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).

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.

At that point you may as well just do the work yourself.