Taldain's position

[idanstark42 he/him]

After reading this topic: 

I thought to look at other places in the cosmere. Most of them are missing some details that would allow similar calculations. Taldain is, however, a very unique system. The planet is placed in the L1 lagange point of a double star system. Those stars are also known to be a blue supergiant and a white dwarf, which gives as an approximation for their size, masses, temperature and luminosity.

Assumptions:

• Dayside is a desert, and water evaporate pretty quickly when outside, so Taldain would be in the lower 30% of the habitable zone
• The Luminosity of the white dwarf is negligable (it's much weaker then the supergiant, and is surrounded by a particulate ring)
• The Luminosity of the blue supergiant is between 10^5-10^6 suns.
• The mass of the white dwarf is about 0.6 suns, and the mass of the supergiant is around 22.5 suns. The mass of the planet is negligable.

Using the same formula from the original post for the distance between the blue supergiant and the planet, we get that the distance between the planet and the supergiant is r=301-342 AU for a supergiant with luminosity 10^5 suns, and r=953-1080 AU for a supergiant with luminosity 10^6.

Using these distances and the formulas for the L1 lagange point i'ts easy to calcuate the distance between the dwarf star and the supergiant (r is the distance between L1 and the dwarf star):

• For L=10^5 we get R=379-430 AU
• For L=10^6 we get R=1199-1359 AU

Using this formula (time period for circular motion in a gravitational system):

The time period is:

• For L=10^5 we get T=37-45 years
• For L=10^6 we get T=210-254 years

Any thoughts?

Edited March 25, 2025 by idanstark42

[DrPhysics he/him]

On 3/25/2025 at 11:35 AM, idanstark42 said:

Any thoughts?

Something is off with your period calculations. When I run the white dwarf as 0.5 solar masses and the giant as 22.5 solar masses with a 400 AU distance, I get a period of 265 years.

 

The planet won't follow there period equation you used because it is at a Lagrange point, so you need to use the giant-dwarf system.

 

Other than that, the logic looks sound.

 

Once, I created a potential Taldain system (though there are several other solutions), and posted my work here:

https://www.17thshard.com/forums/topic/198004-taldain-orbital-system/

 

[idanstark42 he/him]

1 hour ago, DrPhysics said:

Something is off with your period calculations. When I run the white dwarf as 0.5 solar masses and the giant as 22.5 solar masses with a 400 AU distance, I get a period of 265 years.

The planet won't follow there period equation you used because it is at a Lagrange point, so you need to use the giant-dwarf system.

I didn't use the time period equation on the planet and the giant, but on the dward and the giant. The planet will, of course, have the same time period as the whole system, and its mass is negligable.

I did go back to check my calculations, and indeed I made some arithmetical errors (that's what happens when you do math too late at night). I still get something different then you, a much larger time period. Here is my calculations (for giant with luminosity 10^5):

1. R (distance between giant and dwarf) = 400 AU = 5.98391483e13 meters
2. m1 (mass of the dwarf star) = 0.5 Msun = 9.945e29 kg
3. m2 (mass of the dwarf star) = 22.5 Msun = 4.47525e31 kg
4. T (time period) = 5.26650248e10 sec = 1668 years

When putting the distances I got, I get:

• For L=10^5 we get T=1539-1860 years
• For L=10^6 we get T=8660-10,450 years

I think all in all these calculations are still a bit half-harzedous. If you have ideas for something more rigorous I would love to hear. Is there maybe additional information I didn't use that would help us cut some of these ranges?

 

[DrPhysics he/him]

5 hours ago, idanstark42 said:

Here is my calculations (for giant with luminosity 10^5):

Because we define a year as once around our sun (1 solar mass) at a distance of 1 AU, if you stick in those units G=4*pi^2 (try plugging those ones into the period equation and solving for G). It makes entering the values into a calculator much easier.

 

That said, I didn't include the 2pi when I crunched the numbers, so I also get 1660 years for the 400 AU case.

5 hours ago, idanstark42 said:

If you have ideas for something more rigorous I would love to hear.

We could narrow down the intensity at surface range for the supergiant by estimating the planets albedo(which is hard), and knowing that the white dwarf primarily emits in the ultraviolet would let's us narrow down its temperature range using blackbody spectra and white dwarf properties. Beyond that, we just don't have enough information.

 

We also know that since Peter Ahlstrom has a background in astronomy, when they say it is a blue-white supergiant, they probably mean a class B supergiant which limits the size and luminosity more than just Blue Supergiants, which could be from class A, B or O, and your data ranges include those three classes.

Edited March 27, 2025 by DrPhysics
Added information

[idanstark42 he/him]

On 3/27/2025 at 1:06 AM, DrPhysics said:

Because we define a year as once around our sun (1 solar mass) at a distance of 1 AU, if you stick in those units G=4*pi^2 (try plugging those ones into the period equation and solving for G). It makes entering the values into a calculator much easier.

 

That's really cool! I'll start using this

 

 

On 3/27/2025 at 1:06 AM, DrPhysics said:

We could narrow down the intensity at surface range for the supergiant by estimating the planets albedo(which is hard), and knowing that the white dwarf primarily emits in the ultraviolet would let's us narrow down its temperature range using blackbody spectra and white dwarf properties. Beyond that, we just don't have enough information.

 

If we do that, we need to take into account the atmosphere and greenhosue effects