Template:JULIANDAY.JULIAN/doc

This template computes the number of the w:Julian day starting at noon on the date given in parameter (in the w:Julian calendar, including after the dates of transition to the w:Gregorian calendar).

It ignores the inaccuracies of the Julian calendar which occurred only one year after its creation in w:45 BC by Julius Caesar, with different and incorrect rules observed in various locations of the Roman Empire between w:44 BC and w:31 AD. The Julian calendar became then a standard (used from the 17th to the 19th centuries) only starting in w:32 AD after the Roman emperor Augustus had progressively applied the needed corrections.

So this template consider all years before w:32 AD as proleptic Julian years. The result is valid for all proleptic Julian calendar dates starting on March 1, 4801 BC at noon.


Syntax[edit]

{{JULIANDAY.JULIAN/doc|year|[month]|[day]|[hour]|[minute]|[second]}}
  • The year (required) must be astronomical (year=1 in 1 AD (Anno Domini), year=0 in 1 BC, year=-1 in 2 BC).
  • The month (optional, default value 1) is expressed between 1 and 12 from January to December (but offsets are possible for computing other years).
  • The year and month are first converted into a number of months, then rounded to the nearest integer to compute the actual year and month used for computing dates.
  • The day (optional, default value 1) is normally between 1 and 31 (but offsets are possible for computing other months). Decimals are possible for fractions of day.
  • The hour (optional, default value 12) is normally between 0 and 23 (but offsets are possible for computing other days). Note that Julian days begin at noon (hour = 12) and thus hours 0–11 of a solar day are one Julian day earlier than hours 12–23. The value may extend outside of the normal range and is considered as additional number of julian days (a Julian day is 24 hours or 86400 seconds exactly, ignoring any adjustment of leap seconds within the UTC calendar). Decimals are possible for fractions of hour.
  • The minute and second (optional, default value 0) are normally between 0 and 59 (but offsets are possible for computing other hours). Decimals are possible for fractions of minute or second.
  • All parameters can be any valid numeric expression which is evaluated before computing.

Note[edit]

The julian day, when computed modulo 7, grows from 0 (on Monday at noon) to 6 (on Sunday at noon)) and falls back to 0 (on next Monday). This corresponds to the order of days in the ISO week.

Limitations[edit]

Before March 4800 BC, the results may be offseted (by up to 365 or 366 days) due to the limitation of the MediaWiki #expr operators used in the implementation.

This limitation could be fixed (and the implementation simplified a bit) by using a - floor(a / b ) * b (now supported in expressions) or the more recent a fmod b, instead of a mod b already too limited in value range (and actually not used in this template), and instead of a - (a / b + 0.5 round 0) + b, as both are truncating their result towards zero, the equivalent of a ceil() when their parameter is negative.

This template was written and optimized to avoid all conditional expressions and to reduce the template expansions to their strict minimum (avoiding also the inclusion of complex templates for computing cyclic modulos, or euclidian divisions and roundings towards minus infinity), because #expr still does not support temporary local variables to store the template parameters and reuse their current value without more expansions.

All problematic negative values are normally avoided by avoiding excessively negative parameter values (using negative values is safe for the day, hour, minute and second parameters, but not safe for the month and year parameters if their resulting month falls before March 4800 BC).

Examples[edit]

