Career Opportunities in Astronomy
There are plenty of career opportunities for astronomy majors.
If you're talented, commit yourself strongly, and work hard, you may end up as a professional astronomer. Many of these are astronomy professors; others work as researchers for NASA or other research organizations. Virtually everyone in such a position has a Ph.D. in astronomy or physics, so to be a professional you'd need to go to graduate school. The number of new astronomy Ph.D.s generally outstrips the number of permanent jobs, so not everyone who wants to be an astronomer gets to be one. Nonetheless, the situation isn't as bad as people used to think it would be, and there are always jobs for the very best people. And even if you don't `make the cut' somewhere along the way, you still get to work in astronomy for a while -- after the first year or two, graduate school is more like an apprentice scientist program rather than an academic grind, and it can be lots of fun. In addition, nearly all graduate programs pay modest stipends, so unlike your friends in (say) medical school, you don't need to accumulate heavy debts.
There are some jobs which require only an undergraduate degree in astronomy, but they are rather more limited. Observatories often seek support personnel with astronomy majors, but without advanced degrees. The NASA centers (such as the Space Telescope Science Institute) also employ bachelor's degree holders in support roles. It's fairly common for astronomy majors to get one of these jobs and take a breather for a while as they evaluate their career plans; many go on to graduate school.
But even if you don't decide to stay in astronomy, there's plenty you can do. Given the amount of science you will take anyway, it's a fairly simple matter to (for example) fulfill pre-medical requirements and head for medical school. Astronomers need to understand complicated arguments from principle, which is an excellent background for the study of law. With an astronomy background, you would most likely find the much-feared "quantitative" parts of a business school curriculum to be relatively straightforward. To a prospective employer, an astronomy major will stand out from the great herd of history, government, and English majors who troop through their interviews. Dartmouth isn't a place which encourages narrow, pre-professional training, but the talents and habits of mind you create studying astronomy are useful in a wide range of endeavors.
You may want to check out further material from the American Astronomical Society.