Okay, so in another life I was a meteorology major. Had to quit two years in because I love math, but it's an unrequited love. I failed calc II twice.
But I do remember some things, and want to use what I remember to see what a typical sounding of Yih's atmosphere looks like. This is an important question that the research monks have to solve. Before they can get to space they have to get in the air.
Yih has the following relevant stats (relative to Earth)
mass: 0.90
radius: 1.01
surface gravity: 0.88
Or in absolute terms:
Mass: 5.37×10^24 kilograms Radius: 6.442×10^6 meters Area: 5.215×10^14 square meters Gravity: 8.63 meters per second squared
Finding the surface pressure is relatively simple. Let's start by assuming the atmosphere of Yih has the same total mass as Earth's atmosphere, 5.1441×10^18 kilograms (side note, WolframAlpha is your friend when doing stuff like this). Since pressure is force divided by area, and since force is mass times acceleration (of gravity in this case), we can get the surface pressure by multiplying the mass of the atmosphere by surface gravity and dividing by total surface area of the planet. So we get the following pressure:
85100 pascals (0.8399 atmospheres)
That's about the same as the station pressure in Denver.
Now that we have a surface pressure, we can try to find out how it changes with height. For reference the pressure at a typical jet cruising altitude is 200 hectopascals.
Per Wikipedia, the change in pressure with height, geopotential height, is the negative of density times gravity.
dP/dh = -rho*g
And the ideal gas law is
P = rhoRT, where R is a constant specific to dry air.
We can rearrange the ideal gas law to solve for density, and substitute it for density in the equation for geopotential height to arrive at
dP/dh = -Pg/(RT)
And that's kinda where I hit a wall. I'm pretty sure this is a differential equation, and here be dragons as far as my brain is concerned.