One of those values is "ISS total mass." Is that calculated using launch/deorbit weights or is there some kind of sensor on board that can measure that? I figure if you did a specific type of burn you could calculate the weight from that, but I'm wondering if they have something more clever.
It's just an estimate and isn't that accurate. Yes, the closest you can get is orbit determination before and after the reboosts, and acceleration data.
Not an expert but I think its possible, the problem is that the gyroscope alone wouldn't be sufficient. When the gyro rotates once, the massive spacecraft will obviously have rotated exactly once relative to the gyroscope. However if you could track the space station's rotation relative to an independend stationary observer in space (lets say an array of pulsar data), then you could count the amount of turns of both the gyro and the spacestation relative to the background of space. Then the amount of turns of the gyro times the mass of the gyro would give you the mass of the space station minus the independend floating objects. Meaning you'll need to add the mass of the gyro itself as well.
Please correct me if i'm missing something obvious. This should work right?
Not its mass directly, but you can use it to calculate the moment of inertia. Move the CMGs a fixed angle and looking at the responding change in rate of the ISS. Mass can be determined from maneuvers when you fire the thrusters. Assuming you know the force from the thrusters very well (this has its own errors) you can look at the acceleration from the orbit determination before and after the thruster burns and back out the mass.
In a uniform gravitational field, it isn't. On the earth's surface, acceleration due to gravity is 9.8 m/s^2, independent of the mass of the falling object. See Galileo's Leaning Tower of Pisa experiment.
The field is not uniform though. So in theory, if you know the orbit and firld exactly, you can calculate it.
In the present case, I guess the precision with which one knows the orbit and other stuff (like the exact gravitational fiel of the earth) doesn't work out.
If you've never tried it, I highly recommend playing Kerbel Space Program[1] (it works on Linux, Mac, and Windows!).
That game taught me so much about orbital mechanics, which led to rabbit holes of textbooks and videos[2].
The first big lesson KSP taught me was: why, when launching a rocket, you don't just go straight up but, instead, have to lean over pretty aggressively.
