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    Re: Zubenelgenubi occultation
    From: Antoine Couëtte
    Date: 2022 Jan 20, 04:29 -0800

    RE : http://fer3.com/arc/m2.aspx/Zubenelgenubi-occultation-Walden-jan-2022-g51921

    Dear Dave,

    In reply to your Zubenubi occultation quizz, please find one solution here-under.

    (1) Can you get a line of position ?

    Our line of position is at the intersection of a cylinder of radius equal to the Moon Semi-Diameter - i.e. 1,738 km - with it Axis being the Zubenubi - Moon Center line.

    Assuming no refraction and spherical Earth, this Axis crosses Earth surface near the following points (see screen capture as 1st Attachment) :

    - At 11:05:48 near N47°50.4' / W136°44.3' off the California Coast

    - At 12:27:22 near N18°27.2' / W 097°24.9'  near the City of Puebla, State of Puebla in Mexico.

    This information is useful as it reminds us that this Axis-Earth intersection moves to a South-Easterly direction (good to remember) at a Longitude rate here close to 28.9°/h and that by its midpoint, we should derive positions which are definitely occulted by Lady Moon.

    (2) Where are you ?

    After devising differents types of solutions, I fully explored the following one which is both graphical and iterative convergent. It also has the advantage of working directly on the Earth Ellipsoid, with refraction as well as any Observer's Altitude as may be fit.

    2.1 - First iteration (see hand drawn sketch as 2nd Attachment)

    2.1.1 - At Latitude N 36°

    11h05m48s immersion at W108°23.4' and 12h27m22s emersion at W104°59.3'

    2.1.2 - At Latitude N 34°

    11h05h48s immersion at W108°34.9' and 12h27s22 at 107°11.5'

    Draw the equal altitude lines (see 2nd Attachment) which intersect at N32°38' / W108°42' a position in New Mexico for which we find : immersion at 11h06m02s and emersion at 12h26m56s.

    We need to do better.

    2.2 - Second iteration

    We can now better "bracket" our position. And this time from Google Earth we add Altitude = 1,400 m

    2.2.1 - At Latitude N 33°

    11h05m48s immersion at W108°44.5' and 12h27m22s emersion at W108°06.8'

    2.2.2 - At Latitude N 32°30'

    11h05h48s immersion at W108°50.5' and 12h27s22 emersion at 108°32.7'

    Same kind of sketch (not included here) to end up with N32°03' / W108°56' still in New Mexico.

    Given the significant curvature of the emersion curve, we are going to do our second check for N32°00.0' / W108°57.0' with this time updated Google Earth Altitude at 4,500' and a QFE equal to 850 hPa.

    And we get Immersion at 11h05m49s and emersion at 12h27m22s

    Good enough (for GVT purposes) this time.

    Hence I am submitting the position N32°00.0' W 108°57'0 as my own solution.

    Result Accuracy ? The Ephemeris I am computing are accurate to +/- 4" for GHA, DEC and HP. Given the relative configuration of these both Lunars, I am (wet finger) guessing that the occultation times have a maximum error of 12 s of time, hence a position uncertainty of up to 4' in Longitude and 2' in Latitude. And by the way, I am observing that Position N32° / W 109° is included in this uncertainty circle.

    Strange ...

    Thanks again, Dave


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