Roshar's Sun

[DrPhysics he/him]

TLDR:

The Rosharan sun is somewhere between 1.03-1.18 times the mass of our sun.

Post:

I've been toying with figuring out the orbits of Roshar's moons, and while digging, I found this old post trying to figure out the size of Roshar's sun:

and since the sun will probably be important to figuring out the moon's orbits, I wanted to tackle those first.

How I figured it out:

We know that Roshar's period is 1.1 earth years (see the coppermind). We also know from this WOB that the sun is white and larger than ours:

Spoiler

Leiyan

I'm curious about the sun because it's described as white, and our sun is typically yellow. I assume it's a different type of star?

Brandon Sanderson

The yellowing of our sun is not actually caused...so our sun being yellow is not based on the star's actual color.

Leiyan

So is it bigger than our sun? Smaller? If there's anything you want to throw out there I'll take it.

Brandon Sanderson

Okay...I'm having to reach into my memory. This is not canon. Younger and larger, I believe it is both. Younger and larger.

Brandon Sanderson

The star's age, at Roshar...Earth astronomers would say that is a star which could not have planets with life on them.

Words of Radiance Philadelphia signing (March 21, 2014)

The Physics:

We know that the period of an orbit is:

We can find the habitable zone of a star (where surface water can be liquid) using this equation:

 where L is the luminosity of the star, and alpha is a constant (0.53 for the maximum distance in Au if L is in solar luminosities, 1.10 for the minimum distance).

To link the two equations, we can use this equation that relates luminosity to mass for stars that are near the size of our sun:

 (where M0 is the mass of our sun).

 

Combining these and solving for mass gives:

which gives us a mass range of 0.99 - 1.22 solar masses. 

 

However, we know that there are two other planets in the habitable zone, so Roshar will probably be close to the middle. If we limit its orbit to with 10% of the center of the habitable zone, we get a range of solar masses from 1.03-1.16.

Which, (going back to the WOB earlier) is slightly larger than our sun, and is in the main sequence range (G1V-F8V) that a human would say was white (they have masses that range from 1.03-1.18).

So, both the color and the gravity math agree. Roshar's sun is most likely 1.03-1.18 Solar Masses.

[IcedOutPenguin He/Him]

That's very cool, I hope I learn what those numbers/variables mean/know what your talking about, someday (as an aspiring physicist) but it is a very cool idea to quantify the mass/orbit of things in the cosmere, math can do many things.

[The Bookwyrm he/him]

As both a Cosmere and Astrophysics nerd, I approve of this. Calculations are logical. Thanks for doing this!

I didn't realize there were white main sequence stars that were easily habitable. I thought those were mostly A and B class, which I assumed were too hot.

Edited November 16, 2024 by The Bookwyrm

[Moirne she/her]

Brandon has really gone out of his way to show us that Roshar is a created system that shouldn’t naturally exist. I am so curious as to its purpose.

[DrPhysics he/him]

On 11/16/2024 at 2:59 PM, Moirne said:

Brandon has really gone out of his way to show us that Roshar is a created system that shouldn’t naturally exist.

The moons are weird, but everything I've talked about here could naturally exist.