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- Q135 - Navigation Problems: Oceans
445. The great circle distance from LAT 35° 57.2' N, LONG 05° 45.7' W to LAT 24° 25.3' N, LONG 83° 02.6' W is 3966.5 miles and the initial course is 283.7° T. The latitude of the vertex is 38° 09.4' N. What is the longitude of the vertex?
The vertex longitude is calculated using the spherical trigonometry formula cos (Δλ) = tan (φ1) / tan (φv), where φ1 is the departure latitude and φv is the vertex latitude. Applying this formula with the given latitudes yields a longitude difference of approximately 22 32.5', resulting in a vertex longitude of 28 18.2' W.
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