There's a book called Longitude by Dava Sobel which is about how the problem of determining longitude was solved. The Galiilean moons approach is discussed in the book.

I'm busy reading the book so this article caught my eye. It's been really good so far.

I had heard of this, but never understood how it works until now.

Intuitively it makes sense that if you have an accurate universal clock, you can check your longitude by measuring at what time the sun rises/sets (i.e if you fly east 3 time zones, the sun will set 3 hours earlier).

It turns out that Jupiter’s moons can be used as an accurate universal clock, by noting the timing of various eclipses.