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    The "Death to the Intercept Method" revisited?
    From: Tony Oz
    Date: 2017 Sep 1, 10:39 -0700

    Hello!

    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)
    (7.5a)

    cos(A) = [ sin(d2) − sin(d1) · cos(D12) ] / [ cos(d1) · sin(D12) ]
    (7.5b)

    cos(B) = [sin(H2) − cos(D12) · sin(H1) ] / [ sin(D12) · cos(H1) ]
    (7.5c)

    sin(LatA±B) = sin(d1) · sin(H1) + cos(d1) · cos(H1) · cos(A ± B)
    (7.5d)

    cos(LHA1) = [sin(H1) − sin(d1) · sin(LatA±B) ] / [ cos(d1) · cos(LatA±B) ]
    (7.5e)

    Lon = LHA1 − GHA1
    (7.5f)

    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.

    Regards,

    Tony

    PS

    All the formulas and images are by  John H. Karl.



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