Julian date
A non-system unit · quantity: an instant in a continuous count of days
An astronomer who has to subtract one observation date from another finds himself in an awkward position: between them may lie months of unequal length, leap years, the ten days struck out at the passage to the Gregorian calendar, and, where ancient eclipses are concerned, several incompatible systems of counting years as well. The Julian date removes all this at a stroke, because it simply numbers the days one after another, without months and without a year zero: today runs the -th day from the beginning of the count, yesterday ran the one before, and the difference between two observations is found by subtraction.
Joseph Scaliger set the origin of the count at the first of January of the year 4713 before our era in the Julian calendar — not because anything happened there, but because at that point three calendar cycles used in chronology began together. He also made the day start at noon, and that proved a happy choice: a night of observing falls wholly within one whole number, whereas the calendar date changes in the middle of it. Such a count has one drawback, but a noticeable one: the numbers have passed two and a half million, and to avoid writing them out in full a shortened modified date was introduced in 1957.
01 · Definition
The Julian date is the number of days elapsed since noon of the first of January of the year 4713 before our era in the Julian calendar, with a fractional part counting off the portion of the current day. The whole number of days without the fraction is called the Julian day number, and to avoid writing seven digits one subtracts 2 400 000.5 from the date and obtains the modified Julian date, whose day already begins at midnight.
The day was made to begin at noon for the observer's sake: a night from evening to morning falls in the middle of a Julian day, and every record of one shift receives the same whole number, whereas in the calendar the date changes in the middle of that night. The modified date has its origin shifted to midnight precisely because it was meant not for a telescope but for radio tracking of satellites, where the shift works round the clock and it is easier to agree the records with the civil calendar.
The date is called Julian not after the Julian calendar but after Julius Caesar Scaliger, the author's father — an unfortunate coincidence, but nobody is going to correct it now. The origin itself Scaliger chose arithmetically: he took three chronological cycles, the solar of twenty-eight years, the lunar of nineteen and the cycle of indictions of fifteen, and looked for the year in which all three began together. The product of these numbers gives 7980 years, and the next such point will fall only in the year 3268.
The Julian date by itself does not fix a time scale but only a way of writing an instant, so in exacting work one states in which scale the fractional part is taken: JD(UTC) for observations, JD(TT) for ephemerides, and, when light curves are processed, a barycentric correction as well, since light from a star reaches different points of the Earth's orbit with a difference of up to sixteen minutes.
Move time with the slider in universal time and watch two marks: the golden one is the boundary of the Julian day at noon, the red one is civil midnight. While the telescope works, the red line manages to pass through the middle of the shift and the calendar date changes, whereas the golden one stays far aside, so that all the records of the night carry a single whole number.
Light from a distant star does not reach the Earth at the same time in January and in July: it crosses the diameter of the terrestrial orbit in sixteen and a half minutes. For the light curve of a variable star such a quantity is enormous, and therefore observations are referred to the centre of mass of the Solar System and written as a barycentric date, BJD. Neglect of this correction draws false changes of period which do not exist in the star itself.
02 · Conversion
Enter a date or a day number
Conversion between all the shortened forms is exact, since only a subtracted constant separates them from the Julian date. The calendar line is computed by the usual algorithm, but the scale of the fractional part depends on where the time was taken: JD in UTC and JD in terrestrial time differ today by 69.2 seconds.
Dates before 1582 the sheet reads in the Julian calendar, as is customary in chronology; the calendar switch is placed among the sheet's finer settings.
The fractional part of the Julian date and of the modified one are shifted by half a day, and hence a whole MJD falls at midnight while a whole JD falls at noon. An error of that half-day is the commonest in the processing of archival observations: it does not spoil differences within one series, but it moves the phase of a variable star by exactly half a period if series are stitched together.
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03 · Orders of magnitude
logarithmic scale: from a day to the whole period04 · Measuring instruments
What puts a date on an observation
For a century and a half the date of an observation was written into the logbook by hand, and the Julian day number was convenient for that precisely because it did not change in the middle of a shift. Archives of light curves of variable stars gathered in this way are still in use: without a continuous count it would be all but impossible to stitch nineteenth-century observations to present ones.
