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. As per diagram, the earth moves from the point P to Q in one solar day.

Explanation

`implies` As per 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.
`:. ` To cover `361^@` , time taken = 24 h
`:. ` To cover `1^@` , time taken = t,
`t = (24)/(361) xx 1 = 0.066 h `
`= 3.99 min`
`~~ 4 min`
Hence, distant stars would rise 4 min early every successive day .