Sabrina gave some excellent reasons as to why we should study this star at the center of our solar system. You can ask this question of almost any scientific discipline: why do it? Humans have a basic drive to understand our environment, to explore new places, to learn new things. Doing scientific research as a scientist is about exploring something that no one in human history fully understands, it is about creating new knowledge for humankind! In order to do that you have to be comfortable with the fact that no one will be able to tell you if this is the "right answer" or not, because no one knows! You also have to be open to being proven wrong. We make scientific discoveries and progress to the best of our ability, based on current technologies and understandings. But a day, a year, or 100 years in the future someone else might come along and disprove what you figured out. This is a good thing, and this cycle is what leads to progress.
I love this little illustrated guide (
http://matt.might.net/art...school-in-pictures/) which is specifically about getting a PhD, but I think it is applicable to any scientist all throughout their career.