Personally, I think that the concepts of stargazing explained by the book has a sort of relation with the plot of the book itself. I believe that when Sophie realizes that she is not part of the real world, and is a fantasy of a subreal world, she thinks that by doing an action in her fantastic world she may alter the real world. The very best example is what she did with the boat, actually it happened in the real world and Hilde and her father noticed something happened. This can be related with stargazing, because it can be consider a time of travel just that instead of traveling years through the universe, Sophie tries to travel from her unreal world to the real world of Hilde. In that way, Sophie traveled from her world to Hilde's real world, but not in prescence but may be in spirit or something subreal.
I can relate this with a mirror. Maybe Sophie and Alberto where at the other side of the mirror but Hilde and his father were at the front of the mirror. The actual real world is what is seen when you look up in the front of a mirror, and Sophie tried to shape that mirror so that in the actual real world, something in there would change, like if someone at the other side of the mirror makes a colored circle and then appears in the front side of the mirror, not knowing who draw it, as the example of the boat in the book.