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    Re: Early lunars
    From: Robin Stuart
    Date: 2010 Mar 23, 17:03 -0700

    George,

    The phrase "when the moon had just returned to its light" could either mean the end of totality which would be signaled by the first hint of white light returning to the Moon's disk as it begins to exit the umbra or it could mean the end of the partial phase when the last vestiges of the dark umbra disappear from the disk. For a number of reasons, including relative ease of naked eye observation, I would suspect that it is the latter. When you crank the numbers, however, Columbus's report doesn't really line up with the events as they actually happened and there are some arguments out there that his results were fabricated, see http://www.columbusnavigation.com/longi.shtml

    The circumstances of the eclipse of 1504 can be found at http://eclipse.gsfc.nasa.gov/LEcat5/LE1501-1600.html with a graphical summary at http://eclipse.gsfc.nasa.gov/5MCLEmap/1501-1600/LE1504-03-01T.gif (attached). Assuming a position for Santa Gloria of 18 26'45" N, 77 12' 30" W, sunset would be at 23h 15m UT. (http://www.srrb.noaa.gov/highlights/sunrise/sunrise.html)

    The key times in the eclipse are

    Partial phase begins: 23h 2m TD
    Totality begins: 0h 21m TD
    Totality ends: 1h 9m TD
    Partial phase ends: 2h 28m TD

    The difference between UT and TD at the time was TD - UT = 191s and we can ignore for the present purposes.

    None of these is a very convincing match to being "two hours and a half after sunset". Totality and the partial phase ended 1h 54m and 3h 13m after sunset respectively. Columbus would have had to have been at longitude 88 W (in the Yucatan) to see the partial phase end "two hours and a half after sunset". Add another hour or so west for possible misinterpretation of the quoted time in the almanac and you beginning to get to his 7h15m west of Cadiz (i.e. 115 W). Maybe he backed out the eclipse observation to put himself where he wanted to be.

    I have tried to make sense of the figure of the contemporary eclipse tables attached to your posting. I can claim no expertise in this however. The line above the month appears to gives the Julian date (day, hour, minutes) of mid-eclipse with 0h being at local noon for some European location. By comparing with modern predictions, I would guess that the last line is half the duration (hours, minutes) from start to end of the partial phase of the eclipse. This is the time you need to subtract/add to the time of mid-eclipse to get the start/end of the partial phase. If this was standard practice then Columbus's description, "when the moon had just returned to its light", probably referred to the end of the partial phase.

    The scanned text you attach states "and as the beginning thereof was before the sun set" . The beginning of the partial phase would have occurred just prior to sunset from Jamaica but long before sunset from 7h15m west of Cadiz. In fact from that location he would not have seen a total eclipse at all, just the final stages of the partial phase. This conclusion does not depend on Columbus's erroneous estimate of the diameter of the Earth.

    Robin Stuart

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