During the time needed by the Earth to complete a rotation around its axis (a sidereal day), the Earth moves a short distance (around ) along its orbit around the sun. Therefore, after a sidereal day, the Earth still needs to rotate a small extra angular distance before the sun reaches its highest point. A solar day is, therefore, around 4 minutes longer than a sidereal day.
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... units2
Taylor and Wheeler tell a story of a kingdom that measures east-west direction in feet, and the north-south direction in the ``sacred unit'' which is different from a foot. They have a lot of trouble surveying the land because trigonometry doesn't work for them.
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... reduced3
In this calculation, we simply work in the sun's rest frame and lonly transform the length from the lab to in this frame.
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... boosts4
Note this has a minus sign so there is a difference between space and time dimensions.
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