Chronological Julian Dateby Peter Meyer

The

astronomical Julian dateis the number of days and fraction of a day which have elapsed since noon GMT on -4712-01-01 in the proleptic Julian Calendar (January 1st, -4712 JC or 4713 BCE). For example, for 17:13 GMT on 2007-01-19 CE the corresponding astronomical Julian date is 2,454,120.2176.For exact calendrical studies and for the development of calendar software a different real number concept for days is needed, since (i) simply assigning an integer to a day is not precise enough, and (ii) days (nychthemerons, 24-hour periods) in most calendars do not start at noon.

The astronomical Julian date is OK for astronomers, but calendrical scientists normally work with days which begin at midnight (thus the date does

notchange at noon).Also a concept is needed which can be used with calendars in which (i) nychthemerons begin at midnight, but not midnight GMT (the major instance being the Chinese Calendar) and (ii) nychthemerons do not begin at midnight.

Thus arose the concept of the

chronological, as opposed to theastronomical, Julian date.It is important to note that there are three separate concepts:

- Julian day number (an integer)
- Astronomical Julian date (a real number)
- Chronological Julian date (a real number)
The astronomical Julian date was defined above as the time elapsed since noon GMT on -4712-01-01 JC. An informal definition of the Julian day number (JDN) is: The number of days elapsed since ‑4712-01-01 JC. On -4712-01-02 JC one day had elapsed since ‑4712-01-01 JC, thus the JDN of -4712-01-02 JC is 1, from which we may conclude that the JDN of -4712-01-01 JC is 0. A more exact definition is given below.

The

chronological Julian date in the GMT timezoneis the number of days and fraction of a day which have elapsed since midnight GMT at the start of -4712-01-01 in the proleptic Julian Calendar. For example, for 17:13 GMT on 2007-01-19 CE the corresponding chronological Julian date is 2,454,120.7176.This concept of a chronological Julian date refers to a particular timezone, so it is more generally stated as:

The

chronological Julian date at a particular timezoneis the number of days and fraction of a day which have elapsed since midnight in that timezone at the start of -4712-01-01 in the proleptic Julian Calendar. For example, for 01:13 Beijing standard time on 2007-01-20 CE the corresponding chronological Julian date is 2,454,121.0509.The

Julian day numberis the 'floor' of the Julian date (where the floor function is 'the largest integer not larger than', which is simply the integer component for non-negative Julian dates). Thus the JDN at 17:13 GMT on 2007-01-19 CE in London is 2,454,120, whereas the JDN at 01:13 in Beijing on 2007-01-20 CE is 2,454,121. (Note that the dates are relative to the place where the calendar is being used.)Thus the astronomical Julian date is a real number which is timezone independent, whereas the chronological Julian date is timezone-dependent. Since the JDN is defined in terms of the chronological Julian date, the concept of the JDN is also timezone-dependent.

When the concepts of 'chronological Julian date' and 'Julian day number' are used with no reference to a timezone then the timezone defaults to GMT.

The main difference between the concepts of astronomical and chronological Julian dates is not that they differ by 0.5 days (in the GMT timezone), but that one is timezone-dependent and the other is not. A non-timezone-dependent chronological Julian date would introduce unnecessary difficulties into working with calendar dates in calendars whose nychthemerons begin at midnight other than GMT.

The necessity for the distinctions drawn above becomes evident when one studies the Chinese Calendar. In this calendar (when used in the timezone of China, rather than, say, Vietnam) nychthemerons begin 8 hours earlier than those in the GMT timezone, so we have:

chronological Julian date CCT

= chronological Julian date GMT + 1/3

= astronomical Julian date + 1/2 + 1/3

= astronomical Julian date + 5/6

So, for example, we have the following equivalences:

2007-02-10 CE 03:53 GMT 2,454,141.6617 AJD (astronomical Julian date) 2,454,142.1617 CJDL (chronological Julian date London) 2,454,142 (chronological Julian day number London) 2,454,142.4951 CJDC (chronological Julian date Beijing) 2,454,142 (chronological Julian day number Beijing)

2007-02-10 CE 18:53 GMT 2,454,142.2867 AJD (astronomical Julian date) 2,454,142.7867 CJDL (chronological Julian date London) 2,454,142 (chronological Julian day number London) 2,454,143.1201 CJDC (chronological Julian date Beijing) 2,454,143 (chronological Julian day number Beijing)

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