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The one constant in the Universe: StarDate magazine
When does the young Moon first become visible in the evening sky? 
There is no real formula for determining the visibility of the young Moon. It depends on several factors: the angle of the ecliptic (the Moon's path across the sky) with respect to the horizon, the clarity of the sky (how much dust and pollution gunks it up), and even the keenness of the observer's eyesight.

The young Moon becomes visible to the unaided eye much earlier at times when the ecliptic is perpendicular to the horizon, and the Moon pops straight up into the sky. In these cases, it may be possible to see the Moon as little as 24 hours after it was new, although every hour beyond that greatly increases the chances of spotting it. When the ecliptic is at a low angle to the horizon, and the Moon moves almost parallel to the horizon as it rises, the Moon probably doesn't become visible until at least 36 hours past new.

The record for the earliest claimed sighting of the young crescent Moon is around 19 hours, although most experts are suspicious of any claims of times less than about 24 hours.

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