Letcher's Method for Solving Lunars Last Updated: 04/05/2018 These cases can also be used, as-is, to test ReedV2.txt lunars program ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15 Case 16 Case 17 Case 18 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Moon Ho 22?50.7' 23?50.5' 21?04.3' 57?39.4' 49.87500? 53?19.5' 15?21'00" 64?30'00" 22?15'00" 52?54.0' 13?38.3' 50?29.9' 19?51.2' 46?43'00" 31?23'00" 70?47'00" 20?38'00" 35?24.9' Moon Ho HP 58.4' 56.2' 54.9' 54.6' .99000? 59.6' 60'25" 55'29" 58'00" 58.2' 54.3' 59.4' 54.5' 59'40" 55'06" 54'22" 60'56" 54.2' HP Body Ho 59?08.0' 27?49.8' 21?35.1' 31?19.4' 21.17300? 45?00.7' 78?18'00" 48?20'00" 21?35'00" 32?48.4' 30?05.0' 21?08.1' 75?42.3 53?28'00" 14?59'00" 50?31'00" 12?30'00" 38?43.8' Body Ho LDpc 59?48.5' 4?03.5' 119?00.7' 40?22.3' 107.38200? 69?59.4' 65?17'30" 33?15'00" 119?20'34" 63?14.55 78?58.38' 107?22.9' 55?48.5' 79?40'32" 68?19'50" 47?33'48" 81?20'01" 48?40.0' LDpc >Y -0.767 -0.899 -0.620 0.191 -0.61783 -0.461 -0.9561 0.0142 -0.6349 -0.2046 -.4647' -.6194' -0.9407 -0.6841 -0.0713 -0.1824 -0.1652 -0.3235' >Y >R' 1.8' 00.3' 03.2' 01.1' 0.05287? 01.3' 05'46" 00'38" 03'15" 01.33' 02.14' 03.19' 2.4' 01'36" 01'49" 00'53" 01'52" 00.87' >R' >P' -44.8' -50.0' -34.0' 10.4' -0.61165? -27.5' -57'46 00'47" -36'49" -11.91' -25.22' -36.79' -0.513' -40'49" -03'56" -09'55" -10'04" -17.53' >P' >Tot Cor -43.0' -50.2' -30.8' +11.5' -0.55878? -26.1' -54'29" +01'25" -33'34" -10.58' -23.08' -33.60' -0.489' -49'13" -02'07" -09'02" -08'12" -16.67' >Tot Cor >LDc 59?05.5' 3?13.3' 118?29.9' 40?33.8' 106.82322? 69?33.3' 64?23'01" 33?16'25" 118?47'00" 63?03.97' 78?35.3' 106?49.3' 54?59.6 79?01'19" 68?17'43" 47?24'46" 81?11'49" 48?23.3' >LDc 106?49.3' >%Change -1.2% 20.6% -0.4% +0.5% -0.5% -0.6% -1.4% +0.1% -0.5% -0.3% -0.5% -0.5% -1.5% -0.8% -0.1% -0.3% -0.2% -0.6% >%Change >delZcos 0.3588 0.9998 -0.7113 0.7059 -0.9566 -0.5329 0.8120 0.5661 -0.7312 0.0356 -.0869 -0.9724 1.0026 -0.9941 0.2845 -0.2582 -.0814 .4685 >delZcos >delZ 69.0? .8? 135.3? 45.1? 163.1? 122.2? 35.7? 55.5? 137.0? 88.0? 85.0? 166.5? NA 173.8? 73.5? 105.0? 85.3? 62.1? >delZ ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Notes: - Letcher's method based on standard temperature and pressure - In cases 1-9, no observed times or dates are given, no way to see how LDc's GMT computation compares. - Any test case from the Thompson-Bowditch set can be used Case Notes 1) Letcher, p.92, moon-sun 2) Stark, p.vi, moon-venus, basically a vertical alignment case 3) Stark, p.vi, moon-sun 4) Stark, p.vi, moon-Aldebren 5) George Huxtable, "About Lunars" moon-sun, p. 25, fer3.com/arc/imgx/About-Lunars.pdf 6) Sight 2, August 16, 2017, LDo 69?27.2', SDm 16.2' AGm 00.2' SDs 15.8' -> LDpc 69?59.4' Excellent agrement with Frank Reed's lunars calculator and Bowditch-Thimpson method 7) Margetts Linear Lunar Tables 1790, Example VII, p.15 8) Margetts Linear Lunar Tables 1790, Example XII, p.15 9) Margetts Linear Lunar Tables 1790, Example XIII, p.15 10) Reversed engineered to get pure Reed example LDa=62?42.25' KP=42?00.2'N 074?07.5'W Oct 14, 2017 GMT14:43:55 LDpc=62?42.25'+16.1'+16.0'+00.2'=63?14.55' SDs and augmentation 11) Mystic Seaport Workshop, Lunars exercise, November 15, 2014, Popko best sight #4 12) George Huxtable, About Lunars, 3.9 BORDA'S METHOD: AN EXAMPLE, NavList, 2002, fer3.com/arc/imgx/About-Lunars.pdf, pp.22-23. 13) NavList, A Lunar Example: Sun and Moon Vertically Aligned", http://fer3.com/arc/m2.aspx/Lunar-Example-Sun-Moon-vertically-aligned-FrankReed-dec-2017-g40943 14) "An Epitome of Navigation and Nautical Astronomy, with Improved Lunar Tables" by Mrs. Janet Taylor Longitude by Lunar Observations, Ex. 2-1852, March 9d, p.219 https://books.google.com/books?id=rvg_BRfIckEC&pg=RA1-PA92&lpg=RA1-PA92&dq=what+are+secants+in+navigation&source=bl&ots=4Emuo3BbRa&sig=DtNDNc6tTRBTVFlesE_pjnLOL4Y&hl=en&sa=X&ved=0ahUKEwj1oYimnfbZAhVjzlkKHbBLCGo4ChDoAQg6MAY#v=onepage&q=lunar%20distance&f=false 15) The Description and Use of the Sliding Gunter in Navigation – Andrew Mackay, Example I, p.102, Text LDc=69?17'46" Time=05:28:08 https://play.google.com/books/reader?id=z9QyAQAAMAAJ&printsec=frontcover&output=reader&hl=en&pg=GBS.PA101 16) Nathaniel Bowditch, "The New American Practical Navigator: being an Epitome of Navigation", 1821 edition, Lunar Observations, To find the true distance, Example I, pp.154-155 (Adobe Acrobat p.193). True distance = 47?24'49". Excellent comparison! 17) Nathaniel Bowditch, "The New American Practical Navigator: being an Epitome of Navigation", 1821 edition, Lunar Observations, To find the true distance, Example II, pp.155-156 (Adobe Acrobat p.194). True distance = 81?11'51". Excellent comparison! 18) Moon-Jupiter (near) July 25, 2018, Lat 28?41.1N Lon 082?18.3'W Astra IIIB Hyacinth Pl summer stay observation #3 References: John S. Letcher, Jr., "Self-Contained Celestial Navigation with H.O. 208", Chapter "16. Time by Lunar Distance:" pp.87-95.