Taldain Orbital system.

[DrPhysics he/him]

This is something I wrote up years ago (before the Omnibus was available) but with Sanderson working on the prose version of White Sand, I thought it was a good time to pull it from Reddit, update it, and give it a home here.

 

My goal was to see if I could invent a system that matched what we know about Taldain with minimal magic intervention. I couldn't invent one that could completely run on its own, but here's the one that got the closest.

Background info

In Arcanum Unbounded we learn this about Taldain:

•  It is tidally locked between two stars in a Binary system
•  The star that dayside faces is a blue-white super giant
•   From the planet, it looks like it is the same size as our sun (found with a little geometry)
•   The star that darkside faces is a white dwarf that:
•    has a particle ring around it making it "barely visible"
•    is bright enough to leave darkside in twilight but not full daylight
•    the UV part of its spectrum is enough brighter than the visible part that you can see plants fluorescing (When answering this question, Brandon states that it acts like a blacklight)

   
   
Additional info we have on Taldain:

•  it was put there by someone (who put it there is a RAFO)
•   magic can be involved in the planetary dynamics

The Blue-White Super Giant

Climate modeling is hard (weeks to months of super computer time), so instead I used these simple guidlines to calculate distance:

•  Over a 24 hour period, the center of Taldain should absorb the same amount of solar energy as a spot on Earth's equator.
•  Earth, on average absorbs 60% of the incoming sunlight, but deserts only absorb 30%. Sand, especially white sand, is very reflective.
•  If possible, the star should look roughly the same size as our sun,as it does in the graphic novels. (Aside: If I had to break any of these rules, this would be the first. Luckily, I didn't have to.)

Blue-white supergiants have a lot of variability, so when I was putting together the system I pulled in a list of stars with known masses, sizes, etc. and picked the one that fit best (9 Persei for those that want to look it up). 

That puts Taldain's orbit at about 95 AU from the star (1 astronomical unit (AU) is the average distance between the earth and the sun). At that distance, the intesity would be comparable to the sun at high noon in the early fall for those living between 40-50 degree latitudes here on earth. Since the sun never sets, the air would be much hotter, but you wouldn't need as much sunscreen. Cool side effect of this set up: it would probably be beneficial to have lighter skin living on darkside so that your body would produce enough vitamin D and skin cancer would be a lower risk. (Those are the two main evolutionary driving factors for skin color on earth, which is why those whose ancestors lived near the equator have darker skin and those living away from the equator tend to have lighter skin.)

Having the main star be a blue-white supergiant adds some interesting options for an end-of-life for the system. Here are some potential future scenarios:

•  The most probable, but also the most boring: The star continues burning through its fusible materials, slowly inflates into a red giant, then goes supernova. This is far enough in the future that it probably won't affect any plotlines.
• The star turns into a Wolf-Rayet star: If there is enough heat and pressure in the core, the star starts fusing carbon. The extra energy from this makes the star start belching huge amounts of its surface hydrogen. At the distance Taldain sits from the star, Day siders would see a huge hot plume belch out of the sun, then have somewhere between 1 month to 1 year to get to Darkside. When the plume hits, Dayside is annihilated. The star will continue to belch out hot hydrogen, turning the area into a nebula. The neighboring white dwarf will start gathering up the matter, then sometime between 1,000-10,000 years after the initial belch, the white dwarf will have gathered enough matter to reignite, triggering a type I supernova. The only thing left of the entire system would be atoms and dust. There wouldn't even be an asteroid. The initial belch could come at any time (or could still be a million years away).
• The star becomes a luminous blue variable star (slightly less likely than a Wolf-Rayet star). These stars feature many supernova-like outbursts that can come one at a time or several in a small burst, then wait a few thousand to a hundred thousand years inbetween. Dayside is raized, but some of the life living deep underground might survive, depending on the outburst. They'll see the outburst about a month before it hits. Once again, the white dwarf is likely to go supernova eventually, but it will probable take more time.
• The star just goes supernova. It's rare, and we don't know why it happens, but sometimes blue supergiants just explode. Daysiders might be obliterated in the initial gamma ray burst, which would hit them without warning the moment the light from the supernova reached the planet. Or, it could be small enough that people who were outside get radiation poisoning. Standing inside a stone building may be enough protection. They would have somewhere between two weeks and a month to get off-planet before it is destroyed by the ejected gas cloud. The blue supergiant leaves behind a neutron star. The white dwarf probably goes supernova sometime in the next 100,000 years, but no one is around to see it.

Summary: There are a few world-ending scenarios that could easily happen within 1,000-10,000 following White Sand, all of which leave a race against the clock to get off the planet in order to survive.

The White Dwarf

White dwarfs are the left-over remnants of a burnt-out star that wasn't big enough to create a neutron star or a black hole. The intense gravitational forces that arise from having so much matter in such a small space makes their properties much more predictable. Therefore, instead of trying to find a real star that fit, I was able to invent one that fit.

The result: a white dwarf with a temperature of 100,000 K (180,000 F), a mass that is 17% of the sun's mass, and a radius that is 2.2% of the sun's radius. Solar units are traditional and make the math easier, but I think it's fun to point out that the white dwarf fits the mass of 56,000 earths into a sphere that is only 2.5 earths in diameter.

