Uh... the A3000 is an APS-C crop body, not sure why a lens being crop should be an issue with it. And if you wanted to go full frame, then why bother with a $400 e-mount dSLR-lookalike?
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[sorry].
Maybe you did make a mistake. While the A3000 looks like a dSLR, it isn't one, and lenses are the other half of your camera, so when you make the leap from a fixed-lens camera to an interchangeable lens camera
system, the selection of lenses is going to be the main sticking point for the smaller systems. While it's been steadily growing, the NEX/e-mount system is still relatively small.
However. For the astronomy images, if you were planning on using a telescope, not a camera lens, chances are good the A3000 won't be getting in your way, since you just have to adapt it to the telescope, not find a supertele. And for wide-to-normal shooting (landscapes, bug/flower macros, portraits, street), chances are good the e-mount lens selection and serve your needs pretty well. It's only the fast-action/supertele stuff (sports, wildlife, chasing rugrats indoors) where the system (both A-mount and E-mount) are liable to let you down, and you might wish you'd gone with one of the Big Two instead.
Frankly, I shoot both dSLR and mirrorless because of this divide. I have my Canon gear for birding, lighting, and "serious" [full-frame] shooting, and my micro four-thirds gear for everything else.
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My prosumer Canon gear handles like a dream. I swear a lot at my consumer mft camera, but I carrry it most of the time, because it's small and light, which makes it convenient; someday I may upgrade to a prosumer body to reduce the swearing. The Canon gear weighs about two to four times as much, depending on what I'm loading up for, and even loaded up with five different lenses, my mft bag comes in under 5 lbs.
Both types of systems have their advantages and disadvantages. How much do you have to have really long lenses? How fast-moving is the subject matter you're shooting? And are you sure a $200 55-200 can't serve your needs?