Uchuu Senkan Gomora

In 2199, the Earth lies under siege by aliens from Gamila. The surface of the planet has become uninhabitable through bombardment by radioactive meteorites, so the surviving humans live underground. Hope arrives with a message from the planet Iscandar. If humans can somehow travel to Iscandar, they might acquire a device that can cleanse the planet of the radioactive damage. So from the husk of the Japanese WWII battleship Yamato, a powerful new spaceship is built that can fight through the Gamilan blockade and reach Iscandar. Time is of the essence, though: within a year, the built-up radiation will have killed everyone on Earth.