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I would have thought that if the satellite gets stuck up a bit higher, and thus travels faster to maintain position, this would allow it to still be geostationary.

the geostationary orbit height

I've been trying to get my head round the idea that all geostationary orbits have to be at the one possible altitude (~35000 km). I would have thought that if the satellite gets stuck up a bit higher, and thus travels faster to maintain position, this would allow it to still be geostationary. I'd assumed that the height of the orbit would be determined by the mass of the satellite, but apparently the geostationary orbit height is independent of mass. Can someone explain this to me in words - the equations that I've been looking at online are leaving me with a headache.

What about the Lagrange points between the moon and earth?

compared to the 180 satellite slots at 2 degrees separation

And how "full" is the geosynchronous orbit at the moment?