a few nitpicks on roshar's physical characteristics

[king of nowhere]

I have a few minor questions for those who are very well versed in cosmere astrophysics;

1) on roshar, the year lasts 500 days. However, if a planet does not rotate at all, the sun will still rise and set once per year, because of the planet's motion around the star. for example, on earth a day lasts 24 hours, but the planet rotates in 23 hours 56 minutes and something. So, I want to make it clear, what's 1/500th of a year: roshar's day or roshar's roational period?

 

2) we know roshar has an atmosphere richer in oxygen. does it have the same atmospheric pressure of earth, but with a greater amount of oxygen compensated by an equally smaller amount of nitrogen? Or it does have a greater atmospheric pressure overall, and the same oxygen/nitrogen ratio?

3) we know the surface gravity is 0.7 g. that could result from a planet that is as big as earth, but with a lower density (less iron and more silicate in its composition), or from a planet that is as dense as earth, but smaller, or from a combination of lower density and lower radius. do we have an estimate on roshar's size?

i know those points are irrelevant to the story, but I'm just curious.

[cometaryorbit]

1 - 500 day year is from the perspective of the people on-planet, so it has to be solar day (sunrise to sunrise) not sidereal day (rotational period).

2, 3 - I don't think we know.

[Oversleep]

Ad 2 - I think that the expression "rich in oxygen" means that the percentage of the oxygen in the air is higher. It would be a weird way to describe the situation if it's in fact higher pressure. Of course we do not know the exact atmospheric pressure but I guess it's similar to Earth's - Brandon describes Roshar as "high oxygen low gravity world" and has never mentioned anything about pressure being odd. I know lack of evidence is not evidence of the lack of existence but we have to consider that if there was something important about one of Roshar's characteristic Brandon would have mentioned it by now.

[Treamayne]

But we do have possible evidence that the circumference of Roshar is smaller than that of Earth. In one of the highstorm threads:

On 8/23/2016 at 1:50 PM, hwiles said:

I ran some estimates for the circumference of Roshar from the in-book maps with latitudes marked by cross-referencing them with maps of Alethkar that show distance scales and came up with a minimum of 11,000 miles (really small for a planet...) I believe Isaac Stuart, who drew the maps and next to Sanderson would probably know best, has previously suggested the real figure is closer to around 15,000-18,000 miles (Earth's is about 25,000 miles for reference).

 

[king of nowhere]

that would imply a density close to that of earth, and a radius in the upper range of that estimation, because 18000 = 25000 *0,72 and among spherical bodies of the same density, the surface gravity is directly proportional to the radius (physical demonstration under spoiler)

Spoiler

 gravitational acceleration caused by a planet is equal to G*M/r^2, where G is the universal gravity constant, M is the mass of the planet and r the distance from the center of the planet - if we are looking at surface gravity, then it is equal to the radius of the planet. And the mass is equal to volume times density (let's call it P, the closer approximation I have here to the greek letter traditionally used), and the volume of a sphere is 4/3  * pi * r^3. So, a=(G*P*1.333*3.14*r^3)/r^2=K*r, where K contains all the constant factors in this equation.

In practice, the density will not remain constant, as a bigger planet has a greater inner pressure, and that kind of pressure is capable of compressing materials and make them denser. So, if roshar has a circumference of 18000 miles, it would even need a slightly higher iron-to-silica ratio than our planet to rreach a surface gravity of 0.7 g.

to be smaller, roshar would need to be even more dense than our planet, and earth is already very dense - the most dense body of any size in the solar system, close to iron. To have a planet of higher density, it would need a nucleus made mostly of a more dense element, but no such element is very abundant in the universe. granted, the shards could have made one with a lead nucleus, but I think a circumference of 18000 miles (which translates to a radius of roughly 4500 km) and a similar composition to our planet is the most likely guess here.

[cometaryorbit]

7 hours ago, king of nowhere said:

to be smaller, roshar would need to be even more dense than our planet, and earth is already very dense - the most dense body of any size in the solar system, close to iron. To have a planet of higher density, it would need a nucleus made mostly of a more dense element, but no such element is very abundant in the universe.

Earth is so dense largely because of gravitational compression, though. Mercury has a much higher iron/silicate ratio. A planet with Mercury's composition and Earth's mass would be much denser than Earth. Even at Roshar's mass, it should be somewhat denser.

[king of nowhere]

5 minutes ago, cometaryorbit said:

Earth is so dense largely because of gravitational compression, though. Mercury has a much higher iron/silicate ratio. A planet with Mercury's composition and Earth's mass would be much denser than Earth. Even at Roshar's mass, it should be somewhat denser.

yeah, but we're talking 5.5 g/cm^3 for earth against 5.4 for mercury, for an internal composition of 30% silicates for mercury against 45% for earth, and mercury is much smaller than roshar. On going from earth-sized to roshar-sized, compressional effects should cause a change of density lower than 10%. So a density roughly equal to that of earth is still likely.

[+hwiles]

1) I like this theory of a 20 hour orbital period (Rosharan days are 20hrs long fyi). Roshar has 3 moons that appear to rise and set at the same time each night. If you can reconcile this phenomenon with the theory you'll have a good start to changing minds from the conventional wisdom in the community that the moons exist at Lagrange points and Roshar has a 20 hr rotational period. Note first that Roshar has no axial tilt or precession.

2) Earthlike creatures (ie, pigs, horses, minks) and world hoppers breathe the air, so it probably isn't tremendously different. That said, it probably is a little different, and between Roshars smaller size and (according to conventional wisdom) more rapid rotational period, the pressure changes would be very significant (which could contribute to the creation of high storms and would be really hard on arthritis).

3) I think this has been answered well already. I'm pretty sure Isaac Stuart gave an exact circumference of the planet once. Between the 3 moons and the weirdness behind the shape of the continent  (which is believed to have been deliberately created by Adonalasium in the distant past) any oddities in the planet's density can be easily explained away.

[king of nowhere]

4 hours ago, hwiles said:

1) I like this theory of a 20 hour orbital period (Rosharan days are 20hrs long fyi). Roshar has 3 moons that appear to rise and set at the same time each night. If you can reconcile this phenomenon with the theory you'll have a good start to changing minds from the conventional wisdom in the community that the moons exist at Lagrange points and Roshar has a 20 hr rotational period. Note first that Roshar has no axial tilt or precession.

 

The orbit of the moons was discussed in a thread a long time ago. The best explanation was that they were in highly elliptical orbits, with periods of 20 hours, and going in the opposite direction of the planet's rotation. that way, from the point of view of those on the planet, they would rise and set twice each day; in the night, they would streak over the continent very fast, because in an elliptical orbit a body moves faster when it is closer to the planet; therefore, the moons could all rise and set in a matter of hours. During the day, the light of the sun would make them invisible instead.

The moons could be at lagrange points of each other, but either way they are fairly small, and the reciprocal gravitation is weak. While such a configuration would be unstable over astronomical time scales, it could very well be stable for tens of millions of years.

[+hwiles]

@king of nowhere

Thanks for the alternate explanation, I hadn't heard it before. The primary issue with the Lagrange point theory as I understand it is that the distance the moons would need to be from the planet would require them to be absurdly bright, and/or unusually large and low density to function as moons in the traditional sense. I believe someone did the math at some point and showed that the moons would have to be radiating light, not just reflecting it in the scenario I proposed, granted, I can't reproduce the calculation offhand. Your method doesn't seem to suffer this flaw.