NavList:

Many Thanks to you Frank for very kindly having taken the time to post this superb and comprehensive summary on the way Lunars were actually performed some 2 Centuries back.

Navigators then required and used REFRACTED BODY CENTER ALTITUDES i.e. obtained from Sextant Raw Altitudes through performing only Instrument Error + Dip + [geocentric] Semi-Diameter Corrections.

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In order to re-work this example with modern computation tools, and thanks to this "simple and generic "pre-clearing" method used Navigators then it is now possible to reliably reverse-engineer published Altitudes into "updated [modern] Altitudes" corrected for only Instrument Error.

From this such example, we can reliably proceed as follows then:

1st Example Height of Eye 17ft, P 29.92" Hg and T 50° F

From Aug 25th, 1830 (TT-UT = +7.4s), Lunar distance 80°42.45' , SUNL 36°14' , MOONL 44°49' get:

reverse-engineered altitudes corrected for only Instrument Error: SUNL 36°02', MOONL 44°37' (HoE 17ft)

"Modern" Results

Own results: Lunar taken at 17h58m45.7s UT1 from N25°03.9' W034°17.9' , cleared distance 80°48.4'

Your On-line Calculator using Altitudes and not Position, Frank, rates the above result as: Error in Lunar: 0.02' and Cleared LD 80°48.4'

To be compared with:

Navigator's results

DR Latitude N24°51' (apparently some 2h 10m before Lunar was taken), Lunar Longitude W034°11'15".

Discussion: Unfortunate uncertainty (but that's the way they navigated then) about the Latitude apparently computed for a position 2h 10m earlier. Actual Navigator's Longitude error close to 6.7'. 

2nd Example : Height of Eye 17ft, P 29.92" Hg and T 50° F

From Aug 28th, 1830 (TT-UT = +7.4s) ,  Lunar distance 114°42.9' , SUNL 27°25' , MOONL = 28°52' get:

reverse-engineered altitudes corrected for only Instrument Error: SUNL 27°13', MOONL 28°40' (HoE 17ft)

"Modern" Results

Own results: Lunar taken at 18h20m48.2s UT1 from N18°28.8' W030°42.2' , cleared distance 114°35.8'

Your On-line Calculator using Altitudes and not Position, Frank, rates the above result as: Error in Lunar: 0.06' and Cleared LD 114°35.8'

To be compared with:

Navigator's results

DR Latitude N18°20' (apparently some 2h before Lunar was taken), Lunar Longitude W030°39'30" obtained from 3 averaged observations.

Discussion: Unfortunate uncertainty (but that's the way they navigated then) about the Latitude  apparently computed for a position 2h earlier. Actual Navigator's Longitude error close to 2.7'.

Overall discussion : in both cases, and especially on Aug 28th, 1830 the Navigator got excellent if not OUTSTANDING results.

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Further food for thought:

(1) - I have long taken a special interest on the Historical accuracy of Published Celestial Bodies coordinates. Compared to modern Ephemeris it is interesting to see that only from the Mid XXth Century and onwards for the Moon and from only 1984 and onwards for Jupiter and Saturn could the Astronomical Ephemeris (Connaissance des Temps and UK/US Astronomical Ephemeris) - based on the sole Gravity Theories (Newton + Relativity), i.e. no regularly updated extra corrections added for the Moon - consistently achieve better than 6" for the Moon and 4" for Jupiter and Saturn published apparent coordinates. More on this in some upcoming post.

(2) - Modern computation Software enables to not only rework Historical Lunars and grade them as here-above but it also enables - often most reliably, depending on the Bodies Azimuth's differences -  recovering the Navigators' Positions at sea significantly better than the ones they could derive. As earlier mentioned, and just from the published Lunar Distances and Altitudes - i.e. neglecting the published Positions on Account (i.e. the DR positions) then - it is possible to derive 2 distinct Navigators realistic positions at sea. More on this in some extra upcoming post too.

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To conclude, many thanks to you, Modris, for giving us this rare opportunity to rework actual Historical Lunars.

Best Lunarian Regards to all,

Kermit

antoine.m.couette[at]club-internet.fr