An interesting concept, though a decent amount of the mechanics were somewhat hidden, they weren't clearly displayed I guess. For example the core mechanic, while understandable and definitely simple to figure out, I almost entirely ignored, in place of just trying to smash enemies with asteroids. Which was somewhat fun, except for the slow turning speed, so I'd recommend making the "boosters" a short limited time use on a cooldown maybe, that BOOSTS you in the direction you're facing. It would alow for some very quick turns and some more varied dodging.
The tow ray seemed a bit weird, in that when you let go of something it lost almost all of it's momentum. Which made it very difficult to try and hit enemies with the asteroids etc. So maybe making it keep it's velocity for a bit longer would help.
As well the fact that the towers themselves don't rotate was a bit annoying, since they seem to react to enemies they can't directly hit. Which lead to them hitting the player, other towers and the core. So I would recommend tweaking that AI a bit. Maybe adding some rotation towards enemies, or making it easier for the player to rotate it.