It seems like every game this these days has a list of sources that helped inspire it. Rad Astra is no exception! It's very thick with 70s and 80s space epics, scifi, and fantasy.
Here are a few notable influences on the setting:
Gamma World (2nd, 3rd, and 4th editions), Star Frontiers
Star Control, Far Cry 3: Blood Dragon
Star Wars and Star Trek seem like the obvious answers but it's the quick-and-dirty, fast-buck coattails riders that actually get the credit.
Starcrash, Battle Beyond the Stars, Message From Space are the big three. Krull, Mad Max, Beastmaster, Masters of the Universe, Flash Gordon, Ice Pirates are a few more.
Captain Power, The Phoenix, Buck Rogers, Space 1999, 70s Battlestar Galactica
Herculoids, Thundarr, Transformers, Centurions, Star Trek
Dr. Strange, Micronauts, Crystar, Alien Legion, Starblazer, Atari Force, Strikeforce Morituri, Marvel's Star Wars and Battlestar Galactica, Man-Wolf, Skull the Slayer, and Conan