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    Re: Azimuth Formula Questions
    From: George Huxtable
    Date: 2005 Nov 1, 00:58 -0000

    Paul Hirose wrote-
    > George Huxtable wrote:
    >> But now let the observer travel a few feet South, across the equator, to
    >> a
    >> lat of -.001 degrees South.
    >> Plugging in that new value of lat changes Z to 44.967, almost exactly the
    >> same as before (jst as we would expect, for such a small movement of the
    >> observer).
    > That's not what I would expect. Isn't Z measured from the pole nearest
    > the observer? At least, that's how HO 229 defines it. Stepping into the
    > Southern Hemisphere changes the scenario to "latitude CONTRARY name to
    > declination". That means you must use a different HO 229 page (the
    > facing page in the same book opening) to obtain Z. The tabulated value
    > is 135.0 for your example. Then apply the correct rule
    >>> S. Lat
    >>> L.H.A. greater 180..........Zn = 180-Z
    >>> L.H.A. less than 180........Zn = 180+Z
    > and all is well.
    > However, I never used the rules, preferring to plot directly from Z. In
    > your example, Z = S 135 W. On paper I find that as easy to plot as 315,
    > and it eliminates the Zn calculation.
    Reply from George-
    Thank you, Paul, I think you have put your finger on the answer. It's a
    matter of definition.
    As I said, I don't have a copy of HO 229, and am not familiar with those
    tables. I was just following Bill's quotations from HO 229.
    Because it uses tabulations, and table-makers are always keen to minimise
    the number of pages, then presumably HO 229 is constructed so that the same
    table applies to both North and South latitudes, with dec tabulated as
    either "same as lat" or "opposite to lat" as Paul describes it. And then, if
    the resulting Z is defined as being measured from the pole nearest the
    observer, its value will suddenly switch as the observer crosses the
    equator. So then, some mental gymnasics is called for to put Zn in the
    correct quadrant; hence those correction rules. Presumably Zn is defined as
    an angle measured positive clockwise, 0 to 360, from North; is that correct?
    If you decide to get azimuth from the HO229 formula quoted by Bill, instead
    of by an azimuth table, how are you intended to enter the values for lat and
    dec, I wonder? Are you expected to use the negative-south rule for both lat
    and dec? Or do you ignore any North and South signs and enter both as
    positive quantities? If so, how would you tell the formula when dec happened
    to be contrary to lat? Does the HO 229 document make it clear how those
    signs are to be treated? Although those quadrant-correction rules in HO 229
    may give the right answer for Zn when the value for Z is taken from tables,
    that seems not to be the case when Z comes from the HO 229 quoted formula,
    as I showed. Or did I get that wrong?
    Anyway, it's becoming clearer how that discrepancy between the two methods
    arises, thanks to Paul. The Meeus formula, with its sign conventions chosen
    as stated, and its straighforward quadrant-adjustment, seems much more
    simple,  and  demands less in the way of mental contortion. I wonder if
    others agree.
    I have a funny feeling, in the back of my mind, that we have been through
    this argument once before, years ago. Wish I could remember if we agreed on
    an answer, and what that answer was.
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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