Worked: latitude by Polaris
1The lesson in plain words
Polaris's altitude is close to your latitude. Apply three almanac corrections to find the latitude line. Worked on 24 November 2026.
Why it works
Polaris lies only about 37′ from the north celestial pole in 2026 (Navigation: compass error by Polaris). The pole's altitude equals your latitude. Polaris circles the pole once a sidereal day, so its altitude is up to about 37′ more or less than your latitude, depending on LHA Aries.
The tables
The Nautical Almanac's Polaris tables give Latitude = Ho − 1° + a0 + a1 + a2. Ho is the sextant altitude corrected for index error, dip and refraction. Use LHA Aries throughout: interpolate a0 from LHA Aries, then use the matching LHA column for a1 with approximate latitude and a2 with month. All three are positive; the −1° balances the constants built into them.
Worked: the sight
24 November 2026, 1912 UT, at DR 26°05′N 019°10′W. GHA Aries 351°45.5′ − 19°10′ = LHA Aries 332°35.5′. Ho of Polaris is 26°21.8′.
Worked: the answer
For this worked example, use these supplied corrections: a0 = 0°48.7′, a1 = 0.5′, a2 = 1.1′. The lookup arguments are LHA Aries 332°35.5′ throughout, plus latitude about 26° for a1 and November for a2. Latitude = 26°21.8′ − 1° + 48.7′ + 0.5′ + 1.1′ = 26°12.1′N: a position line running east–west, about 7 M north of the DR.
Limits
Polaris is only of magnitude 2, so find it early in twilight with a precomputed altitude, close to your latitude. Near the equator it is very low, with large and uncertain refraction; south of the equator it is normally out of sight. Cross its latitude line with a star line from the east or west for a fix.
2Key data
- Formula
- Latitude = Ho − 1° + a0 + a1 + a2
- Arguments
- a0: LHA; a1: LHA + latitude; a2: LHA + month
- Ho
- Corrected for IE, dip and refraction; no semi-diameter
- Worked LHA Aries
- 351°45.5′ − 19°10′ = 332°35.5′
- Worked latitude
- 26°21.8′ − 1° + 48.7′ + 0.5′ + 1.1′ = 26°12.1′N
- Spanish terms
- Latitud por la Polar; correcciones de la Polar
3Key points
- 1
Polaris's altitude is within about 37′ of your latitude in 2026.
- 2
Latitude = Ho − 1° + a0 + a1 + a2. All use LHA Aries; a1 also uses latitude, a2 also month.
- 3
Find LHA Aries from GHA Aries for the UT of the sight and your longitude.
- 4
Low near the equator and normally unseen south of it; cross the line with an east or west star.
4Frequent mistakes
Wrong: Polaris's altitude is your latitude; no correction is needed.
Right: It can differ by up to about 37′, depending on LHA Aries. Apply the Polaris tables.
Wrong: Forget the −1° because all three corrections are positive.
Right: The constants built into a0, a1 and a2 add up to 1°. Without the −1°, you are 60 M too far north.
Wrong: Enter the a0 table with your longitude.
Right: Enter it with LHA Aries: GHA Aries for the exact UT, minus west longitude or plus east.
5Practice case & exam keys
Another evening, LHA Aries is 227°, so Polaris is near its lowest, about 37′ below the pole. Your corrected altitude is 23°40.0′. A crew member writes latitude 23°40′N. Is that right, roughly?
Show the answer
No. Below the pole, its altitude is less than your latitude, so add about 37′: roughly 24°17′N. Use Latitude = Ho − 1° + a0 + a1 + a2. All use LHA Aries 227°; a1 also needs approximate latitude, a2 the month. Never take the altitude as latitude without the corrections.
Exam keys
- Latitude by Polaris = Ho − 1° + a0 + a1 + a2.
- All use LHA Aries (a0 interpolated); a1 also uses latitude, a2 also month. All three corrections are positive.
- Worked 24 Nov 2026: LHA Aries 332°35.5′, Ho 26°21.8′ → 26°12.1′N.
- Polaris gives an east–west latitude line; not usable south of the equator.
Finish this unit
When you've read it, answer three questions. Get all three right to finish the unit; opening the page alone doesn't count.
My notes for this unit
No notes