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    Re: Longitude by Lunar Occultation
    From: Robin Stuart
    Date: 2020 Jan 4, 13:12 -0800

    Frank,

    Limb features are not included nor is the difference between the geometric centre and centre of mass of the Moon which would require incorporating librations. I am in good company here since this is also not included in NASA’s Eclipse prediction pages. The predicted times depend on the value of k, the ratio of the radius of the Moon to that of the Earth, that is chosen. There seem to be lot of different opinions as to which one is best and how to incorporate adjustments for irradiation etc.

    The aim of the spreadsheet was to produce a simple self-contained application that can produce a list of all possible occultations visible from any location within user defined constraints. There are 148 events potentially observable events involving stars of greater than 7th magnitude visible from Mystic 2020. This out of a total of 3750 worldwide.

    The second aim is to provide a platform to quickly and easily compute longitude from an occultation timing to an accuracy that better than human perception. The almanacs used to list the linear Besselian Elements but that doesn’t always get you to better than a second of time accuracy. Adding the quadratic terms puts you over that threshold. They can be turned on and off by a switch on the “Control” tab.

    As a disclaimer, I’m not seeking to do anything ground breaking or to push the limits of precision beyond what is normal in a nautical context. The aim was to build a convenient and easy to use tool to show what events are available and to perform the reduction. Although it was principally for my own education and use I’m happy to share it with anyone who might be interested in giving an occultation timing a try.

    You wrote: “The case you displayed with your graphic would actually be a grazing occultation”.
    I had thought that the ambiguous solutions I was getting from the code were due to grazes but that’s not what’s going on. If you look at the arrow showing the direction of travel of the Moon and account for the motion of the observer due to the Earth’s rotation, you see that the red dot will be fully hidden by the Moon. This is an effect that actually happens whenever the Moon’s projected disc first crosses a given parallel of latitude. There is initially just one point at that latitude where the star could be seen blinking out tem splits into two such points.

    Incidentally the spreadsheet does not use Raper’s method which I described in my seminar of Worsley’s calculations. It’s the much more straightforward Besselian elements approach,

    Regards,
    Robin

       
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