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A solar day is the time interval between two successive appearances of the Sun overhead at a given longitude-that is, the time for one complete rotation of Earth relative to the Sun. A sidereal day is the time for one complete rotation of Earth relative to the fixed stars-that is, the time interval be- tween two successive overhead observations of a fixed direction in the heavens called the vernal equinox. (a) Show that there is exactly one less (mean) solar day in a year than there are (mean) sidereal days in a year. (b) If the (mean) solar day is exactly 24 hours, how long is a (mean) sidereal day?

A solar day is the time interval between two successive appearances of the Sun overhead at a given longitude-that is, the time for one complete rotation of Earth relative to the Sun. A sidereal day is the time for one complete rotation of Earth relative to the fixed stars-that  is, the time interval be- tween two successive overhead observations of a fixed direction in the heavens called the vernal equinox. (a) Show that there is exactly one less (mean) solar day in a year than there are (mean) sidereal days in a year. (b) If the (mean) solar day is exactly 24 hours, how long is a (mean) sidereal day?

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
(a) Earth rotates by an angle of 360° and completes its sidereal day, however during this time, the Earth also moves around the Sun in its orbit. Therefore, the Earth has to rotate by some extra angle to complete its solar day, and allow the Sun to come at the same longitude.After the year, the Earth will have the same length of the solar day, as it was a year back. Therefore, in a year the extra angle traced by the Earth corresponding to solar day would be 360° or 1 more day. Hence, there is 1 extra solar day in a year than the sidereal days. 233-306_1.PNG

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