"Nuclear batteries" I assume means RTGs? Those don't give you much more power than solar cells. They're great for missions to Jupiter and beyond, and last a really long time. But they aren't powerhouses. An RTG like NASA's might give you several hundred watts.
Another non-nuclear space option is fuel cells. These don't last. They Space Shuttle, for example, can't operate for more than two to three weeks because of limitations of it's fuel cells. Even if you're sucking power from the station, the cells _leak_. There advantages make them _great_ for the brief jaunts to LEO that the Shuttle is designed for.
There are batteries, which just aren't energy dense. They give too little power for their weight, and you're better off with solar.
Fusion and combustion are not relevant. (Even if fusion was made to work, it scales _up_ very well but we need something that scales _down_.)
(All this, by the way, is one reason I don't see Apollo's sample return being faked robotically. Electricity is a bitch to come by in space. Sometimes the height of technology really is a man with a shovel.)
Which brings us to nuclear fission. Technically we're not talking about a naval reactor, it's just an example. You need an orbital nuclear reactor. The Soviets did this a few times, and NASA had a project going at recently as the late 90s.
Nuclear fission is the only power source in the foreseeable future that will suffice.
And you know NASA can't do that right? I mean the Navy can send nuclear powered battleships with nuclear-tipped ballistic missiles (true slaughterfest devices) but if NASA tried to use a tiny bit of plutonium to study Saturn, everyone shits a brick.