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for any a.d. Gregorian calendar date [with a correction, provided by E.M. Standish (private correspondence to EFM) and we note that adding 1 to the answer gives a closer approximation near Oct. 15, 1582, and for the past century], and

Here, subtracting 1 gives a closer result over much of the range for any Julian calendar date. See Van Flandern and Pulkkinen (1979) for a Fortran version (which needs updating). Montenbruck (1989, p. 34) gives a more general formula for calculating JDN, which makes use of auxiliary parameters that are computed from the Y, M, and D numbers and are different for the Gregorian and Julian calendar dates. Such equations provide useful checks on calculations of intervals between events. As an example, consider January 1, 4713 b.c. (Julian calendar16):

The earliest use of the term yuga was for an eight-year period.

16 The Julian calendar is usually applied up to and including the date Oct. 4,1582, the day before the Gregorian calendar was first introduced (in some countries). The latter day was Oct. 5, 1582, in the Julian calendar but Oct. 15, 1582, in the Gregorian. Formally, the Julian calendar came into effect on Jan. 1, 45 b.c. However, back-calculations of both Gregorian and Julian calendar dates are frequently done.

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