's an unstable point. Thus, the best I can offer is 'A Shard Did It'. Or since most worlds appear to have been tinkered with pre-Shattering in various ways, 'Adonalsium Did It'. Dunno, maybe he/it got bored with doing things the 'proper' way and decided to have some fun, knowing it would make astronomers thousands of years later tie themselves in knots trying to figure it out.

I was hoping to avoid the "it's magic" hypothesis, really.

Edited November 28, 2016 by RShara

[ZenBossanova]

Considering it is an unstable point, that just means the Shard will have to occasionally nudge it back into place. We put satellites in unstable Lagrange points all the time. You just have to keep a little closer eye on them. 

And considering how much the Shard modifies the climate, this is probably a lessor worry anyway! 

[RShara]

1 hour ago, ZenBossanova said:

Considering it is an unstable point, that just means the Shard will have to occasionally nudge it back into place. We put satellites in unstable Lagrange points all the time. You just have to keep a little closer eye on them. 

And considering how much the Shard modifies the climate, this is probably a lessor worry anyway! 

Mmmm it wouldn't really be occasional.  Gravity isn't as stable as it seems when talking cosmic scales.  Satellites are much smaller than planets, and they have to make constant course adjustments in order to stay in position.

Source on the Shard significantly affecting the climate?

[ZenBossanova]

40 minutes ago, RShara said:

Mmmm it wouldn't really be occasional.  Gravity isn't as stable as it seems when talking cosmic scales.  Satellites are much smaller than planets, and they have to make constant course adjustments in order to stay in position.

Source on the Shard significantly affecting the climate?

Logically, it would seem it must temper the climate, or the Dayside would burn. 

But while I thought I remembered reading it, I don't know where. 

[RShara]

11 hours ago, ZenBossanova said:

Logically, it would seem it must temper the climate, or the Dayside would burn. 

But while I thought I remembered reading it, I don't know where. 

Not necessarily.  It depends on the temperature of that sun, the distance from the planet, the location of the continent, and a bunch of other things.  Theoretically, it could just be hot.

[Jofwu]

Yeah, this situation is definitely unrealistic. Hate to say it, but you're not going to find a real-world explanation for what's going on.

First a point of clarification: the L1 point isn't the barycenter. The Earth-Sun L1 point is relatively close to Earth while the barycenter is inside the Sun. That said, if both Taldain stars are of equal mass and orbiting in a circle then the two points do coincide. A planet at the barycenter of any two stars is definitely not stable. The L1 point isn't really stable either under natural circumstances.

The moon is even more difficult to explain. With Taldain itself you can argue that magic is keeping it balanced, or perhaps in a halo orbit. But the moon would have to be in some kind of weird... spiraly orbit. Roshar's moons have some unrealistic precession going on as well, but in that case you only have one star. With Taldain's moon it's not just something close where magic bridges the gap. You need a completely fantastical explanation.

[RShara]

21 hours ago, jofwu said:

Yeah, this situation is definitely unrealistic. Hate to say it, but you're not going to find a real-world explanation for what's going on.

First a point of clarification: the L1 point isn't the barycenter. The Earth-Sun L1 point is relatively close to Earth while the barycenter is inside the Sun. That said, if both Taldain stars are of equal mass and orbiting in a circle then the two points do coincide. A planet at the barycenter of any two stars is definitely not stable. The L1 point isn't really stable either under natural circumstances.

The moon is even more difficult to explain. With Taldain itself you can argue that magic is keeping it balanced, or perhaps in a halo orbit. But the moon would have to be in some kind of weird... spiraly orbit. Roshar's moons have some unrealistic precession going on as well, but in that case you only have one star. With Taldain's moon it's not just something close where magic bridges the gap. You need a completely fantastical explanation.

Wouldn't they have to be the same mass, and orbiting in near-circular orbits for the planet to be tidally locked to them both (as seems to be the case)?  That's what I was thinking when I combined the L1 and barycenter points.

 

Yeah I got nothing on the moon.  It just doesn't make any sense without magic

[Jofwu]

I must have misread something (and misremembered) because I was thinking the stars were of equal size. Should have looked at the map again! It got posted (in beautiful color) on Brandon's website today.

I assume the circle that the stars fall along is artistic. Unless the small one is super dense (and the "particulate cloud" isn't super massive as well) then I think it's pretty safe to say that the small star is orbiting the larger. And that means Taldain is definitely at the L1 point of the two, so that it can stay in between them. I'm not an astronomer, but I don't see any reason why this would prevent Taldain from being tidally locked. In fact, I imagine it helps to make that happen.

