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On 6/21/06, Andrew Corl  wrote:

> I have followed the recent posting regarding the subject of determining
> position from two intersecting circles.  As strange as it may seem this is
> what I always thought celestial navigators did.

Well, yes, in principle.  But the math for doing that directly is more
complicated than necessary.  Thus, the most commonly-used method
for reducing sights by hand is to start from an assumed position, and
calculate what the altitude would have been from that position, as well
as an azimuth.  Comparing with the measured altitude tells you how
far you are from the assumed position, and the azimuth tells you in which
direction (and how to draw the line-of-position)


> My question is this, using the sidewalk for a horizon line (and yes it is
> pretty level), do I need any other special corrections to my sight besides
> dip, index error, refraction, semi-diameter (in other words the usual things
> we correct for)?

When you say it's level, I assume you mean that if you lay a carpenter's
level on it, the bubble is in the center.  But that's not what's important for
making a celestial measurement.  Ideally, you want the imaginary line
from your eye to the horizon to be level to within 1 minute of arc (equal
to about 0.07" a 20 feet) -- or to deviate from level by an amount known
to a similar level of precision.

I think you need to make an artificial horizon.  This is typically a large
pan filled with liquid, to form a flat, level reflecting surface.  To avoid
confusion with reflections off the bottom of the pan, it helps if the liquid
is dark; to avoid ripples in the wind it's helpful if it's viscous.  Some people
use Karo corn syrup, while others use motor oil; other choices are
possible too.

To measure the sun in an artificial horizon, ensure you have appropriate
shades in line, then stand so you can see the sun's reflection in the pan.
Bring its image in the index mirror down to touch the image in the pan.
If you touch the "near" edges -- the lower limb of the index-mirror image
touching the upper limb of the image in the pan -- you have made a
"LL" measurement.  If you touch the "far" edges, that's a "UL" measurement.
And if you superimpose the two images, you've measured the altitude
of the sun's center.

To correct these measurements, follow the following steps in order:
  1.  Apply your index correction, to get the true angle between the
       images.
  2.  Divide by two, to get the angle between the measured point and
       the true horizon.
  3.  DO NOT APPLY DIP -- which is an effect of the visible horizon only.
  4.  Apply refraction and semi-diameter.  You can't use the standard
       Sun tables, because they include dip as well.  Use the Stars table
       for refraction, and (unless you measured the center) add or subtract
       the sun's semi-diameter separately.

Hope this helps,
    -- Bill

   

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