I got this from the movie “Timeline.” A lunar base messes up the orbit of the moon and causes a disaster. Could this really happen?
I find it very hard to imagine how a lunar base could significantly alter the orbit of the Moon.
The Moon is very large.
Even if you did change the orbit of the Moon, I think the worst thing that would happen is tides going all screwy. Maybe some earthquakes as the tidal bulge was reoriented.
There are astrophysicists that believe the Moon helps the Earth’s spin axis stay stable. Without the Moon in orbit, over the course of geologic ages, the direction the poles point would wander a lot more than it now does. This would make seasons act very strangely at times, and might lead to the extinction of many species that couldn’t adapt. The tidal influence of the moon may also play a role in the Earth’s internal dynamo, which creates our magnetic field. I have no idea what role, or what reaction you’d expect due to a change.
Of course, other astrophysicists don’t think the Moon is so important to Earth’s stability. What I said above would only apply if the Moon were removed entirely, and it probably wouldn’t lead to something sudden (which is what most people think of when they hear “natural disaster”).
Agreed that there is nothing humans can do that would meaningfully alter the orbit of the moon.
Remember, “It’s Not Science, It’s Michael Crichton™.” 
For other considerations see What If the Moon Didn’t Exist?: Voyages to Earths That Might Have Been, by Neil F. Comins.
The answer depends on how the orbit of the moon is messed up. If the moon ends up crashing into the earth, you’ll have crustal melting, and the end of all life. If the moon is knocked out of orbit entirely, to pursue its own independent course around the sun, you’ll get those effects cecil talked about in x-ray-vision’s link. If the moon’s orbit is changed so that it gets closer to the earth you might have some tide related problems.
In its current orbit, the moon raises land tides of about 20cm twice a day. These regular shifts in elevation cause little damage:
If the moon were to approach to half its current distance from the earth regularly, these land tides would be magnified by a factor of ~4. I don’t think anyone really knows what that’d do to volcanic and earthquake activity, but it’d likely have some effect at least in the short term.
Whoops, tidal force is proportional to distance cubed. So at half the distance you’d get 8 times the land tide. :smack:
Neither here nor there, but I think you mean the movie “The Time Machine.”
Well, I remember seeing something on TV in the '70s, where the moon was ripped out of orbit by an explosion on it’s surface. A lot of thought went into the production of this series - the moon tore out of the solar system within 20 minutes, and once every seven days it came across another civilization where knowledge (and sometimes bodily fluids with alien lifeforms) was exchanged, hilarity ensued, adventures were had by all concerned, and the known basic laws of physics were shredded beyond recognition.
And, oh yeah, the Earth was in a real mess as the Moon left its orbit.
Space: 1999, by Gerry Anderson. He also gave us Thunderbirds and UFO.
The Moon’s orbit is changing now. IIRC, it’s getting a mile farther away every 65,000 years. 
You gotta give Space: 1999 credit for having one of the coolest spaceship designs though. The “Eagle” transport looked like something that NASA ought to be building!
Anybody remember “Thundarr the Barbarian?” A comet passes between the Earth and the moon, causing the moon to shatter and the cataclysmic ending of modern civilization on earth. Pretty heavy stuff for a Saturday morning cartoon! 
Oh yeah. :smack:
Yeah, it was “The Time Machine.”
Yes I believed they used the same model of nuclear device as the one used in Armegeddon to blow up the comet and in Independence Day to destroy the mothership.
Guess I should have thrown a winking smilie in there. Thought it would be obvious I knew it wasn’t a documentary. Still learning.
As for the Eagles, yeah they were the greatest ships in SciFi. But the ships on UFO that chased down the alien spinning tops (the ones that usually launched from the submarine,) - could they have been any less scary? Dodge the only missle they shot at you from the front, and you (the alien) where free to finish your trip.