Course / The intercept method

Part III · The line of position · Page 3 of 8

The triangle on the celestial sphere

The same triangle can be drawn on the celestial sphere, as most textbooks do: the elevated pole, your zenith and the body. The sides are the same angles as on the globe (90° − latitude, 90° ∓ declination and the zenith distance), because the sphere is just the globe projected outward.

SunZenithN poleS pole90° − lat90° − deczenith distancet = 56°
May 21, 15:00 UT. Earth fixed: the sky turns west. Drag to turn the sphere; drag the body to run the clock; drag your zenith to move yourself. Not to scale: the real sphere is so large the Earth would be a point.

Navigational triangle

Elevated pole, zenith and body, joined by great circles. Its sides are 90° − latitude, 90° − declination and the zenith distance; the angle at the pole comes from LHA. Solving it gives Hc and the azimuth.

90° − latitude
50°00.0'
90° ∓ declination
69°46.7'
Zenith distance
51°16.0'

The angle at the pole is the meridian angle, from LHA; the angle at the zenith is the azimuth angle Z. Watch them as you run the clock: the triangle swings with the sky, and the tables follow it.