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On 3/22/07, Bill  wrote:
> Oh. I wondered how you got GHA, LHA or declination when only one leg and one
> angle are given, and no time.  Must be a way, but it is above my head.
>
> Which leaves me with a pocket calculator, watch, sextant and almanac and the
> knowledge an HC and azimuth, and my best guess of 90/270d, is better than a
> time sight.

I think the original question was, how to predict the time at which
the sun has an azimuth of 90 or 270 degrees, given a known or assumed
latitude.  In this case, you have the co-latitude, the co-declination
of the sun, and the azimuth (which is a right angle) as three known
parts of the triangle.  (The sun's declination comes from a calendar,
plus perhaps an estimate of longitude to the nearest 15 degrees.  You
would have to be more careful if using the moon.)
The formulas will come out something simple like
  cos LHA = tan d / tan L  and  sin h = sin d / sin L
I think the intent is to observe until the predicted h occurs, and
record the resulting GMT.  From that and the matching LHA you compute
GHA and Longitude.  Right?  And you use the graphical method to
interpolate to hit the desired h exactly.

From the modern perspective, a sight at this special time gives a LOP
like any other; its main advantage is that the LOP runs exactly north
and south if you're at the assumed latitude, so any error in the
latitude has only a tiny effect on the resulting longitude.
    -- Bill N.

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