How to convert an official DateTime to the astronomically exact DateTime? - date

Question

I've been trying to figure out how to convert a birthday (DateTime) to the astronomically "exact" DateTime value. Timezone: UTC+1.
Example:
My friend was born 1984-01-27 11:35
1984 is a leap year. But 1700, 1800 and 1900 were not leap years. So until the 29. February of the year 2000 we are running behind in astronomoically exact time. In 1984 we are "almost" one day behind. So the astronomoically exact time would be after the official DateTime of my friend's birth, right?
These are the Gregorian calendar tweaks I know of:
Every year has 365 days
Every 4th year is a leap year (= has 366 days instead of 365)
Every 100th year is not a leap year
Every 400th year is a leap year (dispite the previous rule)
The additional day is added at the end of February (February has 29 days in a leap year)
Astronomoically a year has 365,2422 days.
Which means that a day is 24,0159254794 hours long.
A time value where the official and astronomoical times are "exactly" the same would be 2000-03-01T00:00:00, right?
So one would need to figure out how big the discrepancy between the official time and the astronomically exact time is at a given official time.
I've been thinking about it for hours, until my head started hurting. I figured I'll share my headache with you. Maybe you guys know any time library that can calculate this?

Answer 1

I came up with a "solution" that seems to be fairly accurate enough. Here's what it does:
The method starts at 1600-03-01T00:00. 18 years after Pope Gregor XIII. (after whom our Gregorian Calendar system is named) fixed the Julian Calendar (named after Julius Caesar) in 1582 by declaring that after the 4th October (Thursday) the next day would be the 15th October (Friday) - so there is actually no 5th to 14th October 1582 in history books - and also adding the 100th and 400th year rules to the calendar system.
The method sums up the discrepany between the official date and the exact date until the given date is reached.
At leap years it applies the correction added by Pope Gregor XIII. It does so at the end of February.
Code:
public static DateTime OfficialDateTimeToExactDateTime(DateTime dtOfficial)
{
const double dExactDayLengthInHours = 24.0159254794;
DateTime dtParse = new DateTime(1600, 3, 1, 0, 0, 0);
double dErrorInHours = 0.0;
while (dtParse <= dtOfficial)
{
dErrorInHours += dExactDayLengthInHours - 24;
dtParse = dtParse.AddDays(1);
if (dtParse.Month == 3 && dtParse.Day == 1 &&
((dtParse.Year % 4 == 0 && dtParse.Year % 100 != 0) ||
(dtParse.Year % 400 == 0)) )
{
dErrorInHours -= 24;
}
}
dErrorInHours += ((double)dtOfficial.Hour + (double)dtOfficial.Minute / 60 + (double)dtOfficial.Second / 3600) * (dExactDayLengthInHours - 24);
return dtOfficial.AddHours(dErrorInHours * -1);
}
I did some sanity testing:
If you pass a date before 2000-03-01T00:00 you get a negative correction. Because we measure days shorter as they in fact are.
If you pass a date after 2000-03-01T00:00 you get a positive correction. This is because 2000 is a leap year (while 1700, 1800 and 1900 are not), but the correction applied is too big. In 24 x 400 = 4800 years the correction would be about one day too big. So in the year 1600 + 4800 = 6400 (if man is still alive), you would need to delcare 6400 a non-leap year, despite the rules of the Gregorian calendar.