Comments on: Great Circle algorithm https://habitablezone.com/2023/04/14/great-circle-algorithm/ Fri, 17 Apr 2026 05:11:30 -0700 hourly 1 http://wordpress.org/?v=3.3.1 By: ER https://habitablezone.com/2023/04/14/great-circle-algorithm/#comment-51787 ER Sat, 15 Apr 2023 17:24:43 +0000 https://habitablezone.com/?p=99346#comment-51787 What is the intercept and initial course from Los Angeles (34d 03'N, 118d 15'W) TO Manila (14d 35'N, 120d 59'E). INPUT DATA Ho = 90 degrees = 5400'. DEC = 14d 35' GHA = 239d 01' Lat = 34d 03' Lon = -118d 15' INTERMEDIATE VALUES <strong>LHA</strong> = GHA + Lon = 239.01 + (-118d 15') = 120d 46' cos LHA = -.5115 cos DEC x cos LHA = <strong>C</strong> = -.4951 sin DEC = <strong>S</strong> =.2518 sin Lat = .5599 cos Lat = .8285 INTERCEPT CALCULATION Hc = INVsin (( S x Sin Lat ) + ( C x Cos Lat )) Hc = INVsin (-.2692) Hc = -15d 37' = -937' Intercept = Ho – Hc = 5400' - (-937') = <strong> 6337 NM</strong> AZIMUTH CALCULATION X = (( S x Cos Lat) – (C x Sin Lat )) / cos Hc X = ((.2086)-(-.2772))/cos Hc X = (.4858) /.9631 X = .5044 If X is greater than +1 or less than -1 (due to truncation error), just reset it to +1 or -1. A = INVcos ( .5044 ) = 59d 43' If LHA > 180 degrees, then Azimuth Z = A Otherwise, Z = 360-A <strong>Z = 300d</strong> since LHA < 180d What is the intercept and initial course from Los Angeles (34d 03′N, 118d 15′W)
TO Manila (14d 35′N, 120d 59′E).

INPUT DATA
Ho = 90 degrees = 5400′.
DEC = 14d 35′
GHA = 239d 01′
Lat = 34d 03′
Lon = -118d 15′

INTERMEDIATE VALUES
LHA = GHA + Lon = 239.01 + (-118d 15′) = 120d 46′
cos LHA = -.5115
cos DEC x cos LHA = C = -.4951
sin DEC = S =.2518
sin Lat = .5599
cos Lat = .8285

INTERCEPT CALCULATION
Hc = INVsin (( S x Sin Lat ) + ( C x Cos Lat ))
Hc = INVsin (-.2692)
Hc = -15d 37′ = -937′
Intercept = Ho – Hc = 5400′ – (-937′) = 6337 NM

AZIMUTH CALCULATION
X = (( S x Cos Lat) – (C x Sin Lat )) / cos Hc
X = ((.2086)-(-.2772))/cos Hc
X = (.4858) /.9631
X = .5044
If X is greater than +1 or less than -1 (due to truncation error), just reset it to +1 or -1.

A = INVcos ( .5044 ) = 59d 43′

If LHA > 180 degrees, then Azimuth Z = A
Otherwise, Z = 360-A
Z = 300d since LHA < 180d

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