Star Core

The Star core is a quest item in the Fallout 4 add-on Nuka-World.

Characteristics
Star cores (Systemized Telemetry for Automated Robot Control) are redundant multi-purpose control panels consisting of a black circuit board with glowing red lights. They are necessary for taking over the Galactic Zone during the quests Star Control and The Grand Tour, but they can also be picked up during normal exploration. Only 20 of the total 35 star cores are required for the quest. Collecting the full set unlocks the display case which holds the Quantum X-01 Mk.V power armor, provided Nuka-World's power has been restored by completing Power Play or Open Season.

Locations
There are 35 Star cores in total
 * 6 can be found at Vault-Tec: Among the Stars.
 * One in the Arcturus Prime display area guarded by Protectrons, behind a locked door.
 * One in the living room, behind a locked door.
 * One in a highly irradiated room accessible through the living room.
 * Three in the observation center adjacent to the main office, behind a master-locked door.
 * 6 can be found at RobCo Battlezone.
 * Two in the control room overlooking the arena. Behind the locked door in the seating area to the left of the entrance.
 * One in the souvenir shop underneath the seats, on a shelf.
 * One in the tunnels underneath the arena, on a console, guarded by a Sentry Bot.
 * Two in the arena. Trying to leave the area will release three waves of combat robots.
 * 4 can be found at Starlight Interstellar Theater.
 * One in the men's restrooms directly left of the entrance, next to a body inside of a damaged wall section.
 * One through the kitchen to the right of the entrance, outside the backdoor.
 * One in the theater proper, on a console opposite the screen.
 * One in the control room on the upper level.
 * 7 can be found at Nuka-Galaxy.
 * One in the boarding area, behind a door on the right side a short distance down the tracks.
 * From the last room, follow the tracks to a large room with many large planets. On the opposite side are some stairs leading down. The door across this room leads into a corridor, halfway through which another core can be picked up from a console.
 * Down that corridor, and take the elevator to the left. Once in the basement, enter the next room through the opening left of the elevator and pick up the core from the console straight ahead.
 * Past the rocky environment, climb the long set of stairs behind the hidden door. Once back on the ride track, the core can be found on a console up some stairs directly to the left.
 * One in a console at the end of the ride near the disembarkation zone (opposite the mannequin wearing the Nuka-Girl rocketsuit), together with a key.
 * One in the office on the upper floor, accessible through a door that can be opened with the aforementioned key.
 * One in the small control room with some destroyed Protectrons near the office.
 * 5 are scattered around Starport Nuka.
 * One in front of the mainframe, next to a body.
 * One on the upper level above the mainframe, in a locked display case.
 * One on the ground level past the locked gate, next to a body near the sheds.
 * One on a console at the bottom of the long curved ramp known as the Spacewalk.
 * One on the Starport's top floor. This core can only be accessed once power has been restored to the park after completing Power Play or Open Season.
 * 2 are located in other parts of the Galactic Zone.
 * One in the Splashdown control shack directly right of the Nuka-Galaxy entrance.
 * One in the ArcJet G-Force, top of the high staircase.
 * 5 are scattered throughout the whole Nuka-World park.
 * One in the Nuka-Town market, on a table to the left of the general supplies trader.
 * One in the Nuka-Cade, on a weapons workbench in the employee area.
 * One in the Nuka-World junkyard, on the large barn's second level. (Appears to respawn--confirmed. Takes 5 to 7 game days. This allows player access to power armor before turning the Nuka World power on)
 * One next to a body south of Doc Phosphate's Saloon.
 * One in the Nuka-Cola bottling plant, in the Nuka-Cola Quantum area, next to a body.