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I don't understand. It sounds like they don't have bandwidth problems, only latency problems. But lasers travel at the speed of light just like radios; switching to a laser approach isn't going to reduce latency any.
I took it to mean the laser would be based on the station and so could transmit directly to a ground station cutting out the extra 22,000 mile extra hop to the geosync satellite?
Yes.

I wonder how they expect to be able to use this for regular internet access though, I can't imagine the ISS constantly has line of sight of a terrestrial station, as it's not very high up. Even less so with laser since clouds probably block the signal.

This image of the satelitte orbits makes the comparison easier: https://en.wikipedia.org/wiki/Geostationary_orbit#/media/Fil...

The geosync satellites are very high, 5.6 Earth radius above the Earth surface. (The radius of the orbit is 6.6 Earth radius.) And you have to multiply it by 2 because the signal has to go from the ISS to the satellite and then to Earth.

The ISS is only 0.06 Earth radius above the Earth surface approximately. So in this case, most of the latency will come from horizontal travel (and the latency of the usual congestion in the net).

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ISS flights relatively low, so its visibility from earth is just a few minutes. Also laser is limites by weather.
It's a 92 minute orbit, so if a single station works for say 5 minutes you only need 20 of them for full coverage. However, I don't think the .5 second latency is a significant issue.
I'd really like to know if the ISS wifi has a password.
Some people are just really paranoid.
ESA astronaut Alexander Gertz gave a talk* some month ago. About the wifi he said that it is good quality in the central spine of the ISS but the outlying modules have very bad reception. Living in big metal cans seems to have that effect. Nothing about the password though.

* https://www.youtube.com/watch?v=l8tTRgTqLn8 (german)

I'm imagining alien life nearing earth and then deciding to head to the next inhabited planet once they notice the wifi has a password on it much like you or I might drive a little further down the road for free wifi.
So your critical ISS controls share a network with internet browsing endpoints. Nice!
Talk about one helluva beachhead.