Only some of the time! With the exception of the times when the Moon wanders into the shadow of the Earth, the Moon spends its journey around the Earth with half its surface in sunlight, and half its surface in darkness. The far side is harder to watch directly, though, because all of us humans are on the surface of the Earth, which only ever sees the near side. We can observe the far side thanks to the technological advancements that come with sending spacecraft out beyond the Moon, but few human eyeballs have seen the far side of the Moon directly.
Even without going there, we can figure out what should be happening on the far side of the Moon by looking at what isn’t happening on the near side of the Moon. If half the sphere of the Moon is illuminated, and we here on Earth are looking at a full Moon, then the far side of the Moon must be dark. But a full Moon doesn’t last very long- the next night the Moon will begin to look less circular in the sky, until a few days later, you’ll definitely be able to tell that the surface of the Moon facing us is not entirely illuminated.
The rest of that sunlight isn’t missing; it’s illuminating the side of the Moon that’s not facing us. As the month progresses, more and more of the far side of the Moon will be in sunlight, and less and and less of that sunlight will be visible to us on Earth. When we on Earth see a thin crescent Moon, the far side of the Moon is almost totally illuminated.
There are some permanently dark places on the Moon, but the far side of the Moon isn’t where you find them. They’re near the poles of the Moon - craters that are so deep, and the sunlight that reaches them is at such a shallow angle, that the light from our Sun only ever skims the surfaces of them. These are interesting places because they are so dark and cold - they’re one of the places that water seems to exist on the surface of the Moon.
With the exception of these deeply shadowed craters, the rest of the surface of the Moon spends about half its time in the sun, and half in the shade. What’s fun is that these periods of sun and shade each last about two weeks.
This is easiest to think about with the near side of the Moon; imagine some point (you can pick your favorite) on the surface of the Moon. As an example, let’s pick the very center of the near side. When the Moon is dark from our perspective, so is our test point in the middle of the near side. As the Moon progresses through crescent phases, our point in the middle is still dark! That part of the Moon is still in its nighttime period. When half the Moon is illuminated, our point on the Moon is dealing with a sunrise, as it’s right on the boundaries of the daytime and nighttime. From there, the gibbous phase, the full Moon, and right onwards through to the next quarter (where the other half is lit), our central point of the Moon stays in sunlight. If we ever have a human outpost on the Moon, this two weeks of daylight followed by two weeks of night will be something to contend with - though I’m sure folks who have lived in the arctic or antarctic (where night can last several months in winter) can give our explorers some pointers.
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