I had a lot of fun with this game. If I were to critique something I think the extra mechanics(gem astroids and push mechanic) work against the core mechanic of pulling astroids in. Both feel more rewarding with less inherant risk thus incentivising they're usage over pulling in astroids. For the push mechanic I think an easy compensation to this would be to auto break pushed astroids to be very small so they'd be worth less when grinded(on initial glance). Players could still increase individual sized astroids which would add complexity to the game(I guess that wouldn't really solve the critique I have of it not being more risky though :( ). For gem astroids I think it could be fun to allow gems to provide a bonus reward if individual gems are grinded(not while they're stuck in the astroid). Players would engage in both astroid pulling and missile firing by shooting gem astroid last minute before they get grinded for a larger score.
None of these critiques should take away from the fact I had fun with this game and think it's very well executed(and it fits the theme very well). Great job!