Sidereal year the duration taken for one revolution of the earth around the sun with distant star at infinity as datum reference
Time taken for one sidereal year is equal to 365 days and 6 hours
Tropical Year
Tropical year is duration taken for one revolution of the earth around the sun with sun as the datum reference
Duration of tropical year is 365 days, 5 hours, 48 minutes and 45 seconds
Calendar Year
Calendar year is made to keep whole number of days in a year to 365 days instead of 365 days, 5 hours, 48 minutes and 45 seconds
Leap years have 29 days in February to cater for ¼ day short every year
The adjustment to make a usable calendar year is done in three phases
Every fourth year is a leap year while Centuries are not leap years but Fourth centuries are leap years
Sidereal Day
Sidereal day is the time between two meridian transits of the earth with a distant star at infinity as datum
A day is the time taken for one rotation of earth around its axis using any celestial body for measurement
Sidereal day is not related to periods of daylight or darkness and is not usable in day-to-day life
Revolution of earth does not affect sidereal day since the Meridian transit referenced to infinity will remain constant
Apparent Solar Day
Apparent solar day is the time taken between successive meridian transits with the Real sun which is apparent to us as datum
Earth revolves as well as rotates anti-clockwise from north celestial pole requiring additional distance between two meridian transits
Observers’ meridian shift its position between two meridian transits making the apparent solar day longer than the sidereal day
Apparent solar day varies from day to day due to speeds of revolution which in turn varies depending on the distance from the sun
Therefore, Apparent solar day is also unusable for practical purposes
Mean Solar Day
Civil day or Mean Solar Day is the time taken between successive meridian transits with the mean sun as datum
Mean sun is an imaginary sun assumed to circle the earth every 24 hours
Mean solar day is obtained by dividing total length of a year by 365 ¼ days
Since 360 degrees of rotation will take 24 hours, 15 degrees of rotation will take 1 hour and 1 degree of rotation will take 4 minutes
Equation of Time
Equation of time is the time difference between mean and apparent time
Mean solar day is taken as the basis of measurement for mean time which is constant throughout the year
Apparent time depends on the visible sun or the real sun which varies with distance between earth and sun
Equation of Time differs with position of earth in the orbit
Mean time of 12 noon does not mean that the real sun is overhead meridian
Maximum difference between mean and apparent time is 16 minutes in mid-November which means that the real sun is 16 minutes behind the meridian transit
Similarly, the second maximum is 14 minutes in mid-February which means that the real sun is 14 minutes ahead of meridian transit