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[Aklyon]

The rainbow worlds are in two lines, pointing toward the top-right end of the map.

[Haspen]

As far as I remember, Melnorme (unless you call them by the ancient spelling ), have 10 historical items, up to the start of second Ur-Quan civil war.

[Itnetlolor]

Here's how I found all 10 of the Rainbow Worlds with minimal effort (not a bad puzzle, great reward):

Spoiler: Mega spoiler in case anyone else wants to figure this out themselves (click to show/hide)

How I figured it out was I learned of the blue sun twins and Groombridge from the Slylandro first, and the one in Mycon/VUX space from Tanaka later.

Since I also stumbled across the Thraddash one (learned of it from them), I thought for a moment that they were peculiarly setup, and it was even hinted that they were pointing somewhere. A bit of lateral thinking later, I lined up the blue sun with the Thraddash one (I think the Zoq-Fot-Pik told me about that one), and noticed it aimed directly at Groombridge (the big white sun the Slylandro mentioned, but couldn't name, but knew it had an odd name). Did the same thing with Tanaka's coordinates, and did a bit of trial-and-error flying (portal spawner really helped out), and bingo, all 10 rainbow worlds have been discovered, and I was 5000 Credits richer.

Simply put, take the furthest stars (Blue twins and Tanaka), and aim them at Groombridge, and you'll cross 14-16 stars, subtract the 3 (Groombidge cross-point, and the 2 far points), and you have 11-13 stars to explore to find the rainbow worlds. Not all of them are ON the line itself, but close enough.

Your guess was right, they were in a line; actually, 2 lines. Across the northern portion of the map, you'll come across 6 rainbow worlds (#6 being Groombridge, the big white star upper-right), and down the right side towards bottom-center are the last 4.

I had to pat myself on the back for solving it with only the game's clues to assist me.

EDIT;
According to the Ultronomicon, it was normally going to be a sort of eater egg to know the developers or something, but it never completed that far; so basically it's just a really rewarding puzzle.