What I think is a significant question occurred to me tonight while watching Star Wars movies with my girlfriend. We went to Episode 7 recently, and she was a fan of episodes 4-6 but thought very little of 1-3 and had only seen little pieces of them and thought they were stupid, so I showed her "Revenge of the Sith" because I consider it to be an important chapter in the story since it features Anakin's transformation to Darth Vader, the birth of Luke and Leia, etc. In that movie we see Anakin choke his wife Padme (who he believes to be pregnant with just one baby), and then be told later by Palpatine in a lie that that act killed her when in truth she lived on to give birth to two babies (Luke & Leia) before dying. Years later in Empire Strikes Back we see Vader reveal to Luke that he is his father, and then in Return of the Jedi we see Vader read Luke's mind and learn that he also has a daughter, Luke's twin sister. Ok, we've all seen those things.

Here are my questions, which were brought up by my girlfriend and for which I had to admit I had no good answer. How did Vader know that Luke was his son if he believed that Padme died before ever giving birth? Did he just sense it after engaging Luke in aerial combat in the first Death Star battle? And if that's the case, shouldn't he have also sensed that Leia was his daughter when he had her prisoner and spoke to her face to face several times in A New Hope? I have the impression that even in Return of the Jedi when he sensed that he had a daughter he still didn't understand that it was Leia.

Any thoughts, observations, or debates are welcome.