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    Re: Navigation Spreadsheets in 2022
    From: Robin Stuart
    Date: 2021 Nov 14, 12:03 -0800

    Issues concerning the proper motion of binary stars arose recently when reanalyzing the occultation timings made by Shackleton's Imperial Trans-Antarctic Expedition. These were performed in order to rate the chronometers while their vessel, Endurance, was trapped in the ice of the Weddell Sea over the winter of 1915. They had been previously examined in the paper https://www.canterburymuseum.com/assets/DownloadFiles/Navigation-of-the-Shackleton-Expedition-on-the-Weddell-Sea-pack-ice.pdf using the information available from the Nautical Almanac (NA) of the day but we wanted to redo things using modern lunar ephemerides and positions and proper motions from the Hipparcos Catalog.


    The star A Ophiuchi, which was observed on 23 July and 15 September, is a binary system consisting of 2 practically identical components which simplifies matters greatly. In this case the proper motion of centre of mass of the system is the average of the proper motions of the 2 components. It can be extrapolated back to 1915. The Sixth Catalog of Orbits of Visual Binary Stars, http://www.ad.usno.navy.mil/wds/orb6/orb6.html gives the position angle and separation of the components at the time as being 184.1° and 4.24" respectively. This provides the offsets of the components from the centre of mass.

    There is a strange potential ambiguity in the occultation data as provided by 1915 NA. It is labelled "A Ophiuchi (1st star)" however the position angle of 184.1° means that the 2 stars are sitting one above the other at about the same R.A. The star that is occulted first will depend on where on the lunar limb the occultation occurs which in turn depends on the observer's latitude. In the case of the 1915 antarctic timings, on 23 July the A star disappeared first followed by the B star 0.15s later - a negligible difference. On 15 September the B star disappeared first with the A star following 4.24s later. Fortunately this difference is large enough that there is no doubt which disappearance was actually timed.

    Robin Stuart

       
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