Main component for Galactic jewels is Frozen Crystal Compound. Those drop from Cascading Molokh, Novictum Blight and Reprogrammed Mezzorash in Alappaa. While all the Compounds looks almost the same there are really several types that drop. Easiest way to check which one dropped is to try and create jewel (either with shift+t, or in regards to skills needed). Unfortunatly not all correct Arul gems made it in-game.
Galactic Jewel of the Jagged Landscape taken as example
This step requires 1750 Chemistry skill.
Which Galactic jewel you'll create depends on database number of Frozen Crystal Compound. There are several ways to check that : shift+t (you'll see product's name), give tell to helpbot with compound and check Helpbot's store or show compound to someone logged in chat with AORC.