Astronomical Algorithms

Julian Day

The Julian Day number or more simply theJulian Day is a countinuous count of days and fractions thereof from the begining of year -4712.

By tradition the Julian day begins at Greenwich mean noon that is, at 12h Universal Time.

If the Julian Day corresponds to an instant measured in the uniform scale of Dynamic Time, the expression Julian Ephemeris Day (JDE) is often used. For example:
1977 April 26.4 UT = JD 2443259.9
1977 April 26.4 TD = JDE2443259.9

The Gregorian calendar was not at once officially adopted by all countries. This should be kept in mind when making historical research. In Great Britain, for instance, the change was made as late as in 1752, and in Turkey not before 1927. The Julian calendar was established in the Roman Empire by Julius Caesar in the year -45 and reached its final form about the year +8. Nevertheless, we shall follow the astronomers' practice consisting of extrapolating the Julian calendar indefinitely to the past. In this system we can speak, for instance, of the solar eclipse of August 28 of the year -1203, although at that remote time the Roman Empire was not yet founded and the month of August was still to be conceived! There is a disagreement between astronomers and historians about how to count the years preceding the year 1. In this book, the "B.C." years are counted astronomically. Thus, the year before the year + 1 is the year zero, and -the year preceding the latter is the year -1. The year which the historians call 585 B.C. is actually the year -584. (Do not use the mention "B.C." when using negative years! "-584 B.C.", for instance, is incorrect.) The astronomical counting of the negative years is the only one suitable for arithmetical purposes. For example, in the historical practice of counting, the rule of divisibility by 4 revealing the Julian leap years no longer exists; these years are, indeed, 1, 5, 9, 13, ... B.C. In the astronomical sequence, however, these leap years are called 0, -4, -8, -12 ... , and the rule of divisibility by 4 subsists. We will indicate by INT(x) the greatest integer less than or equal to x. For example:

The following method is valid for positive as well as for negative years, but not for negative JD.

Let Y be the year
M the month number (1 for January, 2 for February, etc., to 12 for December)
D the day of the month (with decimals, if any) of the given calendar date.

⦁ If M > 2, leave Y and M unchanged.
If M = 1 or 2, replace Y by Y- 1, and M by M + 12. In other words, if the date is in January or February, it is considered to be in the 13th or 14th month of the preceding year.

⦁ In the Gregorian calendar, calculate;
A = INT( Y/100 )
B = 2 - A+ INT( A/4)

(We will indicate by INT(x) the greatest integer less than or equal to x. For example: INT(7/4) = 1, INT(8/4) = 2, INT(5.02) = 5, INT(S.9999) = 5)

In the Julian calendar, take B = 0.
⦁ The required Julian Day is then
JD = INT (365.25 (Y + 4716)) + INT (30.6001 (M + 1)) + D + B - 1524.5

Select Date Time and time zone to get the Julian Day:

Julian Day JD=