NavList:

Hewitt,

FIRST, a reminder for everyone: you wrote some degrees as asterisks, e.g. 71*. Nothing wrong with that if you like it that way. But, just to remind you, you can easily get proper degree signs in any NavList message, whether sent by email or posted from the message boards, by typing d in square brackets, like [e], except with d. Just type 71°. See? Well, that's the thing, isn't it? --you CAN'T see because it's been converted into a degree symbol! But that's where it came from.

Right, now back to business. :)

You wrote:
"averaging the times for your second and your last moon shots, I get a time of meridian passage of 02-24-53."

Ok. That's a workable procedure, but since the altitude aren't a match on those second and last shots, we can do quite a bit better by drawing a line between the last and the next-to-last sights and finding the time that more closely matches the 33.2' of the second sight. Doing this corresponds to a time around 02:44:15. The earlier (second) shot was at 03:45. Averaging those times gives 02:24:00, which is VERY close, within a few seconds, to what I get by curve folding and also by a manual least squares fit using a parabola with the correct curvature based on the Dec and the DR Lat.

Next, we have to offset the time based on the Moon's speed. Checking the almanac data, I find a speed for the "underMoon point" of 5.4 knots away from us (the Declination is heading south at 5.4' per hour). That doesn't match your 8 knots. Did you maybe look at the previous day?

The offset in time of the peak altitude in seconds is equal to
15.28*v*(tan(Lat)-tan(Dec))
with v in knots. If you prefer the offset in minutes of longitude, naturally you just divide by 4. Using the Moon's mean Dec, -18.4°, a "DR" Lat of 41.3°, and v=5.4 knots yields 99.9 seconds. Call it 100. Now the decreasing Declination is equivalent to a vessel moving away from the Moon so that would depress the curve progressively in time which implies that we observed the peak altitude too early. We have to add those 100 seconds onto the time found from the symmetry of the sights. That gives 02:25:40 (=02:24:00+100s). The Moon's GHA at that exact instant of UT was 71°43.0'. So that's my best estimate of the longitude from those Moon sights. The actual longitude of my observing point was 71°54.3'. That's an error of 11.3' or 8.5 nautical miles. Not bad for the methodology and the uncertain post-twilight horizon. And again I had an error of about 1.5' in latitude. In my experience, these relative scales in error of longitude versus latitude, expect "five-to-one", are typical for meridian curve fixes.

I am attaching my version of a motion offset table. It gives the offset in seconds. Since its primary application is for Sun sights around noon, the entry is by date at the top instead of by Declination. For any other body, you have to estimate when the Sun has the same Dec. Or you can just grab a calculator and work it out from the neat little formula above.

-FER

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