question_answer 53)

                    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 distance star through the zenith point (meridian).                 By drawing appropriate diagram showing earth?s spin and orbital motion, show that mean solar day is four 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:

                                    Earth advances in the orbit by \[{{1}^{o}}\] in every day                 Now \[{{361}^{o}}=24\] hours                 \[\therefore \] \[{{1}^{o}}=\,\frac{24}{361}\times \,1\,=\,0.066\,h=\,3.99\] minutes                 \[\simeq \,\,4\,\,\min utes\]