Question

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 earth’s spin and orbital motion, show that mean solar day is 4 minutes longer than the sidereal day. In other words, distant stars would rise 4 minutes early every successive day. 

(Hint : you may assume circular orbit for the earth).

Answer 1

Let us consider the following diagram, the earth moves from the point A to B in one solar day.

Every day the earth advances in the orbit by approximately 1º . Then, it will have to rotate by 361º (which we define as 1 day) to have sun at zenith point again. Since 361º corresponds to 24 hours.

\(\therefore\) Extra 1º corresponds to approximately 4 minutes [3 min 59 seconds].

i.e. \(\frac{24}{361}\times1\) = 0.666 h = 3.99 min = 4 min

Thus, distant stars would rise 4 minutes early every successive day.