For the next eclipse I’m planning around, one map shows a narrow path of totality while nearby cities are marked for a partial eclipse. I understand that the Moon’s shadow moves across Earth, but I’m not clear on how the viewing line is calculated or why a small change in location can make such a big difference.
How do astronomers work out the eclipse visibility path, and which details—such as the observer’s location or the Moon’s apparent size—determine whether a city gets totality or only a partial view?