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    Haversine ZD formula to Cosine ZD formula in easy stages
    From: David Pike
    Date: 2021 Nov 12, 12:41 -0800

    It’s funny how a discussion on versines and haversines should come up at the same time.  Here’s a little problem I’ve been tinkering with for the last couple of days.  When I did the Staff Navigator Course in 1973 haversines were still part of the course for some problems.  Great circle distances I believe.  The department only had one closely guarded electronic calculator, which was reputed to have cost over £1000, so we lesser mortals had to use log tables.  However, haversines were one of those things you trained yourself to use in the exam, which was purposely time limited to increase the stress, and forgot about 30 minutes later.

    Seeing passing reference to Haversines in ‘Little Ship Astro-Navigation’ and from Tony Oz and Lars Bergman, I decided to try using them again with Nories’s.  I thought it would be a useful exercise to try and obtain the haversine zenith distance formula from the cosine formula.  This soon gave me a headache, so I gave up and tried to work from haversine to cosine instead.  This turned out to be considerably easier apart from explaining why you got the same formula irrespective of which hemisphere latitude and declination were in.  Attached is my homework for marking.  DaveP

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