To take taken planets, you must eliminate all ships related to the government planet to minimize and obliberate strength (strength is protection for the planet). When the strength is negative, the population will start to move away since of "the lack of protection" offered by the government. After that the planet will be unhabitated by anyone, just make sure you get there first before some other people do. I know this since of observing the Lysia goverment. Great game by the way, just one thing, can there be a mute button since I use a machine gun and the sound seems to wreck the speakers.