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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Lunar Distances - trigonometric clearing
From: Henry Halboth
Date: 2004 May 12, 21:05 -0400
From: Henry Halboth
Date: 2004 May 12, 21:05 -0400
As a matter of potential interest, the following is the haversine format
I employed in clearing Lunar Distances before the advent of calculators
and, wherein ...
Hs = sextant altitude Ds = sextant distance
Ha = apparent altitude Da = apparent distance
Hc = true altitude Dc = cleared distance
M = moon S = sun or star
Z = angle at zenith
1) hav Z = (s - sin Ha M) x sin (s - Ha S) x sec Ha M x sec Ha S,
in which ... s = 1/2 (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 ~ Hc S 49-38-48 n hav 0.176241
Dc 74-37-07 n hav 0.367378
To afford a comparison, altitudes here 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.
I hope that this transmits without becoming hopelessly screwed up, as it
has been most difficult to set it up so as to even print with any degree
of accuracy.