To create a semi-stable orbit, the start would be about 18 AU away from the planet. At that distance, there would be about 50 lux of visible light (think living room at night so you've dimmed the lights some). You'd be able to read,  but just barely. From the surface of the planet, it would look roughly the same size as the planet Mars does from earth, but would be much, much brighter.

In order to see the UV effects described, there would need to be something in the atmosphere that keeps ozone from froming on Darkside. That would make UV light 10 times brighter than the visible light and intense enough to make darker skin an evolutionary advantage. The people on darkside would face an exposure to UV that would be comparable to living in the mountains on the equator here on earth. 

It would also explain why plants have adapted to fluoresce. UV light has enough energy per photon that it can easily break many molecular bonds (which is why it can cause cancer). Plants would do much better with an analog of chlorophyl that absorbed some of the UV light and re-emitted it as a lower energy wavelength instead of breaking apart. It would both allow plants to make their own food and protect their DNA from the ionized chunks of molecules (free radicals) that would otherwise be produced.

It is very improbable that a white dwarf and a blue supergiant would naturally form in a binary system (see notes above about the type I supernova), and so it was probably placed there when the planet was placed as well.

Taldain - The Planet

In our made-up system, it would take Taldian 1,200 years to orbit its star. Also, the gravitational forces from it's neighbors are so weak that the supergiant would burn out billions of years before the planet could be tidally locked, but once locked it would stay there. That tells us that the placement and being tidally locked had to be done by whichever power placed it there.

The planet itself would have to sit in what's called a LaGrange point between the two stars. Generally speaking, the closer a planet is to a start, the slower it is. A Lagrange point sits where the second star pulls just hard enough on the planet that the planet can keep pace with the second star when it would normally fall behind. However, these points are what's called an unstable equilibrium. If there are any bumps or jostles (like the ones that come from having a moon orbit around it), the planet will fall out of the equilibrium into a new orbit.

The omnibus refers to this as "Wombear's saddle", which is a nice nod to physics going on. (However, the explanation of finding it through observing stable and unstable orbits around the white dwarf isn't feasible. The orbits are unstable enough that nothing that is big enough to see (even with our modern telescopes) would form there and stay there long enough to figure out its orbit.

Using some orbital simulation code I stole from an astronomer in our department, I found that Taldain would only be able to remain in its orbit for about 50-70 years without something else keeping it in place (most likely some form of investiture).

Which leads to the question: "What would happen if the investiture stopped holding it there?" 

Three orbital bodies create what is called a chaotic system where tiny changes in initial conditions can lead to wildly different outcomes. I ran thousands of simulations to find out. The most common (and boring) was that Taldain settled into a new, slower orbit, no longer tidally locked between the two stars. Also, Taldain is so much lighter than the stars that the stars never significantly altered their orbit.
 Other final orbits that happened:

•  Fairly common: Taldain is sped up and then continues to speed up a bit more each time it passes between the stars, slowly increasing its orbit until it slams into the white dwarf in somewhere between 5,000 and 100,000 years into the future.
•  Fairly common: Taldain starts orbiting around both stars in a figure 8. Everyone freezes to death within 100 years the first time it orbits the white dwarf. It usually happens within 5 orbits (6,0000 years)
•  Rare but super awesome: Taldain is slingshotted out from between the two planets at incredible speeds. Everyone freezes to death within 200 years. Before freezing to death, the acceleration reaches somewhere between 0.25 and 2 g's. If you were standing on the day/night line on one side of the planet, you would feel up to 3 times heavier. On the other side, gravity might not be strong enough to keep you on the surface and you would be left behind, along with rock and other rubble as the planet is torn apart. The lower accelerations aren't strong enough to rip the planet apart, but would be strong enough that you would have to lean into the direction of the acceleration to keep from falling over. Some people would spend their entire lives leaning in as the planet slowly got colder.

The Moon

Taldain's moon constantly orbits the day-night line around the planet, and the residents count each orbit as a day. Due to conservation of momentum, the moon's orbit should drift around the planet as it orbits the larger star. From a space perspective, the moon keeps orbiting in the same plane as the world turns beneath it. We couldn't find any simulations (tiny tweaks in orbital angle) that would keep the moon orbiting the day-night line for more than 10-15 years. Whatever is holding Taldain in place would also have to keep nudging the moon in (probably why the cloud around the white dwarf blinks every seven days, according to the omnibus).

As far as figuring out the orbit goes, we're a lot more limited in the details. Since the text doesn't mention the moon having a tail, we know that it is probably rocky (rather than icy like a comet). If it was comet-like, the tail would always be pointed away from the supergiant, towards Darkside. For stability, we'd want the smallest possible mass that would still be round, which would make the Taldain moon roughly the size of Saturn's moon Mimas. Assuming Taldain is about earth-sized, and that 1 "day" is close enough to one earth day that it matches human biological cycles, the moon's orbit would be 4-8 earth radii away from the surface (which also makes it far enough away that it won't break up due to Taldain's gravity). Therefore, Taldain's moon would appear 1/4 the size of our moon at the smallest up to just a little bit smaller than our moon at the largest.

Edited November 8, 2024 by DrPhysics
Adding Tags