I would put Claude into a loop and let it make screenshots itself, diffing them against the original screenshot, until it has found the right arrangement at the planets‘ starting position (pixel perfect match).
At that point you may as well just do the work yourself.
I would try giving it a tool to work with projections and process axis by axis to see if it works better in 1D than 2D. I dunno how clever claude is about signal processing though. There's no noise here so... I mean really it's just template matching without rotation and without noise so... But I doubt claude can do or reason about basic image processing.