  • {{JULIANDAY.JULIAN|-4800|2|29|23|59|59}} returns -32082.500011574 (proleptic) (in year 4801 BC), the result is still correct
  • {{JULIANDAY.JULIAN|-4800|3|1|0|0|0}} returns -32448.5 (proleptic) (in year 4801 BC), date where the result is false (the returned JD is too large by 365 days)
  • {{JULIANDAY.JULIAN|-4799|2|29|23|59|59}} returns -31717.500011574 (proleptic) (in year 4800 BC), the result is still correct
  • {{JULIANDAY.JULIAN|-4799|3|1|0|0|0}} returns -31717.5 (proleptic) (in year 4800 BC), first Gregorian date where the result is warrantied to be correct
  • {{JULIANDAY.JULIAN|-4799|3|1}} returns -31717 (proleptic) (in year 4800 BC), same date at noon
  • {{JULIANDAY.JULIAN|-4799|3|2}} returns -31716 (proleptic) (in year 4800 BC), tests the 1 day increment
  • {{JULIANDAY.JULIAN|-4713|11|24}} returns -38 (proleptic) (in year 4714 BC)
  • {{JULIANDAY.JULIAN|-4713|11|25}} returns -37 (proleptic) (in year 4714 BC)
  • {{JULIANDAY.JULIAN|0|1|1}} returns 1721058 (proleptic) (in year 1 BC)
  • {{JULIANDAY.JULIAN|0|12|25}} returns 1721417 (proleptic)
  • {{JULIANDAY.JULIAN|0|12|30}} returns 1721422 (proleptic) (Julian Anno Domini, first day in proleptic Julian year 1 AD, or December 30 in proleptic Gregorian year 1 BC)
  • {{JULIANDAY.JULIAN|0|12|31}} returns 1721423 (proleptic)
  • {{JULIANDAY.JULIAN|1|1|1}} returns 1721424 (proleptic) (Gregorian Anno Domini, in proleptic Gregorian year 1 AD, or January 3 in proleptic Julian year 1 AD)
  • {{JULIANDAY.JULIAN|200|2|28}} returns 1794166 (proleptic) (last day of Julian leap year 200 AD, not leap in the proleptic Gregorian calendar)
  • {{JULIANDAY.JULIAN|200|3|1}} returns 1794168 (proleptic) (first day where the Julian and proleptic Gregorian calendars are equivalent)
  • {{JULIANDAY.JULIAN|300|2|28}} returns 1830691 (proleptic) (last day where the Julian and proleptic Gregorian calendars are equivalent)
  • {{JULIANDAY.JULIAN|300|3|1}} returns 1830693 (proleptic) (first day of difference between the Julian and proleptic Gregorian calendars, in leap Julian year 300 AD, not leap in the proleptic Gregorian calendar)
  • {{JULIANDAY.JULIAN|325|3|21}} returns 1839844 (proleptic) (spring equinox observed at the Christian w:First Council of Nicaea, taken as a reference for aligning the Julian calendar to the proleptic Gregorian)
  • {{JULIANDAY.JULIAN|1582|10|14}} returns 2299170 (proleptic) (last proleptic Gregorian day, actually the 4th of October in the Julian calendar)
  • {{JULIANDAY.JULIAN|1582|10|15}} returns 2299171 (first non proleptic Gregorian day, equals the 5th of October in the previous Julian calendar)
  • {{JULIANDAY.JULIAN|1858|11|16|12|00|00}} returns 2400012 (start of epoch for the Reduced Julian Day, RJD)
  • {{JULIANDAY.JULIAN|1858|11|17|00|00|00}} returns 2400012.5 (start of epoch for the Modified Julian Day, MJD)
  • {{JULIANDAY.JULIAN|1968|05|24|00|00|00}} returns 2440013.5 (start of epoch for the NASA's Truncated Julian Day, TJD)
  • {{JULIANDAY.JULIAN|1900|2|28}} returns 2415091
  • {{JULIANDAY.JULIAN|1900|3|1}} returns 2415093
  • {{JULIANDAY.JULIAN|1995|10|10|00|00|00}} returns 2450013.5 (start of epoch for the last NIST's Truncated Julian Day, TJD mod 10000)
  • {{JULIANDAY.JULIAN|1999|12|31}} returns 2451557
  • {{JULIANDAY.JULIAN|2000|1|1}} returns 2451558 (the “Y2K bug's day” and millennium celebrations)
  • {{JULIANDAY.JULIAN|2000|2|29}} returns 2451617
  • {{JULIANDAY.JULIAN|2000|3|1}} returns 2451618
  • {{JULIANDAY.JULIAN|2000|12|31}} returns 2451923 (last day of the w:2nd millennium and of the 20th century in the Gregorian calendar)
  • {{JULIANDAY.JULIAN|2001|1|1}} returns 2451924 (first day of the w:3rd millennium and of the 21st century in the Gregorian calendar)
  • {{JULIANDAY.JULIAN|2023|02|25|00|00|00}} returns 2460013.5 (start of epoch for the current NIST's Truncated Julian Day, TJD mod 10000)
  • {{JULIANDAY.JULIAN|2024|4|30|0|0|0}} returns 2460443.5
  • {{JULIANDAY.JULIAN|2024|4|30|01|35|48}} returns 2460443.5665278
  • {{JULIANDAY.JULIAN|2024|4|30|11|59|60}} returns 2460444
  • {{JULIANDAY.JULIAN|2024|4|30|12.0}} returns 2460444
  • {{JULIANDAY.JULIAN|2024|4|30}} returns 2460444
  • {{JULIANDAY.JULIAN|2024|4|30|23|59|59}} returns 2460444.4999884
  • {{JULIANDAY.JULIAN|2024|5|1|00|00|00}} returns 2460444.5
  • {{JULIANDAY.JULIAN|2024|5|1|12|00|00}} returns 2460445
  • {{JULIANDAY.JULIAN|2024|5|1}} returns 2460445
  • {{JULIANDAY.JULIAN|2132|8|31}} returns 2500014
  • {{JULIANDAY.JULIAN|3501|8|15}} returns 3000025
  • {{JULIANDAY.JULIAN|5287|11|24}} returns 3652462 (10000 years lapse)
  • {{JULIANDAY.JULIAN|10000|1|1}} returns 5373558
  • {{JULIANDAY.JULIAN|26976|8|20|13|46|40}} returns 11574274.074074 (one trillion seconds lapse)


See also[edit]

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