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Astronomy is generally done by those holding a doctorate degree and there aren't that many positions out there. However, not to be discouraging, even if you have a Ph.D. getting a full time faculty position at a university is a very competitive and long process.
Some planetariums hire people with graduate Astronomy degrees (like an M.Sc. or Ph.D.) to help run their public education programs.
Many companies might hire someone with an Astronomy degree for other non-astronomy kinds of positions, simply because they have a solid science background (e.g. oil and gas industry, mining, any industry that has the need for non-specialists positions that require a science degree). My guess would be that this is where most B.Sc. and M.Sc. Astronomy grads might end up.
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