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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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Re: Calculate new coordinates given bearing and distance?
From: Lars Bergman
Date: 2021 Nov 1, 15:16 -0700

Tony,

With the same nomenclature as Geoffrey Kolbe used,

Lat1 and Long1 are your start latitude and longitude.
Lat2 and Long2 are the new coordinates at the given bearing and distance
Diff will be the difference between Long1 and Long2
Dist will be the distance in nautical miles. A nautical mile is equivalent to one minute of arc on a Great Circle, so this is converted to degrees in the formulae by dividing by 60
hav(90°-Lat2) = N + (1-Q)·hav(Bearing)
where N = hav(Lat1 - (90°-Dist/60))
P = hav(Lat1 + (90°-Dist/60))
Q = N + P
hav(Diff) = (hav(Dist/60) - N) / (1-Q)
where N = hav(Lat2 - Lat1)
P = hav(Lat2 + Lat1)
Q = N + P
Long2 = Long1 + Diff
Note that N, P and Q are different in the two formulas. As hav(x) = hav(-x) the longitude difference could be either positive or negative, depending on the bearing. I have checked the formulas for only one case (Lat1=37°, Long1=0°, Bearing=15°, Dist=600'; resulting in Lat2=46°36.3', Long2=3°43.9', with 5-figure haversines) so there may be cases where they do not work.
Lars
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