There are already satellite antennas larger than pizza box that fit into a backback.

Question: what sort of antennas would they use for this? A 1/4wave dipole at 10GHz would be _tiny_ (like 8mm or so, right?) - but presumably insufficiently sensitive for a satellite 800 miles up?

I've got a 5.8GHz "patch antenna" for FPV video from a quad copter which claims 12db gain - but I've got no idea what shape it is inside (it's small, maybe 70 or 80mm square, but it's a literal "black box" with an sma connector on it from my perspective).