Latitude · Tromsø Sextant Nights
Sextant 69°N

Stages 4 and 5

Latitude from one star

The explorers' trick, and the best client demonstration. It takes one measurement and some adding up.

equatoraxis → polelatyour horizonto Polaris (parallel to axis)lat
The pole's height above your horizon equals your latitude. Polaris is almost at the pole, so its altitude is almost your latitude.
poleabove pole: Lat = Ho − 37′below pole: Lat = Ho + 37′beside: Lat ≈ Ho37′
Polaris circles the pole at a distance of 37′ once a day. Table T4 gives the correction for any moment. Find the time, look it up, add it.

A · Polaris against the sea horizon

Use a shore with open sea to the north (the outer coast of Kvaløya or Ringvassøya), at dusk while the horizon is still sharp. Rock the sextant gently: the star swings in an arc, and the lowest point of the arc should just touch the horizon.

12:0014:0016:0018:0020:0022:0001 Oct15 Oct01 Nov15 Nov01 Dec15 Dec01 Jan15 Jan01 Feb15 Feb01 Mar15 Mar25 Mar
Norwegian local time (summer time until 25 Oct). Dark gold: Polaris visible and horizon sharp (sun 6°–9° down), the best window. Light gold: the horizon is fading (9°–12°).

Worked example · 15 Feb 2027, 16:10:00 UTC

1 · Altitude
Sextant reading70°23.0′sea horizon, eye 4 m−Index error (on the arc)2.4′−Dip, eye 4 m3.5′table T7=Ha70°17.1′−Refraction, −15 °C0.4′table T6=Ho70°16.7′
2 · Where is Polaris on its circle?
GHA♈︎ 15 Feb, 00h144°46.8′table T1+16 h240°39.4′table T2+10 min 00 s2°30.4′table T2+Your longitude (E)18°57.0′=LHA♈︎ (drop whole 360s)46°53.6′ ≈ 47°
3 · Latitude
Ho70°16.7′+Correction at LHA♈︎ 47°-37.1′table T4=Latitude69°39.6′ NTrue: 69°39.0′ N. Off by 0.6′ = 1.1 km

B · South star + north star with the tray

Wait until a star is due south (or due north, below the pole). Transit times are in T5. Keep following it with the tangent screw and keep the highest reading (the lowest, for a north star). The time doesn't need to be exact.

N horizonS horizonzenithpole (69° = Lat)equatorPollux, due SHo 49°Deneb, due NHo 25° (below pole)Dec90° − Dec
Looking at the sky from the side, north on the left. When a star is due south, Lat = 90° − Ho + Dec. When a star is due north below the pole, Lat = Ho + 90° − Dec.
Average one south star and one north star. Errors from index error and refraction push the two results in opposite directions and cancel.

Worked example · camp in the valleys SE of Tromsø, 15 Feb 2027

Pollux: due south at 21:46
Highest reading97°42.3′−Index error2.4′÷ 2= Ha48°49.9′−Refraction, −22 °C1.0′table T6=Ho48°49.0′90° − Ho + Dec90° − 48°49.0′ + 27°57.5′Dec from table T3=Latitude69°08.6′ N
Deneb: due north at 22:41
Lowest reading49°09.8′−Index error2.4′÷ 2= Ha24°33.7′−Refraction2.4′=Ho24°31.3′Ho + 90° − Dec24°31.3′ + 90° − 45°22.5′=Latitude69°08.7′ N
Average
=Latitude69°08.6′ NTrue: 69°09.0′ N