That's still $1000 body, $1000 glass, $500 tripod, give or take. So far from cheap if you're starting from scratch. But if you already have a body and some glass, it's not a stretch. Or, if you're ok with hunting for used gear, the body and glass can be ~half off new retail.
I have a d850 full-frame DSLR and either a 200mm 2.8 or 500mm 5.6, with some decent tripods; but earth's rotation tends to get me pretty quickly with any long-exposure photos :(
The basics of astrophotography aren't that expensive, but it gets exponentially more expensive to meaningfully "zoom in". Because DSLRs with typical lenses are pretty zoomed out you can get away with much cheaper gear. You might look into getting a "star tracker". It's like a telescope mount for a camera; it'll keep the still relative to the stars but because they don't need to be as accurate they're far cheaper to make. They'll probably work just fine for your 200mm 2.8 lens for a fraction of the cost of a mount.