I didn't care for the doppler figures the systems guys eyeballed off some graph, so I incorporated some orbital mechanics into my model, instead. I made the Earth a perfect sphere, ripped off the atmosphere, and stopped its rotation to make things easier, but the numbers should still be good to within 10%.
It turns out that low-earth-orbit satellites are spooky. They're visible for only about 12 minutes at a time, and spend half of that flying straight for your head at over 6 km/s. Then they miss you by a hairs-breadth, and scoot off in the other direction, laughing softly.
But the real bitch is the degree to which this movement distorts a modulated signal in a fashion that resembles time dilation. It's not the carrier frequency drift that's the problem, it's the rapidly changing data rate. Modems don't like that.
The speed of light isn't fast enough. This is a third-rate universe.