Both of the sites you linked to talk about the payback period for solar panels installed on your roof. Residential solar is inevitably more expensive than a utility scale solar farm, just as a car that I assembled myself (or hired a mechanic to do it) would be far more costly than a mass-produced car of similar quality. A large solar farm does mass-production of energy, so we can expect enormous economies of scale, and therefore a much shorter payback time.
Where do you get the 3-month payback time for nuclear? (I'm ignoring hydro for now.) If we assume a 1 GWe nuclear plant, and the electricity it generates earns $.10 per kwh, then in 3 months the plant will earn (1 GW) * (0.10 $/kwh) * (3 months) = $219 million. That's a far cry from the $billions cost of a nuclear power plant in the US. So where do you get the 3-month payback time?
As for hydro, we are running out of suitable sites. Hydro won't be anywhere near enough for the world's energy needs.
Nuclear may be enough. But the world will have to build roughly 13,000 one-gigawatt plants -- and hope that no Homer Simpsons are in any of them. Gulp.
Solar will be more than enough, even for the energy needs of the far future. As I calculated previously, with a slight correction, the sun pours down thousands of times more power than the world is currently using -- and the sun will last for billions of years. I invite you to check my calculation.
