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    Moon ephemeris: Meeus vs. JPL
    From: Paul Hirose
    Date: 2015 Oct 24, 22:17 -0700

    In "Astronomical Algorithms" (1st edition, chapter 45) Jean Meeus has a
    method to compute the Moon's geocentric apparent place. He claims an
    accuracy of 10 arc seconds in ecliptic longitude and 4 seconds in latitude.
    I compared his algorithm to the Jet Propulsion Laboratory DE422
    ephemeris at several hundred random times in the 21st century. The root
    mean square angular separation between Moon positions calculated with
    these methods was 3 arc seconds. His accuracy seems comparable to the
    Nautical Almanac. If this performance is confirmed in more extensive
    tests, I may add the Meeus routine to the next release of my SofaJpl
    astronomy DLL. It has the self contained SOFA ephemerides for the Sun
    and planets, but lacks anything for the Moon.
    One annoyance is that the angles in the Meeus formulae are in degrees,
    so you have to convert to radians if an angle is a trig function
    parameter. I don't understand why he did that, especially since in the
    first chapter Meeus says, "There is the added complication that most
    computers can calculate only in radians, not in degrees. It is an
    infernal nuisance having to convert degrees to radians all the time, but
    on most computers this has to be done before calculating a trigonometric
    function of an angle given in degrees."
    Well, yes, if your fundamental angles are computed in degrees it is an
    infernal nuisance! Initially I neglected to convert his additive angles
    A1, A2, and A3 to radians.
    I will say this for Meeus, he includes an example and gives the values
    of several key quantities. Thus I was able to debug my code without
    trouble. The discrepancy was only an arc minute or so, but I was sure
    that was too much. After correcting my code, it matched his values
    within a few millionths of a degree.
    In the same set of tests I also compared geocentric positions of the
    Moon in the 21st century as computed by the JPL long term ephemerides
    DE406 and DE422. Root mean square difference in position was only .01
    arc second. For years I have used the old (1997) DE406 as my main
    reference, and based on this limited test I haven't missed much, at
    least in epochs not far from the present.

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