I tried it just to see what would happen and - nothing.  A couple weeks ago I gave an (i) guy a moon of 4898 fields.  That's pretty small.  I though maybe I could at least damage it.

I clicked on Destroy from teh Galaxy screen.  That took me to the Fleet screen where I selected all my attack vessels (not enough but it was just an experiment).  I hit Attack and waited for the battle report.  It didn't appear that I even attacked the moon itself.

Do you need a Deathstar?  I thought Trident said 200BS could do it.  Please enlighten me.