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    Re: Lunar Calculation Presentation
    From: David Pike
    Date: 2022 Sep 3, 13:56 -0700

    Well, I managed for two day-sails not to steer TIKI onto a mudbank while thinking up the next lesson, so here we go.  Wherever possible answers should be elicited from the students.  We learned that if you knew the Sun’s declination for a particular day then you could work out your latitude from the height of the Sun at local noon (meridian passage).  Q.  That’s fine but how do you know when it’s local noon?  A.  If you follow the Sun’s path through the sky, local noon is when the Sun reaches its highest point in the sky.  The Sun is also due south (or north) of you. 

    Q.  So, if you can work out your latitude easily when the Sun is due south (or north) of you, why can’t you simply measure your longitude when the Sun is due east or west of you?  A.  You can, but it’s a bit more complicated, because the Earth is spinning about an axis through its poles, and to work out your longitude, you need to know the whereabout of the point directly below the Sun on the Earth at the moment you measure the height of the Sun.  To find this point you need to know the time very accurately.  Q.  How accurately? A.  For every minute of time your time is in error, the error in your longitude will be in error by 15 minutes of arc in latitude, about 15 nautical miles at the equator and 7.5 nm at 60 degrees north.  Unfortunately, during the great ages of discovery, the 17th and 18th centuries, whilst mariners had clocks and watches, they were unable to keep correct time over weeks of changing temperature and rolling around at sea, so knowing your exact longitude was always a problem and it led to some dreadful tragedies e.g. it was a possible cause of the Scilly naval disaster of 1707 when the RN lost 4 large ships and up to 2000 personnel.

    Q.  So, if time pieces weren’t accurate enough at sea, what might be done to provide accurate longitude?  A.  Various methods of were suggested and tried e.g.  mapping magnetic variation and dip, but all proved completely wrong or impractical except for two possibilities: a.  to build watches which did keep their time or at least could be rated evenly over long periods afloat, or b. to us use a method based upon the relative positions of the stars and the Moon, the lunar to find the exact time occasionally and use it to correct the unstable clocks and watches which sailors already had.  As we know, more stable clocks and watches, the marine chronometer, were eventually produced from the 1750s, but initially they were rare and very expensive and they did not come into common use until well into the 19th century, so mariners were left with a gap between 1763 and around 1850 when the lunar distance method was the only way for many mariners of monitoring their timepieces at sea.  End of today’s lesson.  More to follow.  DaveP

       
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