Nadesico Series by Kia Asamiya

An alien armada from Jupiter has amassed enough power to destroy all of Earth's defenses. Earth's final hope lies in the Space Battleship Nadesico, a ship created using recently discovered extraterrestrial technology. Can the Nadesico's rag-tag crew overcome their idiosyncrasies and defeat the alien fleet, or will Earth's last hope be lost?

The hapless crew of the Nadesico is between the powerful Earth Federation forces and the mysterious Jupiterians. They have journeyed out to the planet Jupiter in hopes of rescuing Captain Yurika, but what they don't know is that she may not want to be rescued. How can a lone battleship survive against the amassed power of two planets? Don't miss the grand finale of Nadesico!