<P> The names umbra, penumbra and antumbra are often used for the shadows cast by astronomical objects, though they are sometimes used to describe levels of darkness, such as in sunspots . 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, Venus or Jupiter . </P> <P> A shadow cast by the Earth on the Moon is a lunar eclipse . Conversely, a shadow cast by the Moon on the Earth is a solar eclipse . </P> <P> The sun casts shadows which change dramatically through 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) = ∞, shadows can be extremely long . If the sun passes directly overhead, then θ = 90 °, cot (θ) = 0, and shadows are cast directly underneath objects . </P> <P> Such variations have long aided travellers during their travels, especially in barren regions such as the Arabian Desert . </P>

When does an object cast a long shadow
find me the text answering this question