brucephy said:
1) why do we study in astrophysics and what are our targets and what we want to get?
It depends on who you are. If you're a politician, astronomy is motivated by public relations. If you're a physicist, it's a means of testing your models. If you're an astronomer, then the motivation is usually just the pursuit of knowledge.
Most people agree that there aren't currently many practical applications to astronomy, so you need to decide whether or not that's important to you before entering the field.
2) why astrophysics is divided in theoretical and observatable? what is the important for them respectively?
This is sort of an old division, but it's still partially meaningful. Traditionally, the observers collected data and made rather simple, general statements about it. Edwin Hubble is the classic observer because he's famous for discovering "Hubble's Law", a simple linear fit to the velocity-distance relationship for galaxies, by observing nearby galaxies with a powerful telescope. A theorist, however, takes these results and tries to explain them physically. In the case of "Hubble's Law", the relationship was later described theoretically by Einstein's general theory of relativity.
In modern astronomy, there are probably two more categories: instrumentalist and data analyst. Instrumentalists are responsible for building and designing the telescopes/satellites/detectors that we use to observe astronomical objects. They're sort of specialized engineers. Data analysts take pre-observed data sets (usually large ones), and run a vast array of analysis techniques to pull as much information out as possible. They're sort of specialized statisticians.
The best astronomers, of course, do all of the things I mentioned above, but you can make a living by settling into one of those niches.
