I own two starbound characters: one Avian and one Novakid. I need to know how to make a new world for every character. The latter of the two is my first character, and he already exhausted the resources on every planet in the system. I need to know how to generate a new world for my avian, and, if possible, every character after him.
There's no way to generate a new universe, as each character on your PC will share the same planets. This means any buildings you create can be visited by any character, not just the one that built it. You could also place chests full of things for your other characters to pick up and use for themselves.
Given that there are millions, if not billions, of different planets, all you need to is travel to one you haven't been to before. Every system has a moon where you can collect more than enough fuel to travel anywhere in the universe.
There's no way to make a new universe for each character in the game, but there is a workaround you can use. Amongst the folders where Starbound is installed on your computer, you can find a folder called "universe" and a folder called "player." These folders do exactly what it says on the tin: one saves all your universe data, like all the planets you've visited, and the other stores the data for all of your characters, including also their ships and inventories (but, obviously, not any structures or storage they have on a planet -- that's all in the "universe" folder). Because these folders are separate, you could, for example, delete your "universe" folder, and still keep your characters. If you did this and then launched Starbound it would create a brand-new random universe to replace the delted one, and you'd be able to explore it with your existing characters, and whatever items they had on their ships.
Of course you don't have to delete your current universe. You could move its folder somewhere else, or re-name it, and it'd have the same effect -- the game wouldn't recognize it, and would create a new universe in its place. And later you could restore it to its original name/location and get your old universe back.
By using this method you can have a separate universe for each character. Just switch the universes manually, by swapping around different "universe" folders before you launch the game. It's a bit annoying, but totally doable. Incidentally, given how easy it is to do, I am guessing (though this is just a guess) that such a feature will eventually be added into the game -- things seem to be set up for it. Starbound is still in development, after all.
Since all the characters on your pc share the same universe, stuff you leave on the planet will be available for all your characters going there.
So if your first character exhausted the resources of the base planet, you could go haverst some in another system and then bring them back to the base planet and leave them there (in a chest, for instance) so that your second character can come and get them. This would allow your second character to repair the ship and travel to a different location and realy start over there.