Time Precision Needed for Celestial

[El Pinguino]

Originally Posted by Adelie

Worsely used CelNav to fix the island the crew sheltered on.

He then navigated a lifeboat 800mi to South Georgia Island (a 20x100mi target) seeking help. They landed to boats, trekked over some mountains to a whaling station, which got them back to civilization. There they organized a ship to return to the island with the crew.

Elephant Island was charted, they knew where they were. Worsley used a time sight to establish chronometer error.

From the link in post #61

‘Immediately after
breakfast the sun came out obligingly. The first
sunny day with a clear enough horizon for rating
my chronometer.’ No noon sight for latitude was
possible.'

Organising a ship to pick up survivors was a long and complicated business.
Yelcho's bow can still be seen in Pto Williams.

[Uricanejack]

Marc St Hilarie was my prefered method back in the day.
I did use Long By Chrom way back further in the day because it was still often asked by D.O.T. JIK so I was proficient if required.
The position line would be the same. Passing through both the ITP by Marc St Hilaire or the longitude the position line crosses your DR Latitude.

Most common method now. PZX triangle or Napier's rules as per the nautical almanac tables or pocket calculator methode. Which has the disadvantage of having to add or subtract.

Norries or similar. Would be my prefered method for a full prepper scenario?
No I can't recall how to do lunars. I did look it up once upon a time just because. Why not. Its not a something I have at my fingertips. Or ever tried to use as a practical navigational procedure.

Norries is in my book shelf. If I was at sea an up to date nautical almanac, hand bearing compass. sextant, watch and a hand lead line. My log is fouled up and I don't have a walker. (they work quite well, check them daily, or you will be telling people a shark ate it)
For the time it takes me to find land, I expect my watch and rate book would be good enough for reasonable accuracy. even after my shortwave radio died or WWV received a direct hit.

To check my time,
Its not going to give +- 1 second accuracy but close enough for horse shoes and hand grenades.
About 15 minutes before obbs noon. Take a sight. Note your time and the sextant altitude. After you observe noon. Reset and time the same alt.
Apparent Noon is approximately 1/2 way between. This will give you an idea if your watch is reasonably accurate.
Unfortunately the sun continues to move and its declination changes during this process so its close but not spot on. Particularly if you are moving as well.

Slightly more accurate. Time Sunrise and sunset. If you keep track of your latitude. Polaris if you are in the N Hemisphere will do well enough.
Sine Amp = Sine Dec Sec Lat will also give you a latitude. If you observe the amplitude again not precise but close enough.

For finding landfall. Pick something identifiable. Aim a bit offset so you know which way to turn when you sight land.
Or aim a bit offshore for the Latitude of your chosen landfall and turn east or west as the case may be to arrive.

When you do find land.
You now presumably have a known Latitude and Longitude. Do your calculations back and you have the correct time.

[GrowleyMonster]

I must confess that I never learned to do Lunars the "proper" way. This was pre-internet and I had searched a good bit for an edition of Bowditch with the Lunar Distance tables in it, but finally it came to me that at any given time, there is a unique difference between the Ho of the Moon and the Sun or a star or planet. So, I alternately took sights of the Moon and another body, usually the Sun, over a period of several minutes, and graphed Ho with watch time, then picked off the Ho of each for a given watch time and subtracted for the difference in Ho and therefore the difference in Hc at that assumed time.

The next step was to estimate the likely maximum error in time, and calculate the difference in the Hc of the two bodies at approximately 1.5x that potential error in time before and after the averaged assumed (watch) time, as well as the exact assumed time. From there it was simply a matter of interpolating or extrapolating to a better assumed time and closer difference of Hc to the difference of the Ho. Three iterations seemed to suffice, as a fourth was an insignificant improvement. That gave me the actual GMT of the average observation time to compare to the watch time of the average of the observations, for a watch error. Then I had a corrected time that I could compare to the time given by our newfangled GPS or radio time ticks or the ship's chro time, corrected. The whole process took the best part of an hour. I did this three or four times where I was satisfied that I had done everything correctly, and those attempts were all within one minute of the verified watch error. So for all practical purposes, within about 15' of Longitude. Close enough to have been useful back in the day, before chronometers.

Bear in mind that observations were in calm weather on a large ship. I think on a sailboat I would be rather pleased to be within 4 minutes or so with any consistency. Averaging several sights of each body is essential for accuracy. You wouldn't want to just advance or retard one to the other.

I am sure about half a million guys likewise "invented" this method over the course of history. I realized early on that my mathematical skills were not up to applying parallax and semidiameter and reducing a spherical triangle not using a meridian and equator as legs. Comparing difference in Ho to difference in Hc and finding the time when they agreed was much easier for me to wrap my brains around, and I don't think the loss of accuracy is all that much to write home about. Just thought I would throw this out there for the Celestial/math nerds.