The night sky would certainly be a lot less interesting and we wouldn’t be able to see awesome things like eclipses, blood Moons and other phenomena such as how massive the Moon looks when it’s close to the horizon. But that would be the least of our worries.
Most people know that tides are (mostly) dependent on the Moon. They are also dependent on the sun, however, the sun only has 44% of the tidal effect of the moon, meaning tide heights would drop by more than half (see below for comparison and calculation of solar and lunar tides). So what is the result of this tidal drop?
It’s impossible to accurately predict the consequences of this change in tides, but it certainly wouldn’t be positive. Although many ocean currents aren’t solely caused by tides, in many places, especially close to shore, the water would become stagnant as tidal currents have a flushing effect on many coastal areas. The flow of vital nutrients in and out of these areas would dwindle, resulting in many corals and seaweeds dying off as there would be not enough nutrients to support the current amount of life. This would work its way up the food chain, reducing the populations of the small fish and crustaceans that eat these species, and eventually larger fish and mammals such as dolphins and seals.
Although this would result in the extinction of some species, it’s probable that most species living in the ocean would survive. Stagnation of water channels would become rampant in some areas, particularly closed-in and isolated bays, and eventually, the loss of so much marine life would start to take its toll on land-dwelling organisms. As humans rely on farming for food, this wouldn’t likely have a devastating impact on the human race, although for many other life forms this would spell the beginning of the end.
The moon is important for life on planet Earth for many other reasons than tides. The gravitational effect of the moon has protected the Earth from asteroid impacts in the past and could do so again in the future. No Moon would make us more susceptible to a catastrophic meteor impact (although this would still be unlikely in the foreseeable future).
Not only that, the Moon has a profound effect on the Earth’s gravitational field. As the Earth wobbles around its axis, it is currently held in place by the Moon’s gravity. If the moon were to suddenly disappear, its stabilizing effect on the Earth’s rotation would be removed, and the Earth would wobble uncontrollably, potentially taking it slightly further out to space or closer to the sun as the orbit becomes more elliptical. Even a slight change in orbit would spell death for many life-forms on Earth (most of the human race included).
The tilt of the Earth’s axis, currently at 23.5°, would vary greatly without the Moon’s stabilizing effect. It’s possible that at some times the north pole would go through central Africa at a 90° tilt and at other times be perfectly aligned with 0° tilt. This would result in drastic and extreme seasonal climate changes and changes in day and night times throughout the year. These changes would likely happen over hundreds of thousands to millions of years, leaving humans with more than enough time to be ready for them! Although that is not too long by an evolutionary standpoint, most of the remaining animals would be resilient enough to adapt or migrate to greener pastures as the Earth changes.
To answer perhaps the most poignant question here, if the human race would survive, the answer would almost definitely be yes. With the ability to grow and produce our own food and regulate the temperatures indoors, humans would almost definitely live on, though likely not without consequence. The biodiversity we currently enjoy would be gone and our resiliency would be tested as fast technological changes would have to be undertaken to keep as many people as possible alive. Technology has always improved the fastest in times of need, and this would prove no different.
Although the Moon is actually leaving us at a rate of 4cm per year, there’s no need to worry — by the time it would be far enough away to have any serious impact, both the Earth and Moon would be long gone as the Sun morphs into a red giant and engulfs them both.