Ah, but I anticipated that, although my post was less than clear, I admit. By "space cannons", I meant "
orbital space cannons". Here, I'm envisioning some sort of superconducting magnet/railgun sort of thing, of course.
The main drawback I see is similar to what you point out, though - the possibility that a Kennedy or Nadler might remain almost motionless, as the cannons shot off into deep space in the opposite direction...
You need rockets, not cannons! The only problem is lashing a few Saturn Vs together.
Oh! We don't make Saturn Vs anymore? Never mind!