Funding opportunities for an independent researcher
Do you mean being paid a salary to be an (independent) astronomer, or having telescope time, travel, etc. funded so you can do research?
I completed a PhD in astronomy but left when accepting a postdoc position would have meant moving my family across the country and the 'day job' is now in IT. However, I'm still an active research astronomer - this year I had two VLT proposals accepted as a PI (roughly 120k Euros in telescope time), and was co-investigator on four more accepted ESO proposals. I'll publish roughly a dozen papers (including four as first author, three as second), will speak at conferences and last year had an ESO press release on my work which was picked up worldwide. So it's perfectly possible to continue in top-level research without a faculty position - plus I have the advantage of not teaching :)
I apply for telescope time through the usual routes, e.g.
- http://www.eso.org/sci/observing/phase1/proposalsopen.html
- http://www.stsci.edu/hst/proposing
and many sources exist for conference fees, travel, expenses, etc., e.g. amongst others I use
- http://www.ras.org.uk/awards-and-grants/grants-for-studies
- http://royalsociety.org/grants/
(I'm UK-based, which explains those choices.) But if you want something to pay a salary as well then I think options are much more limited. There are a few specialist postdoc support programmes, e.g. for returning to the subject following a career break, but options for ongoing funding are very limited - and would be very competitive. I know a few people who make a living writing for astronomy magazines, etc. alongside their research, but the majority of 'non-faculty' researchers like me that I know of have a traditional 'day job' that pays the bills and is flexible enough to allow high-level research as well.
EDIT: One other avenue of investigation are fellowships from the likes of the Leverhume trust (http://www.leverhulme.ac.uk/funding/ECF/ECF.cfm or http://www.leverhulme.ac.uk/funding/RF/RF.cfm). These are linked to the traditional PhD -> postdoc -> Faculty route, but are somewhat different to the traditional postdoc position. Royal Society fellowships also provide five- or ten-year salary funding (http://royalsociety.org/grants/schemes/university-research/). Again, these are UK options and I'm unsure where you are located, but these would be options I'd very seriously consider if I was ever going to try to return full-time to academic life.
http://www.cccblog.org/2011/07/13/an-alternative-to-science-funding/#more-3846
As research budgets tighten at universities and federal financing agencies, a new crop of Web-savvy scientists is hoping the wisdom — and generosity — of the crowds will come to the rescue. While nonprofit science organizations and medical research centers commonly seek donations from the public, Dr. [Jennifer] Calkins, an adjunct professor of biology at Evergreen State College in Olympia, Wash., and Dr. [Jennifer] Gee may have been the first professional scientists to use a generic “crowd funding” Web site to underwrite basic research.
In May 2010, neither had the principal investigator status required to apply through their institutions for a National Science Foundation grant. But they were eager to begin collecting data about the behavior, appearance, distribution, habitat selection and phylogenic position of the least-studied quail species in the Callipepla genus.
Dr. Calkins, who has published research papers and poetry, turned to the community of artists and microphilanthropists at Kickstarter.com. Her plea to potential backers on the site: “By contributing to this project you will support a study of this little known species as we examine its behavior and evolution in its natural habitat, a space encroached upon by both urban sprawl and tension surrounding narcotics trafficking.” Web sites like Kickstarter, IndieGoGo and RocketHub are an increasingly popular way to bankroll creative projects — usually in film, music and visual arts. It is not very likely that anyone imagined they would be used to finance scientific research. And it is unclear what problems this odd pairing might beget.