Ncert Exercises & Solutions

Q. 28 Mean solar day is the time interval between two successive noon when the sun passes through the zenith point (meridian). Sidereal day is the time interval between two successive transit of a distant star through the zenith point (meridian). By drawing an appropriate diagram showing the earth’s spin and orbital motion, show that the mean solar day is 4 min longer than the sidereal day. In other words, distant stars would rise 4 min early every successive day.

Hint: The earth revolves 1° each day in an orbit around the sun.

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

Step 1: Find the value of 1° in terms of the time of rotation.

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 the zenith point again.

∵

361° corresponds to 24 h.

∵

1° corresponds to

\frac{24}{361}

x 1= 0.066 h = 3.99 min = 4 min
Hence, distant stars would rise 4 min early every successive day.

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