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Latitude by meridian altitude – the noon sight

The noon sight is the simplest celestial fix: at transit the sun lies exactly in your own meridian, and its altitude gives your latitude directly. NauticTools2 finds the time of transit and the declination from date and longitude and calculates the latitude – with the sun bearing south or north.

• Meridian altitude
• Zenith distance
• Declination
• Time of transit
• Sun bearing S or N
• Latitude φ

The principle

At transit, zenith, sun and celestial equator lie in one plane, the observer's meridian. The distance from the zenith to the equator is your latitude φ. It is made up of the sun's zenith distance (z = 90° − Ho) and its declination δ, the sun's distance from the equator.

When do you need it?

• Daily latitude check: One sun sight at noon and the latitude is known – without working a position line.
• Sun-run-noon fix: Together with a morning position line, the noon latitude gives a complete fix.
• Latitude sailing: If you want to sail along a given latitude to your destination, check it daily with the noon sight – as seafarers did for centuries.

Formulas and working

1. Zenith distance

   z = 90° − Ho. If the sun bears south, z is named north; if it bears north, z is named south.

2. Time of transit and declination

   From date and longitude NauticTools2 finds the time of local transit and the sun's declination at that moment.

3. Same name

   If z and δ have the same name (both N or both S): φ = z + δ, with that name.

4. Contrary names

   Otherwise the latitude is the difference: φ = δ − z named like the declination if δ is larger, otherwise φ = z − δ named like the zenith distance.

Worked example

Things to watch out for

• Corrected altitude: Enter the meridian altitude after the sextant altitude corrections, not the sextant reading.
• Measure the greatest altitude: Around noon the sun hardly rises any more. Keep taking sights until the altitude starts to fall; the greatest value is the meridian altitude.
• Choose south or north correctly: In mid-northern latitudes the sun bears south at noon. In the tropics it can be north of the zenith – then the name of the zenith distance changes.

How it works in NauticTools2

1. Choose the bearing

   Does the sun bear south or north at transit?

2. Date, longitude, altitude

   Enter date, DR longitude and the corrected meridian altitude – no time is needed.

3. Calculate

   Zenith distance, meridian passage, time of transit, declination and latitude appear with the working. Inputs can be saved and the result printed.

Frequently asked questions

How do you work a noon sight?

Zenith distance z = 90° − Ho. With same names φ = z + δ, with contrary names the difference – named like the larger value.

Why doesn't it need an exact time?

Around transit the altitude hardly changes, and the declination changes by at most about 1′ per hour. Date and approximate longitude are enough.

Can you get a meridian latitude from stars?

Yes, every body crosses the meridian once a day. For stars that is at night, though, when the horizon is usually not visible. The exception is Polaris, whose altitude is almost directly the latitude.

Related tools

• Meridian passage – when the sun crosses the meridian
• Sextant altitude corrections – from the reading to the corrected altitude
• Meridian diagram – zenith, equator and body at a glance
• Sun-run-noon fix – noon latitude plus the morning sun gives a fix
• Fix from 2 or 3 altitudes – cross the noon latitude with any other position line