Why the Sidereal and Soral days have different length?
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The Sidereal and Solar days have different length because by the time the Earth has full rotation on its axis and the distant star is directly overhead again, the Earth has also moved 0.986 degrees further around its nearby circular orbit around the Sun. As a result at the end of a Sidereal day, the Earth must continue to rotate extra 0.986 degrees until the Sun is overhead to complete a Solar day. This extra rotation takes 4 minutes.
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A solar day is the time it takes for the Earth to rotate about its axis so that the Sun appears in the same position in the sky. The sidereal day is ~4 minutes shorter than the solar day. The sidereal day is the time it takes for the Earth to complete one rotation about its axis with respect to the 'fixed' stars.
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