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    Re: Navigation by the Moon
    From: Geoff Hitchcox
    Date: 2021 Mar 30, 00:44 -0700

    Alexandre Eremenko wrote:

    --------------------------------------------------

    I do not think that 1' difference is important for the question 

    --------------------------------------------------

    It is if you have to multiply by 25 days Alex ;-)

    Alex also wrote:

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    Geoff,

    I was trying to use the data which the master mate could possibly keep in his memory.

    This is the length of the tropical month (period of revolution of the Moon with respect to Sun).

    It is 29.53 days. Now 360 : 29.53 = 12.19 (degrees per day) 

    [ ### Geoff notes a missing divide by 15 degree/hour (earth rotation) at this point ### ]

     = 0.81 (hour/per day) = 48.6 (minutes per day) = approx 49 minutes.

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    [ Note to Alex, 29.53 days is the Synodic Month, not Tropical. ]

    I agree with you Alex, I think that is the most plausible explanation for how the author came up with number "49". 

    I must admit at first blush, I found it all acceptable logic - UNTIL I started to think of exactly what was taking place here. The "Synodic Month" could only be used to give an accurate lag of the Moon, if the beginning and end of the measurement was in exactly the same position in the sky (which it clearly isn't).

    So what astronomical reference should the author have used ?

    The "M2" constituent of the Harmonic Tide of course.

    The author should have done the following Maths Alex.

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    (2 x 360 / "M2") - 24 = Average Moon lag per day (in hours)

    (2 X 360 / 28.984104) - 24 = 0.8412 Hours

    0.8412 Hours x 60 = 50.47 Minutes of Time

    --------------------------------------------------

    To back up the theory, in my previous message I used the JPL DE430 Ephemeris and averaged 14,000 days of timings of the Moon going to the same benchmark in the sky (meridian passage at 180.0 South) - timing to better than 1 microsecond timing precision.

    The average of the 14,000 timings being a lag of 50.47 Minutes of Time! 

    "50" is also a much easier number to multiply than 49, sans calculator ! 

    I wonder, how many other "ye olde" navigators have made the same mistake, of using the duration of the "Synodic Moon" to miscalculate the lag of the Moon as you suggested above Alex ?

    So remember all ye budding and retired "Boy Scouts" (hat tip to David Pike for that) the average Moon Lag is 50 ( NOT 49 ) minutes per day ;-)

    Thank you for the nice comments about my graphic Frank_R.

    BTW team, how good is your pattern recognition ? In the graphic that Frank mentions, there are two sets of the 18.6 year lunar cycle, can you see where they are (hint 18.6 yrs = 6,793 days) ?

    Regards, 

    Geoff Hitchcox

    Christchurch

    New Zealand

       
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