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    Re: Lunar Calculation Presentation
    From: Frank Reed
    Date: 2022 Sep 5, 09:25 -0700

    The technique of using a lunar altitude as a surrogate for a lunar distance observation has been around "forever". Yet another example from recent decades may be found in John Letcher's "Self-Contained Celestial Navigation with H.O. 208" (terrible title for a great book). The earliest example that I have seen of this method was an article from the 1830s (can't find that right now). The calculation is in terms of comparison of time sights rather than lines of position, but of course that's just a different language, a different methodology, using the same principle.

    There are a few problems with this GMT by lunar altitude method, but they can managed with a little care.

    First, a lunar altitude does not necessarily distinguish GMT. Imagine the Moon is at a point in the sky and in its orbit where its altitude does not change much with GMT. For example, the Moon tonight from the western Atlantic will be nearly due South and close to the low point of the ecliptic. Its altitude will change with local time, but it won't be sensitive to absolute time. So a navigator needs to know to avoid those cases. This is not as easy as it sounds. You might think that observing the Moon when nearly east or west would be a good solution. But consider the circumstances of the "Harvest Moon". This was once sighted as the work of our "Beneficent Creator" guaranteeing convenient lighting for the farmers bringing in their crops after dark for several nights at harvest time. This occurs because the ecliptic lies at a shallow angle in the east after sunset in mid-northern latitudes near "harvest time", and the Full Moon rises close to sunset. It is indeed convenient. But the Moon's motion on the celestial sphere is nearly horizontal on these nights from mid-northern latitudes.

    Second, in high latitudes, lunar altitudes don't change much while lunar distances continue to change at useful rates. So avoid GMT by lunar altitudes at latitudes greater than, maybe 60° N/S.

    Third, this process depends on synchronized altitudes or at least altitudes that have been carefully timed. The whole process is designed to detect an error in time, so errors in recording time must be strictly minimized.

    Finally, and most importantly, altitudes by common marine sextant are intrinsically limited in accuracy (better than bubble sextants nonetheless). The sea horizon is not our friend. If we can shoot altitudes from an artificial horizon, this is not a problem, but at sea it's a significant concern, and it represents the limit of "system accuracy" of celestial navigation at sea (which hasn't improved much in 200 years). Moderate anomalous refraction can shift the horizon significantly. Differences in illumination along the horizon can create subjective changes in the horizon. Uncertainties in height of eye (and wave height) can lead to still further uncertainty in altitude corrections. It may be possible to eliminate a large portion of this altitude uncertainty by shooting the altitude of the other bodies on a similar azimuth. That is, for the GMT by lunar altitude method, shoot the Moon's altitude as carefully as possible. Then shoot several altitudes of stars on nearly the same azimuth. Carefully plot the lines of position for the best estimate of GMT. If the Moon LOP does not fall in among the stars' LOPs, adjust the GMT until they agree.

    Frank Reed

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