One important part of the mission is to get access to the manual boom controls. The boom controls should be accessed outside of the space ship. You can go through the airlock.
This is the low-spoiler guide for "Manual boom controls" puzzle in Broken Age. Unlike in normal walkthrough, you get gradual hints on how to solve the puzzle. Click the big button below to see your first hint. If the hint contains a spoiler, you will be warned about it before clicking.