This is a simple image made in Blender showing a ringed planet during the summer solstice. I have stats for the yinrih's homeworld of Yih, density, radius, etc. I used the equation found on the Wikipedia article for Roche limit to determine the dimensions of the ring for this image using the following numbers.
Radius of Yih: 6.44e6 m Density of Yih: 4810 kg/m^3 Density of object to be ringified: 3344 kg/m^3 (I used Earth's moon)
Plugging and chugging gives us a Roche limit of 9.16e6 meters, or 1.42 Yih radii.
I assumed the Roche limit itself represented the outer radius of the ring, and that the inner radius was more or less arbitrary, which I set to about 1.14 radii.
This gives us a ring that's a lot closer than I was imagining, which presents some lore problems. The ring in the image above would look like two glowing horns if one were on the night side in the mid-latitudes and not, as I envision, a partially eclipsed but still obvious arch shape.
It's already well established that the Bright Way uses a golden arch in lieu of a halo in religious art thanks to the ring, and the ring is popularly conceived of as a contiguous arch for at least part of the year, giving rise to phrases such as "chasing the end of the ring" meaning to go on a fool's errand.
If I wanted to keep using the assumptions listed earlier, the only way to change the outer radius of the ring is to increase the density of the doomed celestial body.
I can, of course, ignore this and just make it whatever I want. I'm already ignoring how ephemeral rings are on a geologic time scale. And I could be making mistakes even within the parameters I mentioned because I'm running on 5 hours of sleep 🤷♂️.
I wonder if making the ring faster would help get it further away from Yih's surface. Or would that require making the planet spin faster and messing up the day/night cycle⸮
Making Yih denser sounds like a good solution if you don't mind whatever that would do to the difficulty of rocket launches (i don't remember what propulsion systems yinrih use or how similar they are to modern Earth technology), or to the strength of gravity that yinrih are used to (which would probably make any microgravity problems worse for them).
Or i think you could get a similar effect by making the ring less dense so it's not held so close to Yih. Luna is largely silica and alumina, the former of which is heavier than water and the latter of which is pretty light if i'm understanding Wikipedia right. And i'm sure there are also other compounds you could use that are light enough and have the right colors, toxicity, reactivity, etc.
Could you make the ring narrower and brighter by saying it's made of shinier stuff than moon rock? That might help give it the golden arch look without it having to be so close to the surface.
I hadn't thought of the ring's relative rotational speed, and had assumed the material would have zero ground speed, but that doesn't make sense as that won't provide enough centrifugal force to keep the debris in orbit. This may be another thing I choose to ignore.
After some sleep I realized that having the ring so close shouldn't prevent it from taking on the iconic arch shape in culture. The ring should be faintly visible on summer days with no shadow. The shadow would appear on one side and move across the ring through the course of the night, so the full shape of the ring would be recognizable.
Also, Commonthroat now as a word
rMrmg/chuff, long low strong grunt; chuff, short low strong grunt, short low weak growl/ which means both the shadow cast on the ring by Yih as well as the hand of a clock or the dial of a gauge.When visible during the summer, the shadow would move from right to left counterclockwise across the ring when viewed from the historically more populous southern hemisphere, which reinforces the right to left and counterclockwise directions of screws and analog gauges prompted by the yinrih being predominantly left handed and writing from right to left. This ironically makes "counterclockwise" for humans "clockwise" for yinrih.
Back to the ring's size, the roche limit is the outer radius, and with more research I believe the inner radius should be the edge of Yih's atmosphere. Again, I'm ignoring how brief rings tend to live (I read somewhere they tend to last around 100 thousand years, with Saturn's rings lasting longer thanks to its moons). Culturally, the lower bound of the ring represents the edge of space, and it's the presence of the ring that makes spaceflight so difficult and dangerous at first. But the yinrih's scientific community is also a religion with a strong martyrdom culture. I think of the pre space age Bright Way like OceanGate. Stubborn persistence and zeal win out in the end, though not without a shockingly high body count.