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Shadow Art
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An astronomical object casts human-visible shadows when its apparent magnitude is equal or lower than -4. Currently the only astronomical objects able to produce visible shadows on Earth are the sun, the moon and, in the right conditions, the planet Venus.
Variation with time
Shadow length changes dramatically throughout the day. The length of a shadow cast on the ground is proportional to the cotangent of the sun's elevation angle—its angle θ relative to the horizon. Near sunrise and sunset, when θ = 0° and cot(θ) is infinite, shadows can be extremely long. If the sun passes directly overhead, then θ = 90°, cot(θ)=0, and shadows are cast directly underneath objects.
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