A body on your meridian gives latitude with one subtraction and no accurate time: the noon Sun by day, Polaris and the meridian stars at twilight.
How do I work out the time of local noon for a noon sight?
Take the almanac's Mer Pass, in local mean time, and add your expected longitude in time if west, subtract it if east; 1° is 4 minutes. Mer Pass 1204 at 37°30′W gives noon at 1434 UT.
Local noon is the moment the Sun crosses your meridian, rarely 1200 by the clock. The almanac gives Mer Pass in local mean time; turn the longitude you expect to have reached into time (1° is 4 minutes) and add it if west, subtract it if east.
Start ten minutes early and follow the Sun up. It climbs ever more slowly, hangs, then dips: the highest reading is the meridian altitude. The top of the curve is flat, so a few minutes either way cost almost nothing and the watch need only be roughly right; farther off, work the sight as an ordinary sun line.
Two cases spoil the flat top. A fast boat running north or south shifts the peak off the meridian by its own movement: take the altitude at the computed time. A Sun nearly overhead has a sharp peak and a bearing that swings round in minutes: time sights either side of noon and plot each as a circle of radius z round the Sun's geographical position.
How do I get my latitude from the Sun's noon altitude?
Take the zenith distance, z = 90° − Ho, named opposite to the Sun's bearing, and combine it with Dec: same names add, contrary names subtract, and the latitude takes the name of the larger.
Correct Hs to Ho: index error (on the arc subtract, off the arc add), dip (subtract), then the main correction, plus for the lower limb, minus for the upper.
The sextant measures from the visible horizon, below the horizontal by the dip.
The zenith distance z = 90° − Ho is how far you are from the point under the Sun, whose latitude is its declination. Take Dec for the UT of noon, and note which way you faced.
At noon the Sun lies on the arc through P and Z: the triangle closes up and its sides add or subtract.
Name z opposite to the Sun's bearing: Sun to the south, z is north. Then same names add, contrary names subtract, and the latitude takes the name of the larger.
| Sun bears | z | Dec | Latitude |
|---|---|---|---|
| south, Ho 60° | 30° N | N10° | same, add: 40°N |
| south, Ho 50° | 40° N | S20° | contrary, subtract: 20°N |
| north, Ho 70° | 20° S | N5° | contrary, subtract: 15°S |
Lat = Dec + z with the Sun to the south, Dec − z with it to the north; north plus, south minus.
How do I get latitude from a circumpolar star at lower transit?
Add the polar distance, 90° − Dec, to Ho: at lower transit, below the pole, latitude = Ho + polar distance. Ho 20° with Dec N70° gives 40°N.
The same rule serves a star or planet on your meridian in twilight, when body and horizon both show. Two stars taken together, one north and one south, cancel a constant error: mean the two latitudes.
| Body | After index error and dip | Declination |
|---|---|---|
| Sun | refraction, semi-diameter | changes slowly |
| Star, planet | refraction only | star fixed, planet hourly |
| Moon | refraction, semi-diameter, parallax | fast: use the exact UT |
The Moon is so close that you add parallax, the almanac's HP × cos altitude. It crosses the meridian about 50 minutes later each day.
A circumpolar star (Dec greater than 90° − latitude, same name) never sets and crosses the meridian again below the pole. At this lower transit, latitude = Ho + polar distance, 90° − Dec.
How do I correct a Polaris altitude to get my latitude?
Use the almanac's Polaris table: latitude = Ho − 1° + a0 + a1 + a2, with a0 from LHA Aries, a1 from latitude and a2 from the month.
The altitude of the celestial pole equals your latitude, and Polaris circles within 1° of it. The almanac's Polaris table bridges the gap with three corrections: a0 from LHA Aries (GHA Aries − west longitude, + east), a1 from latitude, a2 from the month.
Latitude = Ho − 1° + a0 + a1 + a2.
Follow the Plough's pointers, Merak to Dubhe, about five times their gap; Cassiopeia's W lies as far away on the other side. Polaris is only second magnitude: at dusk set your DR latitude on the sextant and sweep the horizon due north.
Near the equator it is too low to trust; south of it, below the horizon.
How do I find the south celestial pole without a pole star?
Use the Southern Cross: extend its long axis, Gacrux through Acrux, about 4½ times, and a line at right angles from midway between the Pointers meets it at the pole.
No bright star marks the south celestial pole: Sigma Octantis, about 1° from it, is far too faint. For latitude take a bright star on the meridian, such as Achernar, Canopus or Acrux.
The Southern Cross points the way: extend its long axis, Gacrux through Acrux, about 4½ times, and a line at right angles from midway between the Pointers meets it at the pole. By eye that checks latitude to a degree or so. With the Cross upright, Acrux is on your meridian. The False Cross is larger and dimmer, with no bright Pointers beside it.
How do I get a noon position from a morning sun line?
Carry the morning sun line forward by the course and distance made good, keeping its direction, and cross it with the noon latitude: that crossing is your noon position.
A latitude is a position line running east–west. For a noon position, carry the morning sun line forward by the course and distance made good, keeping its direction, and cross it with the noon latitude. Advanced to dusk, the latitude moves only by the north–south part of the run; a star bearing near east or west cuts it best.
If cloud takes the noon sight, cross two sun lines with a run between them, or take a meridian star or Polaris at dusk.
Latitude sailing needs no longitude. Reach the latitude of your landfall well up-wind and up-current of it, then run along the parallel; each noon sight gives the miles to make good north or south, and a latitude off the DR reveals the north–south part of the current. Unsure of the longitude, slow down and close the land in daylight.
Questions from this topic, as the app asks them. Open one to see the answer.
You are on the ARC route, the GPS has failed and you want a noon latitude. At what UT is the Sun on your meridian?
A. 1409 UT
Mer Pass 1148 LMT + 35°20′ of west longitude in time (2h21m) = 1409 UT; longitude west is added.
Your noon sight on the ARC route gives this. Which working gives your latitude?
D. z 38°59.1′ − Dec 21°22.1′ = 17°37.0′N
Sun south of you: Lat = Dec + z. With Dec south (−21°22.1′): −21°22.1′ + 38°59.1′ = 17°37.0′N.
At dusk between Bermuda and the Azores, Arcturus crosses your meridian bearing south. What is your latitude?
A. 37°08.2′N
z = 90° − 71°57.8′ = 18°02.2′; the star is south of you: Lat = Dec + z = 19°06.0′ + 18°02.2′ = 37°08.2′N.
Bound from the BVI to Bermuda, you take Polaris at evening twilight. What is your latitude?
C. 25°41.7′N
Lat = Ho − 1° + a0 + a1 + a2 = 25°32.0′ − 60′ + 68.8′ + 0.5′ + 0.4′ = 25°41.7′N.
On a night watch in the South Pacific you look for the south celestial pole. Which point is it?
D. A
Extend the Cross's long axis, Gacrux to Acrux, about 4½ times its length; the Pointers' perpendicular bisector meets it there.
On your plotting sheet you have run the morning sun line up to noon and drawn the noon latitude. Which point is your noon position?
D. A
The noon fix is where the run-up morning line (blue) cuts the noon latitude: A. B uses the line before it was run up.
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