At dawn and dusk the sky gives several position lines within minutes: a fix with no run in it. Stars are the simplest bodies to work; planets and the Moon need a little more.
1 · Twilight
Stars and horizon together
When can I take star sights at dusk or dawn?
Between civil twilight, the Sun 6° below the horizon, and nautical twilight, 12° below: only then are star and horizon visible together. The almanac lists both times by latitude in LMT.
A star sight needs star and horizon at once: between civil twilight, the Sun 6° below the horizon, and nautical twilight, 12° below. The almanac lists them by latitude in LMT. In the tropics the window is little over 20 minutes; in high latitudes at midsummer the Sun never gets 12° down and only the brightest bodies show.
Dusk
Dawn
You wait for
the stars
the horizon
Take first
the brightest
the faintest, east before west
Be on deck
sextant preset
early, in the dark
After nautical twilight the horizon is too dim to trust; so may be a horizon under a bright Moon: doubt a star taken beneath it.
2 · Planning
Which stars, and where to look
Which stars should I choose for a good star fix?
Three stars about 120° apart, or four in opposite pairs, 20° to 70° high. HO 249 Volume 1, entered with latitude and LHA Aries, lists seven selected stars and marks the best three.
Choose three stars about 120° apart, or four in opposite pairs, 20° to 70° high: lower, refraction is uncertain; overhead, the sextant is hard to swing. Two stars on one bearing give the same line twice.
120° apart: the lines cut at 60° and a constant error cancels.
The star finder, set to your latitude and the LHA Aries of twilight, shows every navigational star's altitude and azimuth; planets you plot on it yourself. HO 249 Volume 1, entered with latitude and LHA Aries, lists seven selected stars with Hc and Zn and marks the best three; its fix needs Table 5's precession correction.
Preset Hc and look along Zn: the star is in the telescope, up to 1′ off per mile of DR error. For an unknown star note altitude, bearing and time: they give its Dec and SHA. A huge intercept with a bearing far off the prediction means another body; a brilliant steady light beside your star is a planet.
3 · Reducing a star
Aries plus SHA
How do I find the LHA of a star from the almanac?
Add the star's SHA to GHA Aries, then subtract west longitude or add east: LHA★ = GHA Aries + SHA − longitude west. The almanac gives no star's GHA, only Aries and each star's SHA and Dec.
The almanac tabulates no star: it gives the GHA of Aries, a reference point among them, and each star's fixed SHA and Dec. Take GHA Aries for the hour, the increment from the Aries column, add the SHA, then your longitude as for the Sun.
LHA of a star
GHA Aries 300°00.0′
SHA of the star 150°00.0′
DR longitude 060°00.0′W
300° + 150° − 60° = 390°
LHA★ 030°: west of the meridian
Rule
LHA★ = GHA Aries + SHA − longitude west (+ east).
The altitude takes index error, dip and refraction only: a star has no semi-diameter. Hc, Zn and the intercept follow the Sun's rules, a contrary-name Dec negative. In HO 249, Volume 1 serves its selected stars; any body with Dec up to 29° goes in Volumes 2 and 3. Intercepts near 30 miles: rework from the fix.
4 · Planets
Four wanderers, own columns
How do I find a planet's GHA and Dec in the almanac?
Venus, Mars, Jupiter and Saturn each have their own hourly GHA and Dec on the daily page: take the increment from the Sun and planets column, add v (Venus's can be negative) and correct Dec with d.
Venus, Mars, Jupiter and Saturn move among the stars, so the daily page gives each its own hourly GHA and Dec. Take the increment from the Sun and planets column, add v (Venus's can be negative) and correct Dec with d.
Body
GHA
Extra
Altitude extras
Star
Aries + SHA
none
none
Planet
own column
v, can be minus
small extra: Venus, Mars
Moon
own column
v, always plus
parallax, ± semi-diameter
Venus stays within about 47° of the Sun: at dusk it shows first and sets soon, so take it first, above 10°; by day find it with the sextant preset. A brilliant planet high at midnight is Jupiter, not Venus.
5 · Moon
Close, fast and lit on one side
Which limb of the Moon do I bring down to the horizon?
The lit limb, upper or lower, whichever faces the Sun. The Moon also needs parallax, its HP times the cosine of the altitude, and because it moves fast, never skip the d correction.
The Moon moves fast: use the Moon column of the increments, add v, and never skip d: Dec can change many minutes an hour. Bring down the lit limb, upper or lower, whichever faces the Sun.
So near, the Moon needs parallax too.
Parallax is the horizontal parallax HP, 54′ to 61′, times the cosine of the altitude. The Moon tables give it in two parts, the second from HP in the L or U column, less 30′ for an upper limb.
Moon, lower limb
Apparent altitude 60°00.0′, HP 60.0′
Refraction −0.6′
Parallax 60.0′ × cos 60° = +30.0′
Semi-diameter +16.4′
Ho 60°45.8′
Near the quarters the Moon is up by day, about 90° from the Sun: with a sun line it makes a fix with no run.
6 · Plotting
Lines to one moment
How do I plot star sights taken a few minutes apart?
Lay off each intercept from its own AP, towards along Zn or away along the reciprocal, draw the line at right angles, then advance the earlier lines along the course by the run to the last sight.
Plot each intercept from the position it was worked from, its own AP with HO 249, along Zn if towards or the reciprocal if away, and the line at right angles.
The sights are minutes apart: move each earlier line forward along the course by the run to the last sight, or a later one back, adding any current or drift. A dawn star line is advanced the same way to cross a sun line hours later, but a simultaneous star fix outranks any line carried by log and compass.
7 · Cocked hat
How far to trust the fix
Where am I if my three star lines make a cocked hat?
At its centre, if the stars were spread round the horizon: a constant error moves every line the same way and keeps you inside the cocked hat. With all the stars on one side you may be outside it.
Three lines seldom meet in a point. With the stars spread round the horizon a constant error, index or dip, moves every line the same way along its azimuth and you stay inside a small triangle: take its centre. With all the stars on one side you may be outside it.
Stars on one sideyou may be outside the hat
Four lines, one oddtrust the three that agree
A small angle of cut magnifies error: at 30° a mile moves the fix two miles. Two lines always cross and hide a blunder; a fourth or fifth star shows up the odd line: wrong star, mistimed sight, misread degree, intercept laid off the wrong way. A large hat near danger: work from the corner nearest it.
Practice questions
Questions from this topic, as the app asks them. Open one to see the answer.
Almanac, 14 Feb, lat 20°N
Nautical twilight begins 0541 LMT
Civil twilight begins 0607 LMT
Sunrise 0630 LMT
You are running down the trades at 20°N and want a dawn star fix. When do you have both the stars and a usable horizon?
From about 0541 to 0607 LMT
Before 0541 LMT, in full darkness
From about 0607 to 0630 LMT
From 0630 LMT, once the Sun is up
Show the answer
A. From about 0541 to 0607 LMT
Between nautical twilight (Sun 12° down: the horizon appears) and civil twilight (6° down: the stars fade) you have both.
All 100 questions of this topic are in the app: practice by topic with the reason after every answer, your mistakes brought back, and a timed mock exam. Free, no sign-up, in the browser or in Telegram.
