It's OK, but it's not "vastly" superior down here on Earth. Sun's a fusion reactor we don't need to build.

In space… again, there's uses for nuclear, but it's not a slam-dunk for everything. Space is a very good insulator, so there's a limit how hot and for how long you can run your power source — for a lot of scenarios, being closer to the sun than about Mars means that even with PV, too much heat is more of a problem than too little.

(On Mars itself, you probably do want nuclear anyway: global dust storms happen and can last ages, so you can't just geographically distribute solar farms, but on Deimos and Phobos you should just use PV).

Depends on your definition of vastly, and superior but:

    Uranium-235 (fission) ~80,000,000 MJ/kg 1×
    Coal ~24 MJ/kg ~3.3 million× less
    Oil ~42 MJ/kg ~1.9 million× less
    Natural Gas (CH₄) ~55 MJ/kg ~1.45 million× less

1. The part I was responding to was in comparison "to every other form of green energy". None of those other things you list are green energy, and your numbers are incorrect for space purposes anyway as they don't include the mass of the oxygen.

2. Energy-density-vs-mass is relevant for the rocket equation when you burn it as a fuel (and, optionally, use as reaction mass), but not vs. PV where you don't burn it and lose it.

e.g. ion drives, magnetic sails of various kinds, launch loops/space elevators and similar, space stations/bases/almost all planetary industry (which can be PV powered), nor solar sails which directly use the momentum of light (usually the sun's nearly isotropic emission, but in a grand space empire anywhere from here to K2 all bar the entropy losses can be pumped into a single direction by lasers).

How is nuclear energy superior to solar energy?

Within the context of space, solar doesn't work to well when you move away from earth. By mars, you're already down almost 30%!

You could use some sort of beamed power/powersat eventually at those distances (using a sending station from a place with a lot of solar power, like Mercury) but that's signifficant infrastructure and ways of right now.

With the difficulties of cooling things in space, satellites sending/absorbing massive amounts of energy seems like a hard problem.

Solar energy is nuclear energy! ;-)

But it is used, recycled. We only want pristine first order energy sources.