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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Clearing Lunar Distances by trigonometry
From: Henry Halboth
Date: 2004 May 12, 23:10 -0400
From: Henry Halboth
Date: 2004 May 12, 23:10 -0400
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.
