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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Lunar Distances - trigonometric clearing
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.

```
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