The Moon plays a major role in Judaism, from determining months and holidays to its necessity for the mitzvah of Birkat Halevanah (Blessing of the Moon).
The Moon also contains profound spiritual and kabbalistic significance.
But in this post, we'll focus on just the bare scientific necessity for the Moon.
What would our world be like without the Moon?
Everyone knows that the Moon affects tides. The Sun does, too, but to a lesser extent. The reason why the Earth bulges out at the equator is due to its pull on the Earth. This lunar pull also keeps the oceans in check. If the Moon suddenly disappeared, the oceans would flood into every continent, completely changing the map of the world. In fact, the movement of the newly liberated oceans to meet each other would cause 59-foot (the height of a 6-story building) tsunamis all over pushed from behind by the force of the entire ocean.
Every morning, Jews say the blessing "Baruch...rokah ha'aretz al hamayim -- Blessed be...Who spreads the land over the water" to show appreciation for the fact that the water usually stops at the seashore. (Well, that's one of the meanings of the blessing, anyway.) A major reason why it doesn't encroach further is because of the reining-in effect of the Moon as described above.
Without the Moon, the ocean currents would slow down or stop, preventing the transfer of heat around the world.
The Earth as a Drunken Dreidel
The Moon has a stabilizing effect on the Earth. As the Earth spins on its axis, it spins at a tilt that wavers between 22-25 degrees.
Without the Moon, the Earth would swing around like a drunken dreidel, veering from zero degrees (no tilt at all, standing straight up) to an 85-degrees tilt (lying on its side, which would chill the upper hemisphere and shine the Sun directly on the South Pole and presumably cause some major warming and melting down there).
Due to the crazy wobble described above, seasons would just come and go randomly. Antarctica would sometimes be the frozen wasteland we know today and other times be as hot as the tropics. Hot areas of the world would sometimes freeze and cold areas would sometimes bake.
Rotation on Steroids
Without the Moon, the Earth would spin much faster. The Moon acts as a gentle restraint on the Earth (perhaps yet another reason why the Moon is likened to a woman in Jewish allegories and Hebrew grammar). If the Earth spun faster, this would shorten the days to 6-12 hours, which would increase our calendar year to 1000 days. It would also increase the strength of hurricanes, making Category 5 storms the norm.
Of course, there are other results you likely thought of: darker nights, the absence of eclipses, nearly non-existent tides, no asteroid blocker to protect Earth, and so on.
The Torah Blueprint
As you can see from the above, without the Moon, not only would we face the challenge of physical survival, but we wouldn't be able to keep many aspects of the Torah relating to time.
Of course, the monster tidal waves wouldn't occur if the Moon never existed, but only if it suddenly disappeared. However, a steady tilt, predictable seasons, and the present calendar could never have developed without the Moon. (Not to mention how difficult life would be under such conditions.)
So whether we're grateful that Hashem created a Moon (at the perfect size and the perfect distance!) or we're grateful that Hashem allows us to keep the Moon, may you enjoy a very good month and rejoice in the fact that we even have such a thing as a month!
Chodesh Tov! May this Adar see the Redemption in a sweet way.