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 transits 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 four minutes longer than the sidereal day. In other words, distant stars would rise 4 minutes 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 transits 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 four minutes longer than the sidereal day. In other words, distant stars would rise 4 minutes early every successive day.
Step 1: Diagram.
Step 2: Calculations
As per the diagram, 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.
Thus, 361∘ corresponds to 24 h.
Hence, 1∘ corresponds to
24361×1=0.066 h
=3.99 min=4 min
Hence, distant stars would rise 4 min early every successive day.
Step 2: Calculations
As per the diagram, 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.
Thus, 361∘ corresponds to 24 h.
Hence, 1∘ corresponds to
24361×1=0.066 h
=3.99 min=4 min
Hence, distant stars would rise 4 min early every successive day.
