Course / The intercept method

Part III · The line of position · Page 2 of 8

The navigational triangle

Where do the tables get Hc and Z? From one spherical triangle on the globe: the pole (P), you (Z, your zenith) and the body's ground position (X).

90° − lat = 50°00.0'90° − dec = 72°00.0'z = 90° − Hc = 37°18.3'P (pole) · angle t = 35°Z (you) · angle Z = 116°X (GP)N
Three sides, two of them known (90° − latitude and 90° − declination) and the angle between them (from LHA): that fixes the third side, z, and so Hc, and the angle Z.
Pub. 249 is entered with
Lat 40°, Dec 18° same, LHA 35°
and gives Hc = 90° − z
52°41.7'
and Z, the angle at you
116° → Zn 244°

Change any input and every part of the triangle changes with it. That is why the tables need all three arguments.

  • P to you: 90° − your latitude (the AP latitude).
  • P to the GP: 90° − declination (more than 90° when the declination is of contrary name).
  • The angle at P: the meridian angle, from LHA.

Two sides and the angle between them fix the whole triangle: the third side is the zenith distance, so Hc = 90° − z, and the angle at you is Z, the azimuth angle. Pub. 249 is this triangle solved in advance for every whole degree of latitude, declination and LHA, which is why the AP must make those three whole.