So... is Rocket Girls finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: May 18, 2007
Manga finished: August 25, 2007
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Yukari Morita, a high school girl, journeys to the Solomon Islands in search of her missing father.
There, she encounters the Solomon Space Association (SSA), a group striving to launch a rocket into space.
The SSA's director, Nasuda, realizes Yukari's small size makes her a perfect candidate for a previously built, less powerful rocket.
He proposes a deal: Yukari becomes their astronaut, and the SSA will aid in her search for her father.
The story follows Yukari as she considers this extraordinary opportunity and embarks on a potential journey into space.