A sidereal day is shorter than a solar one by nearly four minutes, and the observer's clock ran by the stars so that the telescope could be pointed by right ascension without computation. But an observation cannot be recorded in sidereal time, since it will not serve for differences, and so a second clock, a civil one, always stood beside it, and it was the Julian date that went into the logbook.
In the header of every modern image stand the beginning and the end of the exposure, and for photometry the midpoint is taken. It is written as a modified date, since that is shorter and fits into an ordinary floating-point number without loss of digits, whereas the full Julian date eats up all the precision on its integer part.
An observation receives its date not from the clock on the wall but from a receiver catching the signal of a satellite system, and the accuracy of the stamp reaches tens of nanoseconds. The receiver gives time in the UTC scale, so the processor himself brings the fractional part of the date to terrestrial time, adding the current offset and the constant of 32.184 seconds.
05 · Writing rules
A date without its scale is incomplete
The designations are written in capitals without periods, and the number itself is separated by a space; the scale in which the fractional part is taken is given in brackets, since between JD in UTC and JD in terrestrial time lies more than a minute. Forms of the count are not mixed: the modified date has its own constant and its own midnight, and appending «JD» to it is not permissible even in a draft.
The first writing attaches to a modified number a designation not its own and moves the instant by two and a half million days. The second puts periods inside the designation, which is done neither for JD nor for MJD. The third loses that very half-day owing to which one form begins its day at noon and the other at midnight. And the fourth confuses the origins.
06 · Neighbouring units
Beside it stand all the shortened forms of the same count, devised for different tasks: the truncated date of satellite telemetry, the reduced date of old ephemerides, and also the count of seconds of the POSIX epoch, arranged on the same principle, only from another origin and in other units.
days from noon
days from midnight
five digits in telemetry
Of the Simetrium data sheets nearby stand the UTC, TAI and UT1 scales, which set the fractional part of the date, day as the unit of this count, year numbering, whose origins differ, and century, whose Julian form of 36 525 days enters the epoch formula.
07 · Historical section
A count invented for the sake of subtraction
A year after the Gregorian reform Joseph Scaliger published his work on the emendation of chronology, in which he proposed a count independent of any calendar. He placed the origin in the year where the solar cycle of twenty-eight years, the lunar of nineteen and the cycle of indictions of fifteen came together — so that every ancient date fell inside the period.
John Herschel in his «Outlines of Astronomy» showed how the chronological period is of use to an observer, and gave tables for the conversion. Astronomers adopted it quickly, because their task was exactly the one the count suited: subtract one date from another and obtain a number of days, thinking neither of months nor of leap years.
The tracking of the first artificial satellites was carried on by telegraph and on calculating machines, where every extra digit cost money and errors. Then 2 400 000.5 was taken from the Julian date, removing two million at once and shifting the beginning of the day to midnight, and the resulting modified date became the standard for every service working round the clock.
Every frame of a survey telescope carries in its header the modified date of the middle of the exposure, while catalogues of variable stars give the epoch of maximum as a full Julian date. The count has outlived a calendar reform, a change of time scales and the passage from the photographic plate to the detector, because it describes nothing but the ordinal number of the day.
A quantity with neither a standard nor an error
The Julian date cannot be measured, and there is nothing in it to verify: it is not a property of the world but a way of numbering, and its correctness is secured by arithmetic, not by an instrument. All that can go wrong lies in the fractional part, where real physics appears: there one must know in which scale the time was taken, whether the offset of the atomic clocks was allowed for and whether the instant was referred to the centre of mass.
That is what explains its long life. Calendars were replaced, ten days were struck out by decree, seconds were inserted and are now to be abolished, while the ordinal number of the day went on its way, answering to none of it. An observation recorded as a Julian date in 1860 is subtracted from a present one without a single correction for reforms — and that is exactly what was wanted.
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