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Modified Julian Day

On this page, you can learn about the Gregorian and Julian calendars, and how they relate to the Julian Day and Modified Julian Day numbers used in Teletext. There is also a form-based conversion page which enables you to freely convert between these various systems.

Julian Day

Astronomers and other people who need to deal with events separated by a large span use the Julian Day to refer to time, rather than a date in a particular calendar. The Julian Day is a number which simply increases by 1 every mean solar day. Because there are no discontinuities in the count, the elapsed time between two events expressed as Julian Day numbers can be found by simple subtraction.

Julian Day numbering was invented in 1583 by the French scholar, Joseph Justus Scaliger. He constructed the Julian Period, an interval of 7980 years, based on three cycles of years: the 28-year solar cycle (the time taken before the days of the week next align with the Julian year), the 19-year lunar cycle (when the phase of the moon aligns with the days), and the 15-year Roman indiction cycles (used for taxation, census and other legal purposes which continued to be used in to the Middle ages). Assuming all dates are reckoned in the Julian calendar, for which it was named, the Julian period began at 12 noon, 1st. January 4713 BC and will end end at 12 noon, 1st. January 3268 AD, when all three cycles will once again co-incide. Days are numbered consecutively from zero within the Julian Period, without any subdivisions in to months or years.

Here are some Julian days for some interesting dates:

	Gregorian Date		Julian Day	   MJD
	    Noon 1752-09-14	2361222
	    Noon 1858-11-16	2400000
	Midnight 1858-11-17	2400000.5	     0
	    Noon 1858-11-17	2400001		     0.5
	Midnight 1900-01-01	2415020.5	 15020
	    Noon 1996-09-03	2450330		 50329.5
	Midnight 2000-01-01	2451544.5	 51544
	Midnight 2100-01-01	2488069.5	 88069
	Midnight 2132-08-31	2499999.5	 99999
	Midnight 2132-09-01	2500000.5	100000

Although the Julian Day is very useful for astronomical purposes, it does have some drawbacks:

it begins at noon, rather than at midnight as is civil convention. This offset of 0.5 day makes it awkward to talk about calendar days as single Julian day numbers.
it is rather long, with all the dates in the current and next centuries beginning with the decimal digits``24''.

To remedy these two inconveniences, the Modified Julian Day is defined as the Julian Day minus 2400000.5. Thus MJD 0 is at midnight between the 16 and 17 November 1858 AD Gregorian. For any date in the 20th. and 21st. centuries, the MJD will be at most five decimal digits long.

The Julian Calendar

Before Gaius Julius Caesar (654--710 AUC, 100--44 BC) and the Julian Calendar named for him, the Romans counted years of 355 days ab urbe condita, from the building of the city of Rome. 1 AUC is conventionally taken to be 753 BC, but as we shall see, the correspondence between days and years was sometimes a little confused. Because the Roman year was 10 days short with respect to the solar year, the start of the year quickly got out of step with the constellations. The priesthood arbitrarily added and subtracted days and even months which helped things drifting too far, but even so, by 708 AUC (46 BC) the year was well out of phase with the seasons.

For several years since his triumph over Pompey in 705 AUC (49 BC), Julius Caesar had been in increasingly complete command of Rome, regarded as semi-divine, and Emperor in all but name. Caesar was also a gifted astronomer, and well aware of the difficulties the existing calendar caused. He decreed that 708 AUC (46 BC) should be lengthened to 445 days in order that his new calendar be inaugurated in step with the constellations on 1st. January, 709 AUC (45 BC). His new calendar had a year of 365 days plus a leap year every fourth year with 366 days. This made the average length of the year 365.25 days, a good approximation to the real length of 365.24219 days, and the Julian calendar continued almost unchanged for many centuries.

Julius Caesar's nephew and adopted heir, Gaius Octavian Augustus (691--767 AUC, 63 BC--14 AD) became first Roman Emperor in 727 AUC (27 BC) and renamed the month Quinctilis to Augustus and stole a day from February to give his month 31 days. The base date for the calendar was moved from the founding of Rome to various dates of local importance, and it was not until the 6th. century AD when the scholar Dionysius Exiguus made a study of Easter days that the Anno Domini epoch we now use came in to being.

The Gregorian Calendar

Although small, the Julian Calendar's error of 0.0078 days per year mounted up over the centuries until by the late 1500s, the error was a noticeable 12 days. So in 1582, Pope Gregory XIII (1572--1585) decreed that the day after the 4th. October 1582 would be 15th. October 1582, and henceforth century years would not be leap years unless they were also divisible by 400. England did not adopt the Gregorian calendar until 1752, when the 2nd. September (Julian) was followed by the 14th. September (Gregorian).

Conversions

To explore these calendar systems further, a form-based conversion page is available, which allows dates in the Julian or Gregorian calendars to be converted to and from Julian Day and Modified Julian Day numbers.

This page was created on MJD 50329. It was last updated MJD 50376.9.
Please send comments to Robin O'Leary pdc at ro dot nu