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    Re: Star to Star Distances taken on a Second Hand Sextant
    From: Michael Bradley
    Date: 2019 Dec 5, 08:48 -0800

      

    Brad, you wrote:

    "There is a one time observation of distance, in cells D67 E67 = 22°46'.5.  Can you confirm that is just one observation?  

    Indicated in cell g67 is the Index Error.  5' off the arc.  If its off, put it on, arriving at 22°51'.5 measured, cell 

    You then take the delta, getting -0.013° or -0'.8, given in cell J67.

    Is my understanding of the contents of the file template correct, given Procyon//Pollux?

    Thanks in advance for your time answering my questions.  They are posed as requests for clarifications."

    Your understanding is correct, except that I've confused you over the timings. So in the spirit of clarification .......

    1. Just as in observing normal star sights, it's handy to pre-compute an approximate star to star distance to get the two stars initially into the field of view easily: that is the purpose of the top block of the spreadsheet(s). As part of precalculating these, without a Nautical Almanac in 2018 when I firsted started this investigation, I needed a hack to help look up SHAs from on line sources. Hence the redundant (GHA) Aires at 000 note to myself in the top in the top left hand corner of the spreadsheet. Please disregard it.

    2. The recorded observation time is the value 2115 21/04/2019 (UThhmm, date in UK format) further down the page. Like in a lunar, a precise time is not needed because the star to star distance changes extremely slowly.

    The EP is a known one: the actual observation position was perhaps 300 yards North West, in local parkland. the star to star distance is extremely insensetive to minor changes in EP. most of the  observations were taken towards the west.

    3. The reported individual star to star distance observations are taken from a series of such, collected at the same session. There was a temperature drop for the sextant as it came out of its case. Plastic sextants appeared to me, from these observations, to have a thermal settling time defining their Index Error changes after they come out of the case. To separate out this effect at each observation, a set of star to star distances were recorded, interspersed with an alternate set of Index error measurements. Only when a settled pattern of Index Errors tracking the star to star distance was observed did I count the result as valid and worth recording.

    4. We're dealing with a spherical triangle using the nearest pole, and the Dec and SHA of two stars. We want to calculate the distance between the two stars. We can get the angle at the pole from the difference between the two SHAs, and the length of two sides from the Dec hence Polar Distance of each star.  I ended up using Astron for these.

    I didn't have a conventional horizon in the parkland for these tests.  So initially no measured star altitudes to hand, and so no refraction values. Again I have used Astron, using the EP given and the observation time, to find Hc for each of the stars. Then, copying the value of Hc into the Hs box to get the values of the  'vertical' refraction correction(s). These are entered as  dH  in the spreadsheet; the algebra to calcuate the corrected star to star distance along the arc in the sky between the two stars comes from Frank Reed's lunar web pages.

    I hope this clarifies sufficiently, Brad.

    P.S. I have my own thermodynamic hunches about the sextant settling time processes, but this is maybe not the time and place. What I can usefully report is that the Ebbcos took the  least time to settle, ten minutes at most, and the Index Error changed by no more than 1' during settling. By far the worst example sextant in this regard was the Davis Mk 25, which one observation night had an index error which changed by 13' in half an hour, and was still changing when I gave up on it. 

    Good navigating

    Michael Bradley

       
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