The year is 2203, not long after the Bolar Federation was defeated by Desslok's Galman-Gamilon Empire. A subspace dimensional dislocation has caused a distant Red Galaxy to be relocated in a collision course with the Milky Way. Stars and planets collide, making a wreck of the Galman-Gamilon homeworld. The Star Force is dispatched to investigate. They reach Galmania to find Desslok's palace in ruins. 
As they pay their respects, tossing white roses down to the surface of the planet, a huge red planet crashes into Galmania, forcing to StarForce to escape with an immediate and uncalculated warp. 
(Source: AniDB) 
Note: The 35mm cut for the film has a runtime of 152 minutes. While the 70mm extended cut is 163 minutes long and once held the record for the longest theatrical animated film in the world for 36 years.

A stray missile from a confrontation between the Galman empire and the Bolar Federation crashes into the sun, turning it into a time bomb of radiation. The Star Force once again sets off into space, this time on a quest to look for a new world for the human race.
 
(Source: Anime News Network)

A crisis is approaching Earth with the expansion of a moving black hole, in the year 2220. A plan is devised to move over 300-million people from Earth. When the latest transportation fleet is attacked, Space Battleship Yamato comes to its defense, the ship is now commanded by Susumu Kodai, also aboard is daughter Miyuki, child of Susumu and Yuki.

(Source: FUNimation) 

Note: The Director's Cut is 123 minutes and contains a few different scenes as well as an alternative ending.

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