So how *would* you rip the moon out of orbit without shredding it in the process?
Ooo! The Doorway to Speculation is open wide.
Bear with me because I've had decades to consider this one. :lol
On the old show, it was a huge quantity of nuclear waste material, stored in drums on the far side of the moon, which became "magnetically unstable" and which started releasing energy in a process previously unknown to science (tho Professor Bergman sussed it out easily enough... :rolleyes)
Anyway, it was sci fi handwaving, and Isaac Asimov would have none of it
Space: 1999 Catacombs: Asimov
Space: 1999 Catacombs: Trek vs Space 1999
...which probably explains the name of that vehicle in the teaser poster... :rolleyes
Anyway, I digress. Clearly Space 1999 is not dependent on strict science (for that matter, how did the Moon travel faster than light in order to visit new alien planets every week? Never explained).
So I propose, just put the pedal to the metal. Every science fiction story is entitled to one big inexplicable "what if". So just run with it: an exotic new form of antimatter fusion, being experimented with on the far side of the moon, goes inexplicably supercritical. A rip in the fabric of spacetime is created. Superstrings are severed, dimension gates are torn open, who cares. :lol
The bottom line: the effect is so vast, it shatters the Moon and hurls the biggest chunk (with Alpha on it of course) into some kind of space warp. In the warp, the moon jumps great distances - or alternately, into different parallel universes.
Here's the kicker: We propel the show forward by continuing to jump Alpha. Either it stays in an unstable "warp"continuum that randomly moves at unpredictable intervals, or else the warp effect keeps occurring for some other technobabble reason.
Builds tension, because our people don't know how long they have to explore a new place before Alpha takes off again. Oh, and they can never go back again. People WILL be left behind.
Or they could just have the exploding nuclear waste function as a sort of giant rocket motor, pushing the moon out of orbit. In other words, ignore the problem. :lol
k