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 @60d98082 you don't suppose there could be another explanation? Balloons are a possibility. 
 @9595301e I'm open to any reasonable possibility. Balloons? Yeah maybe, that could work. They wouldn't travel in perfect sine waves (seen from the ground) cos of the wind though.

Railway tracks in the firmament with mobile transmitters? Yeah, why not? You'd have to rotate the firmament every pass though, a lot of engineering to replicate a satellite.

Occam's razor says it's a little box falling forever sideways around a spherical(ish) planet, the math works and it's the simplest explanation. 
 @60d98082 How come satellite dishes are stationery? Shouldn't they also have to follow the moving satellites to some degree? 
 @9595301e Now this I can help you with. Those are satellites in a geostationary orbit. They are big expensive fuckers for TV and shit. They're basically falling in the same speed and direction as the earth is rotating.

I don't track those big boring ones. I track amsats, like AO-27 which scream across the sky in about 8 minutes because they're kinda just chucked into orbit.

https://www.amsat.org/track/index.php