The moon never actually changes colors. Humans perceive it as being different colors due to atmospheric changes, the moon's position in the sky, pollution or the seasonal tilt of the Earth.
Scattered Blue Light
When the moon is rising and setting, you view it through a thicker cross-section of atmosphere, which scatters blue light, so the reds and oranges of the light spectrum shine through the atmosphere more brightly.
The "harvest moon" is the full moon closest to the autumnal equinox. At this time, the moon rides an astronomical line called the ecliptic in the early evening. This forces us to view the moon through a thicker-than-usual section of atmosphere, causing the moon to look both very large and reddish.
Full Luna Eclipse
During a full lunar eclipse, the Earth's shadow covers the face of the moon in two phases. The first is the penumbra, which casts a grayish shadow across the moon. The umbra, however, scatters the blue light and leaves the moon looking fiery red or deep golden in its shadow.
The moon also appears to change color based on the particles in the atmosphere that are between you and the moon. Each has a different effect on the shift in color, and their effects are intensified based on the density of the particles in the atmosphere.
The term "blue moon" doesn't actually refer to the color of the moon. It is an old way of noting the second full moon in a calendar month. This doesn't mean, though, that the moon is incapable of appearing bluish to us; dust particles in the Earth's atmosphere can cause this color effect.
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