A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Tony Oz
Date: 2017 Sep 1, 10:39 -0700
I tried the direct calculation of position - as per the "CELESTIAL NAVIGATION IN THE GPS AGE" by John H. Karl, Chapter 7, the Position without St.Hilaire article.
The formulas are:
cos(D12) = sin(d1) · sin(d2) + cos(d1) · cos(d2) · cos(GHA1−GHA2)
cos(A) = [ sin(d2) − sin(d1) · cos(D12) ] / [ cos(d1) · sin(D12) ]
cos(B) = [sin(H2) − cos(D12) · sin(H1) ] / [ sin(D12) · cos(H1) ]
sin(LatA±B) = sin(d1) · sin(H1) + cos(d1) · cos(H1) · cos(A ± B)
cos(LHA1) = [sin(H1) − sin(d1) · sin(LatA±B) ] / [ cos(d1) · cos(LatA±B) ]
Lon = LHA1 − GHA1
Where the GHAi, di, Hi are the GHA, declination and HObserved of the bodyi respectively.
I guess - the H1 and H2 must correspond to the same moment in time. So in real life I will need either account for the MOB (the movement of body), for the MOA (movement of observer), or do both advancements to the H1 before I may start using the formulas.
So I'm stuck here: I need to know the relative angle between my course T and the azimuth of body1 to be able to obtain the correct value from the V[kn] · cos(Zn - T) · t[hour] formula. (The "V" is my speed, the "t" is the interval between the sights)
Is there a way to do it without any plotting at all? - here (the original "Death..." post) Frank still used some DR and paper graphs.
Thank you in advance.
All the formulas and images are by John H. Karl.