Era Bases and Day Numbers

For keeping track of time over intervals longer than a year, era bases are used. They permit the reckoning of the number of days (as do the Julian Day Numbers of our present era) or the number of years from a particular event in the past. The year of the accession of a king was one traditional way of maintaining records. Thus, in Mesopotamia, the era of Nabonassar began on Feb. 26,747 b.c., which had been back-calculated as the beginning of the first year of the reign of Nabonassar. Ptolemy used the Nabonassar era base because that was the era from which his oldest observational data came. The Greeks and other Near-Eastern cultures used the date of the royal accession of Seleukos Nikator, one of Alexander's generals, as year 1; in the case of Seleukos, however, this became the base of an era count that continued into the medieval period, and even later. Year 1 of the Seleucid era base begins at 312 b.c. The dynasty itself lasted from 312 to 64 b.c.

An important era base was that used by the Roman Empire—the founding of the city of Rome (753 b.c., according to a calculation of the birth of Christ by Dionysius Exiguus, writing in the 6th century)—a date adopted by the Synod of Whitby in 664 a.d. The use of this era base is identified by the phrase ab urbe condita ("from the founding of the city") or AUC.

The modern era base is also derived from the medieval calculation of the birth of Christ, hence, the designation for subsequent years, Anno Domini (now often referred to as the "Christian era" or "Common era," either abbreviated CE). In a later section, when we discuss the nature of the star of Bethlehem, we will review the evidence concerning the historicity and dating of that event. The base of the Christian era is the year 1 a.d. (or a.d. 1). The year before 1 a.d. is 1 b.c. Thus, the year 1 b.c. is 753 AUC, and the year 1 a.d. is 754 AUC. Many calendricists and astronomers, to maintain a mathematically continuous flow of time, refer to the year 1 b.c. as year 0. The year 2 b.c. is thus the year -1, and so on. Although this is not normal practice among historians, calculations are much easier when no discontinuity occurs in the middle of the count. Regardless of which technique is used, the relationship is given by x = y +1,

where y = lyl, is the absolute value of the negative date and x is the b.c. date.

Another important era base is the Kaliyuga (also Kali Yuga or Kalyuga) era base used in India. The word "yuga" means cycle, but it now has another, more specific meaning as a particular interval of length: 4,320,000 years.15 It is one of about 20 time divisions, the smallest of which is the time for a sharp needle to pierce the petal of a lotus flower [~1/10,000 of the "twinkling of an eye" to "100 years of Brahma", i.e., Brahma's lifetime (an interval of time amounting to -3.135-1014 years)]. This cycle length exceeds by more than 15,000 times the modern scientific determination of the age of the known universe. The present Yuga is called "Kali." The Kaliyuga was supposed to begin when the Sun, Moon, and planets were at the vernal equinox. Ginzel (1906, p. 338) gives this date as either JDN 588 465 or 588 466, actually midnight, Thursday, February 17, 3102 b.c., or sunrise, Friday, February 18, 3102 b.c., at the meridian of Ujjain (see below for the definition of JDN). It appears that Ginzel applied the difference between Julian and Gregorian calendar dates in the wrong direction, however. The correct corresponding dates for the vernal equinox in 3102 b.c., would be April 16 and 17, in the Julian calendar. Unfortunately, it appears that a mass conjunction did not take place at either set of dates, but a broadly-defined "conjunction" occurring at other times in the year cannot be excluded. Of course, if the event were purely back-calculated, the actual occurrence is not critical to any astronomical or historical purpose. The Kaliyuga era base was used also as the start of a count of days (comparable to a Julian Day Number) by all Indian astronomers after Aryabhata (see §9).

The Astronomical Almanac lists the chronological eras and cycles in various historical calendars. In addition to announcing the start of the new year from the different era bases, it notes also the ecclesiastical parameters that are used to regulate some church calendars, for example, The "Dominical Letter (the letters A to G represent the first day of the year that falls on a Sunday; e.g., if January 2, the Dominical Letter is B)," the "Epacts (a set of numbers, indicating the Moon's age at the beginning of the year)," and the "Golden Number (year in a 19-year cycle)" of lunar cycles. Further discussion of these topics we leave to Ginzel (1906) and others.

One era base used by present-day astronomers is that from which the Julian Day Numbers (JDN) are measured: January 1, 4713 b.c. (Julian calendar). The JDN system was invented by Julius Caesar Scaliger (1484-1558). The JDN begins at noon, U.T., on the day beginning at the preceding midnight. Noon of the date December 31, 1949, was the onset of JDN 2,433,282, and on noon, December 31, 2050, the JDN will be 2,469,807; the difference in numbers of days between these two dates is exactly 36,525d. This scheme is extremely useful in computations that involve large intervals of time. Note that the JDN is not strictly speaking a calendar date; it is a tally of days. Despite widespread usage among astronomers of the term "Julian Date" for JDN (for example, in the Astronomical Almanac, in the 2000 edition on p. K4), under no circumstances should it be confused with the Julian Calendar. An interesting byproduct is that the integer remainder after division by seven yields the day of the week on which the JDN begins: 0 = Monday, 1 = Tuesday, ..., 6 = Sunday. For example, on noon of January 1, 2000, JDN = 2451545.0000, which modulo 7 (an operation that is equivalent to dividing by seven and multiplying the decimal portion of the quotient by seven), the JDN remainder is five, and thus indicates a Saturday, which a glance at a calendar will confirm. In addition to the Astronomical Almanac, the Handbook of the Royal Astronomical Society of Canada also lists the JDNs for the various Gregorian calendar dates for the year of publication (but unlike the AA, only for a few other years). Formulae given by Muller (1975) and reproduced by Stephenson (1997) relate the JDN to Gregorian and Julian Calendar dates (expressed in Y year, M month, and D day number format) by the following approximation:

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