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    Re: Celestial Course
    From: Joe Shields
    Date: 1998 Mar 17, 3:27 PM

    Forget Algebra and Trigonometry.  To practice Celestial Navigation you
    only need to be able to look things up and add and subtract numbers.
    I think the more important thing  (and the thing that makes it fun) is
    understanding what is going on out there.  Understanding that the
    earth doesn't go around the Sun exactly like clockwork - that its
    orbit is eliptical so that sometimes it is going uphill (so to speak)
    and slows down and at other times it is racing down hill towards the
    Sun at a pace that puts it ahead of our "mean" time clocks.  If the
    earth revolved  around the Sun in a nice circular orbit, perfectly
    matching our accurate timepieces, we wouldn't need an almanac to find
    out what portion of the earth is precisely under the Sun at a given
    moment in time, we could figure it out from our clocks alone (sort
    of).  However, because there is this speeding up and slowing down of
    the earth as it revolves around the Sun each year, you need to have an
    Almanac (computed by someone who does need to know Algebra and
    Trigonometry and probably some Calculus too) that lists the GHA
    (Greenwich Hour Angle) for every hour of every day of the year (You
    have to buy a new Almanac every year, unless you buy MICA, but that is
    another story).  The Greenwich Hour Angle is a measure (in degrees) of
    how far away the portion of the earth that falls directly below the
    Sun is from Greenwich, England at that exact time.  The name given to
    that portion of the earth that falls directly under the Sun's
    East-West (apparent) movement at any one time is called a meridian.
    When the earth is at that point in it's daily rotation such that the
    Observatory at Greenwich, England falls directly under the Sun, the
    GHA is zero because the Sun is on the Prime meridian.  This occurs
    roughly (not precisely - again due to the speeding up and slowing down
    of the earth's revolution) at noon Greenwich Mean Time (GMT - which is
    now commonly referred to as Universal Time UT).   For example, when I
    wake up in Pittsburgh and see the sun shining through my window on a
    Saturday morning (which happens infrequently in Pittsburgh), I quickly
    grab my $30 Davis sextant and artificial horizon and shoot the Sun
    through my living room window.  By the time I can get a clear shot of
    the Sun (Pittsburgh is hilly), the GHA of the Sun is around 10-11
    degrees.  Which means the earth has rotated to the point where the Sun
    is now directly over a meridian in the Atlantic Ocean about 10-11
    degrees of longitude west of Greenwich.  Since I am interested in
    finding my LHA or Local Hour Angle (needed for the looking up portion
    of the Celestial Nav. process) I subtract the GHA of 11 degrees from
    my Pittsburgh longitude of 80 degrees West to yield a LHA of 69
    degrees.  That means the earth still has to rotate 69 degrees before
    the Sun will be directly over Pittsburgh (My Local Noon).  I can
    figure out how long that will take time wise, since the earth rotates
    360 degrees in one day or 24 hours.  Dividing 360 degrees by 24 hours
    gives me 15 degrees/hour.  That is, the earth rotates at a speed such
    that the Sun appears to move across the sky at a rate of 15 degrees
    per hour.  Dividing 69 degrees by 15 degrees/hour gives me 4 hours and
    36 minutes (There is also a table in the Almanac for converting
    degrees of longitude to time).  After doing many successful sights in
    Pittsburgh, the thing that drove me completely batty was when we were
    vacationing in Virginia Beach and my sights weren't working out at all
    (boy was I crabby).  I was just following my procedure cookbook
    fashion, doing the same thing I did in Pittsburgh.  What finally
    helped me (and saved our vacation) was going back over the meaning of
    what I was doing.  Once I examined the meaning of LHA, I realized that
    now I was catching the rising Sun earlier -- before it had even moved
    across the Prime Meridian.  I had been mistakenly computing my LHA
    using the same procedure that worked in Pittsburgh.  By understanding
    what LHA is I was able to see that now I needed to subtract GHA from
    360 and then ADD that to my longitude.
    This is a simplified explanation of how and why we use an Almanac to
    find the GHA of the sun so that we can then find the LHA of the sun.
    The thing that I left out is - we usually need to know this for an odd
    sort of time like 09:43:17 est, because that was our exact local time
    when we shot the Sun.  What we need to do is first add our Time Zone
    (5 for Pittsburgh in the Eastern Time Zone which is 5 hours from
    Greenwich) to get a Universal time of 14:43:17.  Then we look up the
    GHA for UT = 14 hours on todays daily page and then use the yellow
    "Interpolation" pages in the back of the almanac for arriving at a GHA
    correction for the minutes and seconds portion of our time that is
    added to the GHA at 14 hours to arrive at a GHA for a time that falls
    in between the hourly GHAs listed on the daily pages of the Almanac.
    ...this may just be making it worse.  I dont know.  However I've been
    meaning to write up some notes for some Sailing Club buddies who have
    been asking me to explain how to do celestial navigation, so I thought
    your questions might serve to help me try and come up with something.
    Any way, unless people start sending me nasty notes threatening me
    bodily harm unless I stop, next I will talk about the earth's axis and
    declination (the other thing you need besides LHA in doing celestial
    ...now I need whiskey!!   -- Joe
    ---Ruth Summers  wrote:
    > re
    > 'http://peck.ipph.purdue.edu/al/space.html'.
    > 'Intro Questions and Answers
    >  Is it hard to do?'
    >  OK folks. This is the first page and it says '
    >  'But anyone who can understand high school algebra and trig can
    feel '
    >  At that point my brain fell out of my head. When I went to high
    school one who
    > was talking business courses took business math. I did not take
    algebra until
    >  I was in college and I flunked it. Later, I have taken intro to
    >  and that was fine. I have tried to take 2 algebra classes, I have
    floppy disks
    > at home of the math lab. I have bought Math Blaster for my pc.
    >  Lets just say at this point I am math challenged. I know there are
    more people
    >  like me out there !
    >  So, I'd really like to see something we all could work together on.
    >  I am currently working with another lady to figure out this
    celestial stuff.
    >  We have books, tables, more books, I just ordered some videos.
    >  For crying out loud, what makes this so damned hard !!
    >  -ha probably the *&^%$ math.
    >  Although I can see after my minor investigation into this that I
    think the
    > angles of measurement is where the math is needed, ie-usually the
    boat is tilted
    >  but the GP is that line coming out of the earth and it's straight.
    >  I need coffee....
    >  Ruth
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