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
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
Every day the earth advances in the orbit by approximately $1^{\circ}$. Then, it will have to rotate by
$361^{\circ}$ (which we define as 1 day) to have the sun at zenith point again.
$\because \text { To cover } 361^{\circ} \text {, time taken }=24 \mathrm{~h}$ $\because \text { To cover } 1^{\circ} \text {, time taken }=t \text {, }$ $t=\frac{24}{361} \times 1=0.066 \mathrm{~h}$ $=3.99 \mathrm{~min}$ $\approx 4 \mathrm{~min}$
Hence, distant stars would rise $4 \mathrm{~min}$ early every successive day.
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- [AIPMT 1994]
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