The Collapsed Star Core is a resource that occasionally drops from around LvL23-Bosses like Tech-Hunters and Guardians.
With Patch 15.3 (May 4th 2015) the drop rate of "star materials" was increased by 10%.
Collapsed Star Core is needed to build (and to upgrade) StarGates which will transport your character to other planets. These planets already have a set return-stargate that you can see on your compass when you're there.
Recipe for Stargate Low-Level Planets:Edit
|Collapsed Star Core||1|
Recipe for Stargate Mid-Level Planets:Edit
|Collapsed Star Core||2|