Roy Smith wrote:

The Sirius Satellite Radio (www.sirius.com) says:

"our three state-of-the-art satellites that rotate in figure eight,
geo-synchronous orbits around the earth"

I know what a geo synchronous orbit is, but what's the "figure eight"
part all about?

You're probably thinking of geostationary orbits, where the satellite
orbits in the equatorial plane at exactly the right distance, so that it
appears to be stationary from the point of view of an observer on the
ground. Geosynchronous orbits, though, simply mean an orbit which has a
period equal to the rotation period of the Earth, e.g., 24 hours,
although often the latter is used colloquially to mean the former.

An elliptical, inclined geosynchronous orbit can indeed have the "figure
eight" properties you describe; every 24 hours it will return to the
same point in the sky relative to an observer on the ground, but in the
meantime it can meander.

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