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Re: Clearing Lunar Distances by trigonometry
From: Dan Allen
Date: 2004 May 15, 15:30 -0700
From: Dan Allen
Date: 2004 May 15, 15:30 -0700
I have posted a web page that contains this formatted correctly. It is located at: http://danallen46.home.comcast.net/Halboth.htm Dan Allen -----Original Message----- From: Navigation Mailing List [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]On Behalf Of Henry C. Halboth Sent: Wednesday, May 12, 2004 8:11 PM To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM Subject: Clearing Lunar Distances by trigonometry I make one more effort this evening to get this format across straight - hope it works this time. As a matter of potential interest, the following is the haversine format I employed in clearing Lunar Distances by spherical trigonometry, before the advent of calculators and, wherein ... Hs = sextant altitude.............. Ds = sextant distance.............S = sun Ha = apparent altitude............ Da = apparent distance.......... M = moon Hc = true altitude.................... Dc = calculated distance........ Z = angle at zenith 1) hav Z = sin (s - Ha M) x sin (s - Ha S) x sec Ha M x sec Ha S in which ... s = ? (Ha M + Ha S + Da) 2) hav Dc = hav (Hc M ~ Hc S) + cos Hc M x cos Hc S x hav Z, therefore ... Ha M 75-07-00 l sec 0.590318 Ha S 25-45-03 l sec 0.045424 Da 74-46-17 2s 175-38-20 s 87-49-10 s - Ha M 12-42-10 l sin 9.342213 s - Ha S 62-04-07 l sin 9.946211 Z l hav 9.924166 l hav 9.924166 Hc M 75-22-00 l cos 9.402489 Hc S 25-43-12 l cos 9.954689 l hav 9.281344 n hav 0.191137 Hc M~S 49-38-48 n hav 0.176241 Dc 74-37-07 n hav 0.367378 To afford a comparison, the altitudes used, both apparent and true, are as employed in an example of Borda's method, set forth on page 417 of Norie's 1889 edition where the cleared distance is found to be 74-37-10 - all of 3" greater than that found by the haversine formulae stated above.