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Mean solar day is the time interval betw...

Mean solar day is the time interval between two successive noon when sun passes through zenith point (meridian).
Sidereal day is the time interval between two successive transit of a distant star through the zenith point (meridian).
By drawing appropriate diagram showing the earth's spin and orbital motion, show that mean solar day is 4 min longer than the sidereal day. In other words, distant stars would rise 4 min early every successive day.

Text Solution

Verified by Experts

Consider the diagram below, the earth moves from the point P to Q in one solar day.

Every day the earth advances in the orbit by approximately `1^(@)`. Then, it will have to rotate by `361^(@)` (which we define as 1 day) to have the sun at zenith point again.
`:. 361^(@)` corresponds to 24 h.
`:. 1^(@)` corresponds to `(24)/(361) xx 1 = 0.066h = 3.99 min = 4 min`
Hence, distant stars would rise 4 min early every successive day.
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