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    Longitude by Lunar Occultation
    From: Robin Stuart
    Date: 2019 Jan 8, 08:27 -0800

    Having spent a great deal of time analysing the occultations in Worsley’s log book I thought it only right that I should try it for myself. In an earlier post I described my experiments with Skyfield. Because Skyfield can easily generate high precision positions for the Moon based on JPL Ephemerides and access the entire Hipparcos catalog this makes it an ideal tool to search for possible occultation and compute their Besselian elements and other data needed to accurately calculate local circumstances and find longitude.

    I have put together an Excel spreadsheet that does this. The one attached here has precomputed data for 2019. It’s currently set up to compute positions at Mystic Seaport. Enter your position on the “Control” tab, hit “Clear Local Circumstances” then “Compute Local Circumstances” to see a list of possible events at your location. When an occultation has been observed enter the required information on the “Find Longitude” and click the button. Either GMT or Local Mean Time is required. In Worsley’s case, latitude by meridian and local mean time by time sight, carried forward by the chronometer, were used. I have used the spreadsheet to replicate all 10 occultation reductions given in Worsley’s log. The modern user probably has a pretty good handle on GMT but may have neglected to take a time sight observation prior to the occultation. For such an individual it is possible to select and enter “Greenwich Mean Time” for the event directly. From a purely practical standpoint immersions on the dark limb of the Moon are the most easily time which means that the Moon should be waxing.

    From my location, 4th magnitude xi2 Ceti was to be occulted on 18 December, 2018 at around 17:57 local time. I set up a small telescope and watched the star approach the dark limb of the Moon. Then unceremoniously at 17:37:13 it wasn’t there anymore. This is to be compared to the predicted time of 17:37:13.3. My longitude comes out to be correct to 12.5" of longitude or about 1/6 of a nautical mile. To be realistic this is likely something of a fluke. There are some effects that I have not and do not intend to take into account. The geometric centre of the Moon is known to be offset by about 0.6" from its centre of mass and I use linear Besselian elements which approximates path of the Moon across the fundamental plane as a straight line. Also the result you get depends somewhat on the value adopted for, k, the ratio of Moon’s radius to that of the Earth. I use the value k = 0.2726 as recommended by the 1915 Nautical Almanac.

    In any event I’m making this spreadsheet available for anyone interested in experimenting with occultations. I think it has been fairly well shaken down but please let me know if use it and find an odd behaviour,

    Robin Stuart

    File:
    OccultationCalc2019.zip
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