At the present time, 132 Phd's in astronomy enter the job market each year. When I got by Phd at Harvard in 1982, the rate was about 95 per year. Since then I have noticed several trends in employment that you should be mindful of, but beware of this advice: In astronomy, 10 years is a long time and the overall job market may be very different from what I will now describe when the current crop of undergraduates get their Phds in the first decade of the next century.
In rough terms, 30 percent of all jobs in astronomy are in academic positions such as postdocs, lectureships, assistant professorships and tenured faculty. The second 30 percent is in government positions which usually means you are in government service and have reasonably stable job prospects. the final 40 percent are in various contracting positions in private industry which are usually supported by some government research contract.
The only stable, long term positions are tenured academic positions and government service 'GS' positions at major labs such as JPL, Goddard etc. The government positions are almost completely supported by NASA, with some small number in the Department of Defense. All other positions are inherently unstable. Postdocs last 1 - 2 years, and if you haven't graduated into a more permanent position after your second postdoc, some people may consider you 'damaged goods', making future employment difficult UNLESS you can bring down research grants, then it seems that your inability to secure more permanent employment can be forgiven.
If you are an assistant professor and do not make Tenure, then you can have the option of looking for another assistant professorship elsewhere in an apparently endless series of moves, but eventually by the time you reach your mid 40's, it is expected that you will have secured a permanent position somewhere. I know of no 45 year old assistant professors in astronomy. Academic positions are highly sought after, with typically 100 to 200 applications for a single assistant professorship being fairly common these days. There are a LOT of 35 year old astronomers still looking for a chance at joining the academic world.
Many astronomers out of graduate school end up working at a government lab with the hope that their postdoc will evolve into either a government service 'career' position, or a chance at an academic position and tenure. As we all know, the government is downsizing, and most labs open to astronomers seem to have some kind of hiring freeze in place so that government positions only become available when other astronomers retire, or move to other positions elsewhere.
A rapidly growing pool of astronomers live entirely on contracts and work in private industry. Many companies such as Hughes, ARC, SAIC etc have astronomers on their staff who do research, and are paid by NASA contracts that their companies have won, often with the help of the astronomers in writing the winning proposal. This will continue to be a viable long term career option only so long as NASA and DOD continue to make these contracts available for companies to bid on. As you know, NASA is going through a weight loss phase and is greatly trimming back many of its research programs. The Big programs which used to employ dozens of contract astronomers, are being replaced by smaller programs that only support a dozen of the most highly qualified, and specialized, astronomers. This trend will continue well into the next century so far as the present indicators seem to be pointing. By the way, where does NASA get the money for these contract positions? From approved NASA missions developed in collaboration with the astronomers in government service positions and in the tenured academic positions! Contract astronomers, and assistant professors are almost never involved in proposing new NASA missions.
Contract astronomers, therefore, exist almost solely at the discression of other astronomers who have tenure or government service positions that are stable. This has recently caused considerable stress within the profession between the 'haves' and the 'have-not' astronomers.
I think that the long term prognosis for a career in astronomy is not good, at least until some of the Baby Boomers retire. They are, however, a healthy bunch so far, and there is the dreadful prospect, born out by some disturbing trends, that when they do retire, their positions also disappear with them as part of government/academic downsizing.
If I were an undergraduate today, I would be a hell of a lot more mercenary about my future than I was back in the early 1970's when we had just landed on the Moon and people were talking about colonies on Mars. Sure there are astronomers out there discovering new planets, but you will not be one of them! Unless you are at the top of your undergraduate class in physics, and have linked up with an AGGRESSIVE mentor in astronomy, the odds for finally getting a long term career in astronomy are rather slim. Keep in mind that, 20 years ago a postdoc did not have to compete with fellow astronomers that had 10 - 15 more years research experience behind them. Now this is common place. Also, it is almost a certainty that you will not get a tenured position unless you can demonstrate the ability to bring in SERIOUS sums of grant money. Since very few postdoc positions let you be a Principle Investigator on such a grant, you have a real problem to face in finding support.
There are rumors afoot that in another few years, some NASA facilities may move towards not allowing contract astronomers to submit grant proposals to NASA as independent Principle Investigators. This means you can ONLY do the research that your government astronomer lets you do under his/her grant. There is also even scarier gossip that at some government installations, NO contract astronomers will be employed. All of the work on new missions and NASA grants will be the exclusive domain of government 'civil service' astronomers.
The first of these is demoralizing to the literally thousands of professional astronomers in this country who work with government astronomers. Henceforth, your career will be circumscribed by what the government astronomers permit you to do. The second of these developments spells the out right end to a career in astronomy, because there would then be no contracts for companies to go after in astronomy, and no need to hire astronomers.
As an undergraduate, you MUST be aware of these gloomy prospects. You need advice from someone that has recently gone through TODAYS job market. Don't ask a 45-50 year old tenured professor in astronomy to tell you the story. They got their position in a way that, statistically speaking, you probably NEVER will experience after you get your Phd.
Good luck to you, and to all us other folks who are still trying to make our dreams come true, even at the age of 40!