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The Julian date is the interval of time (measured in days) elapsed from the epoch January 1, 4713 BC, at 12:00 noon. Within the period bewteen March 1, 1900 and February 28, 2100, the following formula can be used to evaluate the Julian date, given the year, month, date, hour, minute, and second:

JD = 367 * year - int{ 7( year + int{ ( month + 9 )/12 } )/4 } + int( 275*month / 9 ) + day + 1721031.5 + ( 1/24 ){ ( 1/60 )( seconds / 60 + minutes ) + hours }

where the year is 4-digit, the month is 1-12, and the hour is 00-23 (in UTC). "int" denotes integer part, and because it's such a long formula, I've tried to alternate between parentheses and braces (for some reason, the text turns blue and underlined when I try to use square brackets *wink*).

This formula only applies to a 200-year window because, while the regular calendar contains skips (leap years, added seconds), the Julian calendar is continuous from 4713 BC. For those who require extrapolations into the far past or distant future, the following algorithm should be sufficient to scare you away from that idea:

If B = 2 - int( year / 100 ) + int{ int( year /100 )/4 }

and C = { ( seconds/60 + minutes )/60 + hours }/24

then JD = int{ 365.25( year + 4716 ) } + int{ 30.6001( month + 1 ) } + day + B - 15424.5 + C

where the calendar runs from March to February -- i.e., March = 3, February = 14. That is, if month = 1 or 2, year = year - 1 and month = month + 12.

As you can imagine, these numbers are really, really huge. The Julian date of October 26, 1996, at 2:20 PM was 2,450,383.09722222. Dropping decimal places means losing accuracy majorly. To get rid of a few significant figures, you can use the Modified Julian day: JD - 2,400,000.5. This scale is a bit more recent; its epoch falls on midnight of November 1, 1858. Another convenient epoch, used often in astronomy and astrodynamics, is the J2000 epoch, which is zeroed at January 1, 2000, at 12:00 noon UTC.

Why the noon start, for J2000 and normal Julian, and not midnight, as most people are accustomed to? Well, two reasons. First of all, astronomers usually do their work at night when the stars are out - with the clock ticking over at noon, they can record all their observations from one night as occuring on the same "day". Secondly, noon is the easiest yardstick to measure solar days - it's much simpler to tell when the sun is directly above you than when it's exactly on the other side of the Earth (from an Earth-centered reference frame, of course).

Interestingly, the Julian day was not named for Julius Caesar, like that calendar was - it was named for Julius Caesar Scaliger, the father of Joseph Scaliger, the French humanist who combined the solar cycle (28 years), Metonic cycle (19 years), and Roman Indication (15 years) in 1582 to create the Julian period (7980 Julian years). As you may have guessed, all these cycles intersect in 4713 BC.

References include my astrodynamics class notes, my textbook Fundamentals of Astrodynamics and Applications by David A. Vallado, and a Google search for Joseph Scaliger.