What's the context in the "Hail" part of Hail Mary?

I was just thinking, that's a strange greeting. Didn't people back then usually say "hail" in the context of "Hail Caesar"? And apparently Mary thought that was a strange greeting too, even stranger than the fact that it was an Angel who greeted her thus. So, according to the Catholic Church, does Hail (or Ave) in the sense that Gabriel uses it in Luke, actually have anything to do with addressing royalty? Has it ever been posited that the Archangel Gabriel would use that terminology only in reference to the Holy Mother of God?