[Out_of_Characte]

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?