Jupiter's horizon

[ffutures]

In The Struggle For Empire, the source book for FF XII, Jupiter, Saturn, Uranus and Neptune are earth-like and habitable, just very big (but don't have crushingly high gravity). So I've started to think about what things would be like there, ignoring the sheer implausibility of this idea and assuming Earth-normal temperature, pressure, atmosphere etc.

One of the questions to cross my mind is if it would be possible to see things coming over the horizon. Which leads to the question "how far away is the horizon?" Fortunately someone has already worked that one out:
http://vastfrontier.blogspot.com/2010/07/horizon-distance.html

So the next question is how far it is theoretically possible to see through the atmosphere at sea level pressure? The answer seems to be more than far enough - the definitive source for this is probably Ringworld, which has visibility in the thousands of kilometers, and it seems plausible given that we can see stars from the bottom of our atmosphere. Anyone able to confirm this? And what would refraction effects do? Extend the distance?

While looking up Ringworld I found this rather nice animation

and there appear to be dozens of others on Youtube, Nifty!