Part III · The line of position · Page 3 of 4
The radius, in miles
The angle from straight overhead (your zenith) down to the Sun is the zenith distance, z = 90° − Ho. Because the Sun's light arrives parallel, the same angle z is the arc between you and the GP at the Earth's center.
- Ho
- 50°00.0'
- z = 90° − Ho
- 40°00.0'
- z in minutes of arc
- 2,400′
- Your distance from the GP
- 2,400 nm
The Sun's light arrives parallel everywhere, so the angle from your zenith down to the Sun equals the angle at the Earth's center between you and the GP. Each minute of that angle is one nautical mile along the surface.
Radius of the circle = z = 90° − Ho, and 1′ of arc = 1 nautical mile
The Sun's GHA is 47°12.4′ and its declination N 15°03.2′. You measure Ho 52°18.6′.
GP: N 15°03.2′ (the declination), W 047°12.4′ (GHA under 180° is west longitude).
z = 90° − 52°18.6′ = 37°41.4′ (borrow 60′, not 100′).
Radius = 37 × 60 + 41.4 = 2,261.4 nm.
If the GHA is over 180°, the GP is in east longitude: 360° − GHA. A GHA of 300° puts the GP at E 060°.