sidereal.py: Internal maintenance specification

The number B is used in Section 14.3, “SiderealTime.utc(): Find Universal Time” and Section 14.7, “SiderealTime.fromDatetime(): Convert UTC to GST (static method)”. The algorith is given in section 12 of Duffett-Smith. It is a function of the year, and expresses the GST at 0:00 on January 0 of the year.

# - - -   S i d e r e a l T i m e . f a c t o r B

#   @staticmethod
    def factorB ( yyyy ):
        """Compute sidereal conversion factor B for a given year.

          [ yyyy is a year number as an int ->
              return the GST at time yyyy-01-00T00:00 ]
        """

Step 1: “Calculate the Julian date of January 0.0 of year in question.” Unfortunately, we can't just blithely pass the datetime.datetime() constructor that date, because it's not a proper date (“ValueError: day is out of range for month”). So we'll get around that by finding the JD of Jan. 1, converting it to a float, and subtracting 1.0.

        #-- 1 --
        # [ janJD  :=  the Julian date of January 0.0 of year
        #              (yyyy), as a float ]
        janDT  =  datetime.datetime ( yyyy, 1, 1 )
        janJD  =  float(JulianDate.fromDatetime(janDT)) - 1.0

Steps 2–4 are exactly as described in Duffett-Smith, except that we rearrange the polynomial (6.646 065 6+(2400.051 262×T)+(0.000 025 81×T²) to the computationally more straightforward form.

        #-- 2 --
        s  =  janJD - 2415020.0

        #-- 3 --
        t  =  s / 36525.0

        #-- 4 --
        r  =  ( 0.00002581 * t +
                2400.051262 ) * t + 6.6460656

Step 5: “Calculate U=R-(24×(year-1900)).” Step 6: “Subtract U from 24. This is B.”

        #-- 5 --
        u = r - 24 * ( yyyy-1900)

        #-- 6 --
        return 24.0 - u

    factorB = staticmethod(factorB)