Which moon phase provides the most ideal conditions for all-night meteor viewing?
Answer
New Moon.
The phase of the moon acts as a primary form of natural light pollution. A Full Moon, or even a bright gibbous moon, casts enough illumination to wash out the faint meteors that typically comprise the majority of a shower's activity. A New Moon provides the darkest possible sky, which is the essential condition for maximizing the contrast between the dark backdrop of space and the fleeting trails of light created by burning space debris. Any other moon phase introduces competing light that will inevitably reduce the number of meteors an observer can successfully detect.

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