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    Re: Henning Umland's long term almanac. Is it wrong?
    From: Paul Hirose
    Date: 2016 Feb 26, 13:19 -0800

    On 2016-02-25 21:43, I wrote:
    > Henning's code is based on the work of Jean Meeus (Astronomical
    > Algorithms, ch. 45, Position of the Moon). Meeus says, "To avoid working
    > with large angles, reduce them to less than 360°.". Perhaps he's
    > unnecessarily fussy. I wrote a complete implementation of the same
    > chapter and reported results last October:
    > http://fer3.com/arc/m2.aspx/Moon-ephemeris-Meeus-vs-JPL-Hirose-oct-2015-g33245
    > My code doesn't normalize any angles.
    I added an option to normalize the five fundamental angles that are
    obtained from polynomials. For instance, the Moon's mean longitude
    polynomial contains the term 481 267.881 342 36 * T, where T is the
    number of centuries since 2000 Jan 1. Consequently it generates a great
    number of multiples of 360 unless the date is near the turn of the
    My program tests 1000 random times in each century and reports the root
    mean squared error in the Moon geocentric apparent place compared to the
    JPL DE422 ephemeris. Results:
                   Meeus  Meeus*
    1800 - 1899    3.1″   3.2″
    1900 - 1999    2.9    2.8
    2000 - 2099    2.9    2.9
    * Moon mean longitude, mean elongation of the Moon from the Sun, mean
    anomaly of the Sun, mean anomaly of the Moon, and Moon's argument of
    latitude are all put in the range 0 - 360°.
    In each century the two columns come from separate runs of the program,
    and therefore are calculated from different sets of random dates.

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