# NavList:

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

**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(D_{12}) = sin(d_{1}) · sin(d_{2}) + cos(d_{1}) · cos(d_{2}) · cos(GHA_{1}−GHA_{2})

(7.5a)

cos(A) = [ sin(d_{2}) − sin(d_{1}) · cos(D_{12}) ] / [ cos(d_{1}) · sin(D_{12}) ]

(7.5b)

cos(B) = [sin(H_{2}) − cos(D_{12}) · sin(H_{1}) ] / [ sin(D_{12}) · cos(H_{1}) ]

(7.5c)

sin(Lat_{A±B}) = sin(d_{1}) · sin(H_{1}) + cos(d_{1}) · cos(H_{1}) · cos(A ± B)

(7.5d)

cos(LHA_{1}) = [sin(H1) − sin(d1) · sin(Lat_{A±B}) ] / [ cos(d1) · cos(Lat_{A±B}) ]

(7.5e)

Lon = LHA_{1} − GHA_{1}

(7.5f)

Where the GHA_{i}, d_{i}, H_{i} are the GHA, declination and H_{Observed} of the body_{i} respectively.

I guess - the H_{1} and H_{2} 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 H_{1} 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 body_{1} 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.