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There are four factors that the Moon's visibility can be affected by:The Earth itself might be blocking you from seeing the Moon (you could see it if the Earth was transparent)The light that's coming from the Sun might be too bright for you to see the Moon's surface which only reflects sunlight, it does not emit it (if this is a case, it's probably a daytime).The third factor is the Earth's atmosphere: if the clouds are too thick for the moonlight too break through, you won't see the Moon.The person trying to take a look at the Moon's surface might be fully or partly blind, therefore permitting a person to see the Moon.
The moon is constantly orbiting around the earth. It takes around 28 days to go around the earth one time. Whether the sun is out or not the moon is there, you might not be able to see it in the day.
In a clear sky you might not see the Moon because of the rotation of the Earth on its axis. The Moon will rise about 50 minutes later each day due to its orbit around the Earth, so it will depend on both the time of day and where it is in its monthly orbit.
As it orbits the Earth there are times it can see the moon and there are times when it is on the opposite side of the Earth to the moon, so it can't see it.
The phases of the moon as it orbits the earth
We see a crescent moon.
To see the Earth, look down. To see the Moon, you have to be outside and look at the sky. Note that the Moon is not always above the horizon.
If you were standing on the Moon, it would be easy to notice a solar eclipse; the Earth would block out the Sun, all over the Moon, for an hour or so. On the Earth, we would have called it a lunar eclipse. From the Moon, it would be difficult to notice an Earth eclipse; the shadow of the Moon on the Earth, so obvious when you're in the dark at midday, wouldn't be so obvious from 250K miles away; a small dark circle on the Earth.
If you can see a full moon at your position on Earth, then someone on the exact opposite side of the world will see a new moon. This is because the full moon is when the side of the moon facing Earth is fully illuminated by the sun, so the side facing away from Earth is in shadow.
The earth.
From earth we see the same side of the moon but depending on the position of the moon, earth, sun we see different portions of the moon- these are known as the phases of the moon.
Half-moon Half-Earth