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Celestial navigation

Meridian diagram – how high does a body stand at meridian passage?

The meridian diagram is the classic construction of celestial navigation: zenith, celestial pole, celestial equator and body in one drawing. NauticTools2 draws it for any latitude and declination, calculates the upper and lower meridian altitude and shows whether a body rises and sets, is circumpolar or never rises.

• Zenith · nadir
• Celestial pole
• Celestial equator
• Meridian altitude
• Circumpolar
• Altitude and azimuth

What is the meridian diagram?

The circle is the plane of the observer's meridian: zenith at the top, nadir at the bottom, the rational horizon across with north and south. The celestial pole stands exactly the observer's latitude φ above the horizon, the celestial equator at right angles to it. A body with declination δ lies δ away from the equator – and on its daily circle, parallel to the equator, it crosses the meridian once a day at the top, the upper transit, and once at the bottom, the lower transit.

When do you need it?

• Understanding the noon sight: The formula φ = 90° − h + δ follows directly from the meridian diagram – once you have drawn it, you won't mix up the signs again.
• Planning observations: How high is the sun at noon, does a star cross the meridian to the north or south, does it rise at all?
• Recognising circumpolar bodies: Stars that never set can be shot all night – even at their lower transit.
• A feel for celestial navigation: Moving the sliders shows at once how latitude, declination and hour angle relate.

Formulas and working

1. Zenith distance

   z = φ − δ, north positive, south negative. If z ≥ 0, the body crosses the meridian on the equator side of the zenith (in the northern hemisphere to the south), otherwise on the pole side.

2. Upper transit

   h = 90° − |z|. If it is 0° or less, the body never rises.

3. Lower transit

   h = |φ + δ| − 90°, on the pole side. If it is 0° or more, the body is circumpolar and never sets.

4. Altitude and azimuth at any time

   For any local hour angle t: H = asin(sinφ · sinδ + cosφ · cosδ · cos t) and Az = atan2(−sin t, cosφ · tanδ − sinφ · cos t).

Worked examples

Things to watch out for

• Signs: Use signed latitude and declination – north positive, south negative. With contrary names (e.g. 51° N and 20° S), z becomes larger than φ.
• Rational horizon: The diagram shows altitudes above the rational horizon. Sextant altitudes must be corrected first (dip, refraction, semi-diameter, parallax).
• In-between positions: Strictly, a body lies in the meridian plane only at transit. Between upper and lower transit the movement in the diagram is a simplified picture – the altitude and azimuth shown next to it are still calculated exactly.

How it works in NauticTools2

1. Set latitude and declination

   With the sliders or the arrows next to them, one degree at a time; north and south of the equator.

2. Move the hour angle

   The hour-angle slider takes the body once through the whole day (0° to 360°): at 0° it is at upper culmination, at 180° at lower culmination. Two buttons jump straight there.

3. Read the result

   Current altitude and azimuth, the status “rises and sets”, “circumpolar – never sets” or “never rises”, and the working with both meridian altitudes.

4. Print

   Inputs, result, working and the diagram can be printed as a record or saved as a PDF.

Frequently asked questions

What is meridian passage?

The moment a body crosses the observer's meridian. At upper transit it reaches its greatest altitude, at lower transit its smallest – which you only see for circumpolar bodies.

When is a body circumpolar?

When its lower transit is above the horizon too: |φ + δ| ≥ 90°, with latitude and declination of the same name. At 54° N this applies to all stars with more than 36° N declination.

How does the meridian diagram relate to the noon sight?

The noon sight is the meridian diagram worked backwards: from the measured meridian altitude h and the declination δ you get the latitude φ = 90° − h + δ (for a southern transit in the northern hemisphere).

Related tools

• Fix from 2 or 3 altitudes – position lines and fix from celestial sights
• All celestial navigation tools – from the star chart to the compass check