Julian date

The Julian date, Julian day or DJ (JD, for its acronym in English) is the number of days and fraction elapsed since noon on January 1, 4713 B.C. c.

To date distant astronomical or historical phenomena, it is difficult to consider the changes that have taken place in the calendars of different cultures. Even considering exclusively the history of Western Europe, in 1582 the Gregorian reform occurred, whereby the secular years not divisible by 400 were suppressed as leap years (thus 1700, 1800 and 1900 cease to be leap years) and also 10 days are suppressed, the which go from October 5 to 14, 1582. This reform was not immediately accepted by Protestants and Orthodox Christians, who still use the Julian calendar to set the date of Easter each year.

If we intend to find out the time elapsed between two distant eclipses, even if they are from the same calendar, we must keep track of the elapsed leap years, which is even more complicated if one is from the Julian calendar and the other from the Gregorian. For this reason, in the same year 1582, Joseph Scaliger of Leiden created a continuous time scale setting its origin (beginning of day 1) at noon on January 1, 4713 B.C. C. of the proleptic Julian calendar and counting the solar days correlatively. This number is called the Julian date. On August 4, 2019 at 12 noon UT it is completed on day 2,458,700.

Thus, if 12,3,-3283 is entered for the date, it means the year 3284 BC. C. The first way of designating the date is called astronomical and the second historical date.

The Julian date is a continuous count of days and fractions counted from a fixed starting point. Right now, on the day you are viewing this article (April 6, 2023, 12:59 UT), the Julian date is 2460041.0409722. The integer part (2460041) corresponds to today (from past noon to next noon); the fraction indicates the fraction of the day since the last noon (so 0.5 would be midnight UT).

In computing, a double-precision (64-bit) floating-point variable allows a Julian date to be represented with 1 millisecond precision.

Calculation

The Julian day can be calculated using the following formula:

JD= 365,25(And+4716) + 30,6001(M+1) +D+B− − 1524,5{textstyle JD=lfloor 365,25(Y+4716)rfloor +lfloor 30,6001(M+1)rfloor +D+B-1524,5}

Where:

x {displaystyle lfloor xrfloor } It's the floor function.

M is the month number of the date to convert (March=3, April=4, May=5, etc.). If the month is January or February (1 and 2 respectively), 12 is added to the value of the month.

Y is the year. If the date to convert is in January or February, 1 is subtracted from the year value. Also, if the year to be converted is BC, 1 is added to the value of the year.

D is the day of the month at 00:00:00 UTC. To calculate the date in a specific time the formula is used: Dm+h24+m1440+s86400{displaystyle D_{m}+{frac {h}{24}}}} +{frac {m}{1440}}}}{frac {s}{86400}}}}}Where Dm{displaystyle D_{m}} It's the day of the month, h It's the number of hours, m It's the number of minutes and s It's the number of seconds.

A is the first auxiliary quantity. It is calculated as follows: And100 {displaystyle leftlfloor {frac {Y}{100}}rightrfloor }.

B is the second auxiliary quantity. It is calculated as follows: 2− − A+ A4 {displaystyle 2-A+leftlfloor {frac {A}{4}}rightrfloor }for 15 October 1582 or later dates. If the date to be converted is before or equal to October 4, 1582, the value of B It's 0.

NOTE: Due to the Gregorian reform of the calendar in 1582, it was changed from Thursday, October 4 to Friday, October 15, so the days in between never existed.

Example

Calculate the Julian day of January 1, 2019 at 12:00:00 UTC

And=2019− − 1=2018{displaystyle Y=2019-1=2018}

M=1+12=13{displaystyle M=1+12=13}

D=1+1224+01440+086400=1,5{displaystyle D=1+{frac {12}{24}}} +{frac {0}{1440}}}}}} +{frac {0}{86400}}}=1.5}

A= 2018100 =20{displaystyle A=leftlfloor {frac {2018}{100}}}rightrfloor =}20

B=2− − 20+ 204 =− − 13{displaystyle B=2-20+leftlfloor {frac {20}{4}{rightrfloor =-13}

DJ= 365,25(2018+4716) + 30,6001(13+1) +1,5+(− − 13)− − 1524,5=2458485,000{displaystyle DJ=lfloor 365,25(2018+4716)rfloor +lfloor 30,6001(13+1)rfloor +1,5+(-13)-1524,5=2458485,00000}

Calculus Explained

The Julian day number (JD) will be the result of adding the following terms:

YY: Numbers of days corresponding to the number of full years since the start of the Julian period.

MM: Numbers of days corresponding to the complete months elapsed since the beginning of the year.

DD: Number of whole days elapsed since the beginning of the month + fraction of day corresponding to the hour.

