Information about calendars

Start dates of different calendars

Julian Day 0 is noon on January 1, 4713 BC Julian (November 24, 4714 BC Gregorian).

Modified Julian Day 0 is midnight on November 16, AD 1858 Gregorian (November 4, AD 1858 Julian).

Difference between Gregorian and Julian calendar dates over the centuries

As you can see, the 3rd C AD was the only century in which the two calendars were in step!

The Gregorian calendar was introduced on 1582 supposedly to bring the calendar back into line with where it had been at the time of the Council of Nicaea. Only 9 days should have been omitted but 10 days made it easier to correct old calendars by inserting an “X”, and 10 days would allow the Gregorian year of 365.2425 days to remain accurate for longer before it becomes out of step with the true (tropical) year of 365.2422 days. The Gregorian year will have fallen behind the true year by about one day by the year 4000.

Dates of introduction of the Gregorian calendar in various countries

Exact definitions of days, months and years

Calendar (SI) day: D_C = 86,400 seconds.

Mean solar day: D_Sol = 86,400.0026 seconds in AD 2009.

Sidereal day: D_Sid = 86,164.0932 seconds (relative to a precessing timeframe), or 23 hours, 56 minutes, 4.0932 seconds.

Stellar day: D_Stel = 86,164.0990 seconds (relative to an inertial timeframe) in AD 2009, or 23 hours, 56 minutes, 4.0990 seconds.

The mean solar day was exactly 86,400 seconds in AD 1820.

The stellar day was 86,164.0989 seconds in AD 2000.

The length of the day is increasing by 1.4 ms per century. Therefore, a leap second has to be inserted every 378 days, on average.

Julian year: Y_J = 365.25 SI days, which is Y_J × D_C = 31,557,600 seconds.

Gregorian year: Y_G = 365.2425 SI days, which is Y_G × D_C = 31,556,952 seconds.

Tropical year: Y_T = 31,556,925.2044 seconds in AD 2009, which is Y_T/D_C = 365.242189865 SI days, or T_Sol = Y_T/D_Sol = 365.242178680 mean solar days, or T_Sid = Y_T/D_Sid = 366.242178680 sidereal days. (Notice also that T_Sid = T_Sol + 1).

Sidereal year: Y_Sjd = 31,558,149.7157 seconds in AD 2009, which is Y_Sid/D_C = 365.256362450 SI days, or Y_Sid/D_Sol = 365.256351264 mean solar days, or Y_Sid/D_Sid = 366.256390068 sidereal days.

The tropical year was 31,556,925.2522 seconds long in AD 2000.

The sidereal year was 31,558,149.7635 seconds long in AD 2000.

The length of the year is decreasing by 530 ms per century.

Moon’s synodic period (relative to the Sun): M_Syn = 2,551,442.8251 seconds, which is M_Syn/D_C = 29.5305883 SI days (29 days, 12 hours, 44 minutes, 2.83 seconds).

Moon’s sidereal orbital period (relative to the stars): M_Sid = 1/[(1/M_Syn)+(1/Y_T)] = 2,360,584.6616 < style='mso-spacerun:yes'> seconds in AD 2009, which is M_Sid/D_C = 27.3215817 SI days (27 days, 7 hours, 43 minutes, 4.66 seconds).

The sidereal month was 2,360,584.6574 seconds long in AD 2000.

The length of the month is increasing by 47 ms per century.

Time between successive high tides: (D_C/2)*(1+(D_C/M_Syn)) = 44,662.8899 seconds (12 hours, 24 minutes, 22.89 seconds).