Also, there's this brand new WoB thanks to @Necarion:

Quote

Necarion: Is Taldain orbiting at a Lagrangian point?
Brandon: [Laughs]
Necarion: It would make the orbits work
Brandon: [Long pause] I’m not sure the implications, I have to think through implications before answering questions
Necarion: The situation I’m thinking of, it would orbit the big star but at the same period as the smaller star.
Brandon: Yeah, well, I’ll just say ‘yes’, but I want to make sure I’m not saying ‘yes’, without...well, yes that’s how it has to work
Necarion: Right
Brandon: Because [Taldain] I want to be not like Roshar where we have unstable orbits and things. Uh, but I… I’m saying yes, but I hope that doesn’t get me into trouble scientifically.
           [Necarion’s note 1: While the L1 Lagrange point is an equilibrium point in the three-body problem, it is technically an unstable one. However, this seems a system that could be corrected with a small input of Shardic intervention, far less than would be required by any other astronomical arrangement I can think of]
           [Necarion’s note 2: Note the comment about ‘unstable orbits’ in the Rosharan system. This might account for the rapid variation in seasons on the planet]

Hate to be the bearer of bad news, but this definitely means Taldain is in an unstable orbit. L1 isn't stable. Of course, keeping the planet at a Lagrange point is much more reasonable than Roshar's crazy moon situation.

As for Taldain's moon (Nizh Da?)... Yeah... There's just NO way it could precess around in it's polar orbit such that it straddles two halves of the planet. Just doesn't work that way. However... Are we sure it does this? I haven't read White Sand Prose. The moon is on the horizon in WS vol. 1, which fits this star map. But perhaps this changes over the course of the year. How else would Daysiders measure a year if NOT by using the moon? They can't see the stars and the sun just sits in the same spot. They have no means to measure the length of the year (besides heading towards Darkside) if NOT for this possibility. Unless their "year" has some other meaning. This seems unlikely, but fingers crossed? Is there a WoB to the contrary?

[Necarion]

8 minutes ago, jofwu said:

Hate to be the bearer of bad news, but this definitely means Taldain is in an unstable orbit. L1 isn't stable. Of course, keeping the planet at a Lagrange point is much more reasonable than Roshar's crazy moon situation.

As for Taldain's moon (Nizh Da?)... Yeah... There's just NO way it could precess around in it's polar orbit such that it straddles two halves of the planet. Just doesn't work that way. However... Are we sure it does this? I haven't read White Sand Prose. The moon is on the horizon in WS vol. 1, which fits this star map. But perhaps this changes over the course of the year. How else would Daysiders measure a year if NOT by using the moon? They can't see the stars and the sun just sits in the same spot. They have no means to measure the length of the year (besides heading towards Darkside) if NOT for this possibility. Unless their "year" has some other meaning. This seems unlikely, but fingers crossed? Is there a WoB to the contrary?

There is another simpler option for how they measure a year: a year is 12 "months" of a complete lunar orbit, which would be terms inherited from Yolan (or whatnot).

I think your term 'precess' works well for an alternate explation.  While a moon would be able to maintain a polar orbit in this situation, the orbit would not be 'closed' (i.e., return to the same location in its orbit every time).  Instead, a polar orbit would precess around the planet, where it could start by being parallel with the terminator and half a 'year' later be perpendicular to the terminator.

I don't know whether this is Canon or not, but the terminator should have some crazy storms as well.

[Jofwu]

Ah, you're totally right. I didn't think about measuring time in terms of how many orbits the moon makes. But I like my explanation better since it doesn't require a magically moving moon.

Right, so I was referring to the orbit itself precessing. If the moon has a stable, "natural" orbit then you would see it spiral around the sky over the course of a year. Year begins with the moon moving clockwise around the horizon and half a year later it's moving counterclockwise around the horizon. At the quarter points it would on a path crossing the sun, straight above. Something like that.

[cometaryorbit]

On 11/28/2016 at 10:05 AM, RShara said:

Not necessarily.  It depends on the temperature of that sun, the distance from the planet, the location of the continent, and a bunch of other things.  Theoretically, it could just be hot.

Yeah, a tidally locked planet can probably have habitable temperatures, at least if it has oceans. They distribute heat well. Somebody did a simulation where they tidally locked Earth to the Sun, and they got temperatures of about 50 C at the hottest point and -50 at the coldest. They only ran it for 50 years or so though. The "morning/evening" band would be pretty habitable.

If Taldain was just a bit colder overall than Earth (farther from the sun or dimmer sun or less greenhouse effect) the central dayside might be fairly habitable.

The Moon gets larger temperature differences in just 14 days because it has no atmosphere or ocean to distribute heat.