365.2421896698 - 0.00000615359 T - 7.29E-10 T2 + 2.64E-10 T3 (days)where T = (JD - 2451545.0) / 36525 and JD is the Julian day number. The value of the mean tropical year for the epoch of J2010.0 (Julian day of 2455197.5, and thus T = 0.1) was calculated with Laskar's equation above.
All the progressive solar calendars since Old Egyptian times are arithmetical calendars. This means an easy rule to try to reach the best possible astronomical value.
In the history of solar calendars notably these five
rules (approximations) shown below were used, are used, or are proposed.
|Old Egyptian||365||= 365. 000 000 000|
|Julian||365 + ¼||= 365. 250 000 000|
|Gregorian||365 + 97/400||= 365. 242 500 000|
|Khayyam||365 + 8/33||= 365. 24 24 24 24|
|Revised Julian||365 + 218/900||= 365. 24 22 22 22|
|von Mädler||365 + 31/128||= 365. 242 187 500|
|Mean tropical year at epoch J2010.0||= 365. 242 189 054 433 974|
The currently widely-used Gregorian calendar has an average year of:
However, according to von Mädler, if the years
3200, 6400, 9600, 12,800,
16,000, and so on are NOT
leap years (an additional rule to the ones already in use with the
the duration of the mean Gregorian
year will then be 365.2421875 days,
of the mean tropical
year which lasts 365.24219 days.
error of only
3.125 - 3.100 = 0.025 days in 10,000 years.
I had figured out a better system than the Gregorian-von Mädler one for leap year
decisions, but I plan on using it only if the Cesidian
calendar becomes adopted worldwide.
HMRD Cesidio Tallini