Later on though, as with OTL Juno, solar panel technology advances may very well allow missions as far as Jupiter. There have even been serious-ish proposals out to Uranus on solar cells, but those would need advanced (ie., expensive and risky) technology.
Looked it up. With 8-9 w/m2 at Jupiter's distance from the Sun, they need 60 m2 to power all the systems using it's solar cell tech - indicating 10-12% efficiency of the cells, not including degredation of said cells due to Jupiter's magnetic fields and radiation belts.
For Saturn, you'd need 4x the solar cell area or solar cell efficiency for the same amount of power. Possible, but by that point, RTG could well turn out to be more mass-efficient than solar cells.
So while this makes Jupiter missions an option, for anything further out, they will need to work with another space agency.
Also, if they use SEP, they could do better than 2597. Just saying...
As for Solar Electric Propulsion (SEP). IIRC, with Smart 1, they've already proven that it works OTL, and it should be viable for certain missions. But they have their own problem. While extremely efficient - about 5,000s Isp - they are just as extremely power-hungry, requiring power loads in the region of Megawatts and more to provide substantial thrust.
Although, in space, they can be operated for days and weeks on end to accumilate a large delta-v for a mission. So you could use it up to the asteroid belt to build up some serious velocity, but after that, you won't be able to provide enough power for it and it becomes deadweight IMHO.
Still plenty of ways to make use of it. And it's more vastly more controversial cousin, Nuclear Electric Propulsion (NEP), is something to look into - though adoption of such a system is next to impossible.