Top wo Nerae! Gunbuster

Synopsis

Noriko and Kazumi arrive at the space fleet led by the space battleship Exelion. The girls get introduced to a hot shot female fighter named Jung Freud. During one of their mech training sessions, Jung spars with Kazumi, and end up in a part of the station where they discover one of the mechs of their enemy. Later on, Noriko and Kazumi are sent to partake in a special mission to investigate an object traveling at near light speed. With the laws of quantum physics and time dilation, the mission that would normally take just a few minutes will span several months. But they discover the object is the Lexion, the ship that Noriko's dad used to command.

(Source: TV.com)