Space: 1999 was an entertaining show based on the idea that a ginormous explosion has ripped the moon from Earth’s orbit and sent inhabitants of the moon on an incredible voyage.
But what would actually happen to Earth’s environment, both short and long term, afterwards?
Top of head:
In a span of a month or so tides would moderate a bunch, with the greatest tides at any/every coastal spot on Earth being maybe 2/3rds of what they had been, but also with the variability from large to small tides at any/every location settling down to be just medium all the time. How that affects the local bio-/ecology situation will vary vastly from place to place and is beyond my ken. At a minimum the flora and fauna who live near the highest-of-high-tides lines will be trapped high and dry for good. That probably is unhealthy / fatal for them.
There are some animals that care a lot about moonlight cycles. Some need the bright full moon, other need the absent new Moon. They’re going to need to adapt or die. Even the ones that need no moon probably identify that condition as being 14 days pre- or post- the full moon. When suddenly there’s no full moon to sync the clocks of all those individuals, will they have a population crash when all the horny males and horny females show up on different nights, never achieving the critical mass it takes to find each other in the briny vastness? Oops.
Extremely long term the Earth won’t be exchanging rotational momentum with the Moon. And so the Earth’s rotation will slow less than it would if the Moon remained in place. The difference will be practically negligible for millions of years; obvious to astronomers and nobody else. But it will give the very far future different outcomes in unpredictable (to me) ways.
The Earth’s axis will destabilize, tho more on the order of thousands of years.
I think an explosion big enough to accelerate the Moon out of its orbit would itself be pretty devastating to Earth. On the other hand, a certain amount of ignoring of physical law is necessary, since an explosion of that magnitude would probably not leave the Moon in one piece.
Yeah, I know…But I would like to keep this real world as much as possible.
Happy Doperversary there @Czarcasm!
And a 99er no less. People, we are in the presence of an Elder AristoDoper. All hail our betters! 
it will be alot darker at night.
But with more stars.
Why would earths axis destabilize? Mercury, venus and Mars don’t seem to have axis issues despite the absence of large moons.
If there is crazy fast disco guitar interspersed with symphonic fanfare though, I’m all in.
They do.
Here ya go:
The moon has long been recognized as a significant stabilizer of Earth’s orbital axis. Without it, astronomers have predicted that Earth’s tilt could vary as much as 85 degrees. In such a scenario, the sun would swing from being directly over the equator to directly over the poles over the course of a few million years, a change which could result in dramatic climatic shifts.
First wolf to second wolf, “Hey, isn’t it supposed to be our howling night?”
First, Mercury and Venus are very slow rotators, esp. when compared to their orbital times.
That leaves Mars. Decent rotation time. Closer to Jupiter. But not nearly as massive as Earth. Barely over 10%. The titled axis is comparable to Earth’s.
Here’s an article about a change to the tilt 3+ BY ago due to volcanic activity. Apparently no comparable disruption to tilt from other causes since.
I think the smaller mass could be the main explanation.
In the episode “Another Time, Another Place” Alpher returns to earth and finds a five degree axial shift has resulted in almost all of earth being uninhabitable. Except for SoCal, which is, now and forever, awesome. 
I’d worry more about an Endor Apocalypse, with all the megatons of blasted moon rock falling to earth. You can see the enormous ray crater in some shots of the moon.
Episode of what, if I might ask?
Yeah, what @Czarcasm said. Episode of what? [Some Googling indicates it was a film in 1958 and an episode of Space:1999] I’m betting on the latter.
See also Seveneves:
Really interesting. Once again the dope amazes.
Never read that Neal Stevenson, really enjoyed Anathem.
Seriously?
I do not remember this episode at all. I don’t even remember reading this premise.
In an infinite universe, why would anyone assume ANYTHING would be “unique”?
Because the writers of space.com are not the same people who did the actual study, and used that word in the headline, even though it was not a word used by the study.
The researchers used the word “rare”, not “unique”.
Blame clickbait, not science.