Leiji Matsumoto

Meguru and Mayu are two future-wanderers hoping to find the mythical Mirror of Arei that is said to allow all who glimpse it to pass beyond the edge if the universe. Highjacked by renegade android Zero, the trio joins forces when they realise that they are all searching for the same thing.

Be Forever Yamato, set in the year 2202, sees the Black Nebula Empire launch a powerful weapon at Earth, a hyperon bomb which will annihilate humanity if they resist a full-scale invasion. The Yamato, under new captain, Yamanami, travels to the aliens' home galaxy only to discover what appears to be a future Earth--defeated and ruled by the enemy. (Wikipedia)

This time around, earth is in the same predicament as Gamilus was in the first series, and most of the series, Yamato (with several other unnamed ships which are implied to be upon the same task) seeks for another planet for humanity to migrate to. Somewhere deep in space, Desslok is engaging in a war against another superpower, the Bolar Federation, and soon Musumu Kodai and his friends are in the middle of this armed conflict. (imdb)

The Comet Empire approaches, and the Yamato is ready to face them. But this will be the last battle for both sides. (imdb)

A year has passed since the Star Force returned to save the Earth but another danger now approaches from deep space. A gigantic White Comet hurtles toward our galaxy, obliterating everything in its path. But it is no ordinary comet--it is the deadly Comet Empire, conqueror of worlds... and Earth is the next target! Against orders, the Star Force blasts off to investigate, but even if they can get past the flagship Andromeda, they don't yet know the true nature of their new enemy! (myanimelist.net)

The story on Arcadia's mystery, on which the 13th television episode was based.

In the distant future, the war between the human race and the Gamilon has taken its toll on the planet Earth. Constant bombardment of radioactive asteroids has rendered the planet's atmosphere uninhabitable. As a means of relief aid, Queen Starsha of the planet Iscandar offers the Earth Forces a device that can completely neutralize the radiation off the planet. For this task, the space battleship Yamato is launched from the remains of its World War II ancestor on a 148,000 light-year journey. (myanimelist.net)