Peripheral vision accuracy when focusing on a moving target

I was listening to an audiobook, today, at my computer, and a command-prompt was before me. As I sometimes do, I typed various characters while I listened. Then I started holding keys down and watching. I noticed that when I focused on the cursor/caret as it moved, then the details of all the letters on the screen were blurred from my peripheral vision, but if I started with a stationary one and followed pre-existing ones, even if they were close to the cursor/caret as it moved (creating new ones), they looked clearly visible in my peripheral vision, of course.

Anyway, I don't know if this has been studied, but it sounds like something people would study.