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    Differential lunars
    From: Peter Monta
    Date: 2013 Jul 30, 08:06 -0700
    I wonder if a differential scheme for taking lunars would be practical.  It would remove most of the need for a high-accuracy sextant, which might have been valuable back in the day.  A little more computation is needed, though.

    The idea is to do some pre-planning to find a star-star distance very close to the intended lunar.  Then simply wait until a little before that time and do the star-star sight, leaving the sextant set up exactly for that distance.  (Whether the sextant shows this distance accurately is immaterial; we're just doing a local calibration against the sky.)  Now, without touching the sextant (except for shades maybe), sight the moon and the intended star and wait for a touch.  Note the time.

    Unless I'm missing something, we now have all the information we need.  Assuming reasonable altitudes are available (whether measured or computed), we compute the star-star distance to high accuracy by accounting for refraction.  Then this same distance is our lunar distance, and everything proceeds normally.  The sextant need not even be graduated.

    Obviously this works only at night when many star sources are available, and one might have to use fainter stars to get close to the right distance (but the number of distances increases quadratically with the number of visible sources).

    If you trust your sextant to accurately show small changes in angle (up to 5 or 10 arcminutes maybe, so that any worm errors still largely drop out), then the flexibility increases because one need not wait for the times when lunar distances are exactly equal to a star distance, merely approximately so.

    I'm still trying to assess my sextant's arc error with star-star sights.  Now I'm wondering:  why bother?

    Cheers,
    Peter

    ps: well, day sights might be available, but too rarely to be useful.  One can imagine a geometry in which a Sun-Venus distance is the calibration source, then the Venus-Moon or Sun-Moon distance is the lunar.  These will be equal a couple of times a month during those parts of the year in which Venus has useful elongation.

       
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