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    Re: 1901 May, 22 Lunar example by French Navy Captain Arago
    From: Antoine Couëtte
    Date: 2010 Feb 22, 03:55 -0800

    Feb 22, 2010

    Dear Paul,

    As regards our now well known Mar 02, 1901 occultation example, and in further and complementary reply to your both posts hereafter :

    - #11684 dated 30 Jan 2010 15:10 ,and

    - #11803 dated 06 Feb 2010 16:46,

    first of all, thank you very much for your replies which I found extremely interesting.


    Thank you also Frank for your very valuable insights in Navlist # 11804 dated 6 Feb 2010 20:24


    Paul, in Navlist #11684, you gave the following information on your geocentric position computations :


    estimated time:
    1901-03-02T22:43:38.40 UT1
    1901-03-02T22:43:37.17 Terrestrial Time
    -1.235 seconds delta T


    geocentric coordinates (true equator and equinox):
    9h01m43.73s +11°47'53.5" Moon RA and dec.
    15'10.0" apparent semidiameter
    9h02m25.79s +11°03'44.2" kappa Cancri RA and dec.
    0'00.0" semidiameter


    Your k CNC position has been derived from the Hipparcos Catalog. From the NGC catalog, I find a position which is almost 1" apart in RA, which would already account for a possible error of 2 seconds of time in my results. This difference in RA between our both results is well above anything I could expect. Would you then indicate the relevant k CNC Hipparcos data (most preferably referred to 2000.0 rather than to 1991.25), or at least be so kind as to tell me where I can find them on the net. BTW, what is k CNC Hipparcos Ref # ?


    In Navlist #11803, you indicated :


    I can make one small improvement. The Astronomical Almanac eclipse
    predictions have adjustments of +.5" in the Moon's longitude and -.25"
    in latitude to correct for the difference between its center of mass and
    center of figure. My program has an option to apply that adjustment, but
    I normally disable it to make the output compatible with other programs.
    With the option enabled, the occultation is 1.7 seconds earlier. In
    Paris astronomical time, the results are:

    10:53:17.3 Arago
    10:52:59.3 Hirose (no corrections)
    10:52:57.6 Hirose (with corrections)


    Yes, I am also using this correction since a Navigator is concerned much more with the Moon geometrical Center rather than to its gravity Center.

    Now, since you seem using DE405 full theory which (and unless I am mistaken) does include Libration, I would have thought that you would be using its exact Libration values which accordingly would enable you to compute the exact apparent topocentric difference between both geometrical and gravity centers. You instead seem to be using the NA "approximate" correction which you earlier quoted. True ... and I still confess that for our current application here, this is a most minor point.

    The results I am currently finding - given the NGC position currently used for k CNC as addressed hereabove - are :

    with delta T = -1.1 s

    IMMERSION at UT=22h43m33.4s, with translates into Paris Time = 10h52m54.3s, which is 3.3 s from your results, and

    EMERSION at UT=23h59m31.4s, which translates into Paris Time = 12h08s52.3s

    Would you be so kind as to compute Emersion too on your side so that we can compare results.


    In Navlist #11684, I noticed that you can enter an observer's altitude. So I went to find another Occultation example, this time on a "more conventional" Star, i.e. Aldebaran, so that we can also compare results with Frank's On Line Lunar Computer used this time as an "Occultation Computer".

    The example I am quoting hereafter is an excerpt from our Great Jean Meeus, whom I admire very much for all his numerous and outstanding contributions in widely disseminating and spurring public interest into computational astronomy.

    In his "Astronomical Tables of the Sun, Moon, and Planets", Copyright 1983, ISBN 0-943396-02-6 and Edition 1983 (?) which I own and which is a GREAT book, we can find on pages 5-8 and 5-9 the following example :

    Occultation of Aldebaran, 1997 October 19, at Palomar Mountain Observatory, for which we have :

    Lat = N +33°.3562, Lon = + W 116°.8640, Altitude + 1 706 m (above ellipsoid),

    delta T = +68s

    For IMMERSION, Jean Meeus finds UT = 07h44m41s, and
    for EMERSION, he finds UT = 09h02m44s

    You will find here-under the results I am computing through using Hipparcos Star # 21421 (Aldebaran).

    With delta T = +68s and Altitude +1706 m, I find :

    IMMERSION TIME : 07h44m40.5s and EMERSION TIME : 09h02m40.4s


    You will have noticed that this example is quite difficult to compare "per se" to Frank's On Line Lunar Computer results since Jean Meeus's 1983 best predicted then delta T value for 1997 (+68s) is significantly greater than the subsequently observed one (close to +62.8s).

    So, I have reworked Jean Meeus's example as follows :

    I am using delta T = 62.8 s, which I am guessing/feeling is much closer from your own value and FER's On Line Computer value, and I reworked this example for 3 different altitudes :

    - (fictitious) Altitude = 0 meter, and

    - (true) Altitude = +1706 m, and

    - (fictitious) Altitude = +4000 m in order to best see altitude
    effect on occultation times in this example.

    Here are my results


    Alt = 0000 m / 0000 ' UT = 07h44m48.2s UT = 09h02m51.8s

    FER's Computer results : dist=-0.1', Lon=2.9' dist=-0.2', Lon=5.3'


    Alt = +1760 m / 5597 ' UT = 07h44m47.3s UT = 09h02m21.2s

    FER's Computer results : dist=-0.1', Lon=3.0' dist=-0.2', Lon=5.1'


    Alt = +4000 m / 13123 ' UT = 07h44m46.2s UT = 09h02m50.3s

    FER's Computer results : dist=-0.1', Lon=3.0' dist=-0.2', Lon=4.9'


    Well, ... when I compare my results with Frank's On Line Computer results, I am getting differences up to ... 0.2' for distances and 5.1' for Longitudes in the case of the Emersions. It is true that I cannot fully check my numbers against Frank's ones since I cannot enter tenths of seconds of time on his On Line Computer, and I am also restricted to tenths of arc minutes. This constraint certainly may have a significant, but quite limited effect here, but ...

    ... Given the fact that for "conventional" Lunars, I always get within 0.3' of FER's results for Longitude differences, which always equate to 0.0' in Distances, I am just surprised that for occultations, our differences are so (relatively) important.

    Such differences would almost amount to being quite frightening !!! :-)))

    So, and if you have time, would you be so kind as to fully rework the hereabove examples and give your results so that we may have a fully independent third party check on this example.


    Dear Paul, thank you again for your Kind and Courteous Attention, and Best Regards from

    Antoine M. "Kermit" Couëtte

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