B: Adjustment of NON-leap days.

The last term (1461 + 62 + 1.5) is necessary as a calculation device, as explained below.

Astronomical Numbering of Years:

Calculations are made based on the astronomical year, which establishes a zero year and negative previous years (... -2 -1 0 1 2...)

Astronomical numbering sets the year 0 to 1 BC. C., so that the year 2 a. C. is the year -1, and so on. The years d. C. are kept as is.

Introducing a zero year and negative years allows us to apply the rule that leap years always correspond to a number divisible by 4.

The first astronomical year is -4712 (year 4713 BC of the proleptic Julian calendar)

Leap Years:

In order to include leap years in the calculation, the beginning of the year is made to coincide with March 1, so that the months of January and February are considered from the previous year.

The first month is month 3 and the last month is 14 (January = 13, February = 14).

For computation, if month < 3, we subtract a year and add 12 months, so the resulting number of days is not affected by this change.

Year: SI Month < 3 THEN Year = Astronomical Year - 1 ELSE Year = Astronomical Year

Month: SI Month < 3 THEN Month = Month + 12 ELSE Month

Terms in the calculation:

The calculation for each of the indicated factors is explained below:

AA - Factor due to number of years:

We multiply 365.25 average days for each year, considering the Year, plus 4712 years (beginning of the Julian period), plus 4 extra years:

When considering 365.25 average days per year, leap years are included in the calculation (3 years of 365 + 1 year of 366 days).

Adding 4712 years allows both positive and negative years to be included in the same calculation, and makes JD=0 occur in the year -4712.

The 4 extra years along with the fraction of day (0.25) are the key: by reducing the product to the smallest whole, every 4 years includes one more day (leap year).

These 4 extra years (1461 days) must be subtracted at the end of the calculation.

MM - Factor due to the number of complete months elapsed since the beginning of the year:

The number of complete months elapsed since the beginning of the year is M - 1.

The average number of days in a month is 365.25/12 = 30.4375

The number of days corresponding to (Month - 1) months, approximately coincides with the number of average days multiplied by the number of previous months:

However, we cannot directly use the number of average days as a factor, as it would not produce the values matching the actual number of days in each month.

We have to use a multiplication factor that produces the same offset for all months, so that the excess days can be compensated at the end of the calculation by a single subtraction.

The factors that meet this requirement are 30.6 and (Month + 1). The factor LESS_INTEGER (30.6001 * (Month + 1)) produces an excess of 62 days for all values of M, so we can use it to calculate the days corresponding to previous months if we then compensate for the excess of 62 days produced. The explanation of this calculation artifice can be better understood in the following table:

DD - Number of whole days elapsed since the beginning of the month + the fraction of the day corresponding to the hour, minutes and seconds:

Since the first value for JD = 0 occurs at 12 o'clock on day 1 (1.5 days), we have to subtract this value (1.5) to the final computation in order to get the correct JD value.

Gregorian Leap Years:

So far, the computation considers a leap year every 4 years, which is true for the Julian calendar and its pre-Common Era negative proleptic extension, but not for years in the Gregorian calendar, where years are multiples of 100 are not leap years, unless they are also 400. This forces us to introduce a correction factor (B) for dates after 10/4/1582:

• SI Date ≤ 15/1852 (Julian calendar): B = 0

• SINO (Gregorian calendar): B = ENTERO_MENOR (Year/100) - ENTERO_MENOR(Year/400) - 2

Factor B computes the days corresponding to the years that are NOT leap years in the Gregorian calendar, that is, the multiples of 100 that are not multiples of 400, plus the 10 days of lag corrected with the change from the Julian calendar to the Gregorian calendar.

Until 1582 there are 15 multiples of 100 and 3 multiples of 400: (15 - 3) = 12 non-leap years according to the Gregorian reckoning. Since the first value of B for 10/15/1582 must equal 10 (no NON-leap years to correct for yet), we need to subtract 2 to convert the initial 12-day value to the desired 10-day value, which justifies the need to subtract 2 in the calculation of B.

The table shows the calculation steps for explanatory dates, with leap years marked in orange:

Table of example calculations.

J2000.0

In astronomy, J2000.0 refers to the Julian date 2451545.0 TT (Earth Time), or January 1, 2000, noon TT. It is equivalent to January 1, 2000, 11:59:27.816 TAI, or January 1, 2000, 11:58:55.816 UTC.

This date is widely used to indicate an instant in standard time for measuring the positions of celestial bodies and other stellar events. For example, although imperceptibly to the naked eye, the stars move in space, and it is necessary, to describe their position in the firmament, to specify the date to which said position refers.

Variants

See also

• Epoch (astronomy)