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I suspect that there are many more unposted attempts at Jeremy's exercises, 
behind the scenes, than actually turn up on Navlist.

Here's my go at #12.

Date 28 May 08

Start with a position line for the Sun. Without a 2008 almanac, I have to 
rely on my pocket calculator. Its Sun predictions should be good, and should 
correspond to the Almanac's. Someone please tell me if they don't.

at UT 21h 06m 15s, I get Sun dec +21� 37.5', GHA 137� 13.2', semidiam 15.8'

corrected altitude from Sun LL is obtained from-

 16� 43.1     Sun sextant altitude
-       9.9'    dip from 106 ft. up
-       3.2     refraction
+    15.8     semidiameter
+      0.1     parallax
======
16�45.9 corrected altitude.

Without having alt-az tables for that latitude band, I have to calculate the 
Sun altitude using a program which gives me great-circle course and distance 
in miles from A to B. From an assumed position of N 14� 37.9' and long of E 
145� 18.6, to Sun at N 21� 37.5', W 137� 13.2', I get a course (= Sun 
azimuth) of 71.4�, and a great-circle distance of 4394.9 miles, 
corresponding to 73�15' zenith distance, or 16� 45' altitude, to compare 
with 16� 45.9' corrected altitude. At the moment of the Sun sight, then, the 
Sun was actually 0.9' higher in the sky, and therefore 0.9 miles closer to 
the Sun's GP, than  was assumed. So it's on a position line, displaced from 
that assumed position  by 0.9 miles in the direction of 71.4�, the line 
being drawn at right angles to that displacement.

The Sun was on that line at 21h 06m 15s, but with its course due East at 
14.3 knots, then at 21h 00m it was 1.5 miles further West, so next we shift 
that position line bodily sideways by 1.5 miles to the West.

Now for the Moon. Averaging the 8 observations, I get the mean altitude of 
72� 26.0', at a mean time of 21h 01m 57s. Hope others agree.

For that moment, my pocket calculator predicts Moon dec = -3� 05.2', GHA 
214�58.6. It's less precise, for the Moon, than it is for the Sun, so I 
wonder what others get. In this exercise, the geometry is such that only the 
dec matters, not the GHA.

Working from the same Assumed Position as before, and using the same 
technique as for the Sun, I get the calculated Moon altitude to be 72� 16.9 
at an aziimuth of 179.8�. So the Moon is very nearly due South, and what we 
are finding from it is simply our latitude.

We need to compare that altitude with the sextant altitude, after all 
corrections have been made, so the next step is to make those corrections.

72� 26.0'   Moon sextant altitude.
-       9.9'   Dip from 106 ft. up
-       0.3'  refraction
-     15.5'  semidiameter Moon (using UL)
+    17.6'  parallax taking HP = 57.6  and calculating HPcos alt.
==========
72� 17.9' corrected Moon altitude. This is just 1 mile greater than the 
altitude we calculated from the AP, so therefore we are just 1 mile closer 
to the Moon's position, or 1 arc-minute further South, which puts us on an 
E-W position line at N 14� 36.9. In this case, because that position line 
runs E-W, and the ship travels due East, the position line doesn't shift: it 
was in the same place at 21 h, near as dammit. And a bit of rough sketching 
gives a final longitude just 0.1 miles East of our AP, at 145� 19.6.

So we can congratulate the people in Fort Worth for doing a remarkably good 
job in the GPS positions they are puttting out.

Jeremy says "the latitude is consistently off", but it's only a mile out 
from GPS, according to me, so nothing to be ashamed of there. Indeed, it's 
well within the margin of error that can be caused by natural changes in the 
refractive part of the dip. Rather more interesting, to me, is the scatter 
in those Moon altitudes. I wonder why. Was the sea state good, at that time? 
Often, with a high Moon, contrast can be low, especially if the sky is a 
touch milky. That gets worse if you use an all-over horizon mirror, rather 
than a half-and-half split job. If Jeremy had recorded a number of altitudes 
for the Sun, as he did for the Moon, I wonder whether thet, too, might have 
shown scatter. What's his experience?

I didn't really need to do all those hand-corrections, but could have left 
the lot to my calculator software instead. However, that inflexibly chooses 
a height-of-eye appropriate to the "bridge" of my little craft, at 6ft above 
sea level, rather than to Jeremy's 106 ft. If I adapt Jeremy's altitudes by 
subtracting 7.6' from them first, then it gives the same answer.

George.

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.

================================

Exercise #12  Daylight Sun/Moon fix.

This exercise is for our math friends.  It is a series of Moon lines
taken near meridian transit, crossed with an early AM sunline.
Plotting these lines, you will notice an averaged Moon line giving a
decent position with lines within 5 degrees of the horizontal.   The
sun line will be nearly vertical and gives a good Longitude line as a
cross.
In this case, my calculations show that Latitude is consistently off,
but the Longitude is within a couple of tenths.  I am guessing that my
I wasn�t seeing the actual limb of the moon and therefore was off with
the sextant observations by better than a minute of arc.  The moon is
a strange mistress to try and shoot with the sextant.

----------------------------------
UTC date is 28 May 2008.  The 21h 00m UTC  GPS fix was Latitude 14deg
37.9� North, Longitude 145deg 18.6� East.  The Ship is sailing course
090 at 14.3 knots.  Height of eye is 106 feet, Temp/Pressure is 84 F
and 1010 MB.  Index error is 0.0.  The following observations were
made (times in UTC):
Sun (LL): Hs 16deg 43.1� @ 21h 06m 15s

Moon (UL) Hs 72deg 25.6� @ 20h 57m 43s

Moon (UL) Hs 72deg 25.8� @ 20h 59m 14s

Moon (UL) Hs 72deg 25.8� @ 21h 00m 48s

Moon (UL) Hs 72deg 27.2� @ 21h 01m 40s

Moon (UL) Hs 72deg 25.8� @ 21h 02m 20s

Moon (UL) Hs 72deg 26.4� @ 21h 03m 22s

Moon (UL) Hs 72deg 26.0� @ 21h 03m 57s

Moon (UL) Hs 72deg 25.2� @ 21h 05m 08s


Determine a fix at 21h 00 UTC (07h 00m Local)

Jeremy




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