How to Calculate Latitude from Sun at Meridian Passage: MCA OOW Oral Exam Guide

Latitude by Meridian Passage: The Answer

The vessel's latitude is 29°50'S. The zenith distance is 9°50'. Because the sun bears north at noon, the zenith distance is named south. Declination (20°S) and zenith distance (9°50'S) have the same name, so you add them: 20°00'S + 9°50' = 29°50'S.

Why This Question Matters for Your OOW and Chief Mate Oral Exam

Celestial navigation, and in particular latitude by the sun's meridian passage, remains a cornerstone of maritime competence. In the MCA oral exam, examiners want to see not just that you can do the arithmetic, but that you understand why you add or subtract, and that you can check your answer against your DR position.

The Data in the Question

• DR Position: 30°S, 025°W (used to work out the time of meridian passage and as a check on your answer).
• Observation: The sun at meridian passage (local apparent noon), when it is at its highest altitude and bears due north or due south.
• Sun's Declination: 20°S.
• True (corrected) Altitude: 80°10', after index error, dip and the total correction for the lower limb (refraction, semi-diameter and parallax) have been applied.
• Sun's Bearing at Meridian Passage: North.

The Calculation

Step 1: Zenith Distance

The zenith distance (ZD) is the angular distance from the observer's zenith to the sun.

• ZD = 90° − True Altitude
• ZD = 90°00' − 80°10' = 9°50'

Step 2: Name the Zenith Distance

Name the zenith distance opposite to the sun's bearing. The sun bears north, so the observer is south of the sun, and the zenith distance is named south.

• Examiner's Insight: This is where most mistakes happen. If the sun bears north, you are south of it. If it bears south, you are north of it.

Step 3: Apply the Rule

Latitude = Declination ± Zenith Distance

• Same names, add: if declination and zenith distance are both north or both south, add them, and the latitude takes that name.
• Different names, subtract: subtract the smaller from the larger, and the latitude takes the name of the larger.

In this question:

• Declination: 20°00'S
• Zenith distance: 9°50'S
• Same names, so add: Latitude = 29°50'S

Sanity check: The DR latitude is 30°S, so 29°50'S is 10 miles north of the DR, which is sensible. And with the sun nearly overhead (altitude 80°) bearing north, you'd expect to be a little south of the sun's declination — which you are.

Examiner's Perspective: What They're Looking For

1. Correct Calculation: Accuracy in the arithmetic.
2. Understanding of Principles: Can you explain why you added rather than subtracted?
3. Correct Naming: Naming the zenith distance opposite to the bearing of the sun.
4. A Check Against the DR: Does the answer make sense for where you think the ship is?
5. Clear Explanation: Can you talk through your reasoning concisely, using correct terminology?

Common Pitfalls and How to Avoid Them

• Naming the ZD the same as the bearing: The sun bearing north means your zenith is south of the sun. Getting this backwards gives a latitude on the wrong side of the declination.
• Adding vs. Subtracting: Same names add, different names subtract.
• Forgetting the Altitude Corrections: In the exam you may be given a sextant altitude and need to apply index error, dip and the total correction (refraction, semi-diameter and parallax for the sun) before finding the ZD.
• Arithmetic Errors: Simple slips with degrees and minutes. Write it out.
• Missing the Time of Meridian Passage: You need the ship's longitude to work out the time of meridian passage, and that time to take the declination from the almanac.

Exam Tips for Celestial Navigation Questions

• Practise: Work through as many meridian passage problems as possible, including ones where the declination and zenith distance have different names.
• Draw It: Sketch the observer's meridian with the zenith, equator and sun marked. The diagram makes the naming rule obvious.
• Understand the Almanac: Be comfortable taking declination and its 'd' correction from the Nautical Almanac for the time of meridian passage.
• Explain Your Work: Talk the examiner through your steps rather than just giving the answer.
• Check Your Answer: Compare your observed latitude with the DR. A large difference means you should re-check your working.

Conclusion

Answering a meridian passage question confidently comes down to three things: find the zenith distance, name it opposite to the sun's bearing, and apply "same names add, different names subtract." Here that gives 29°50'S. Master this and you will handle any version of the question the examiner gives you.

Updated 25 October 2026: corrected the naming of the zenith distance (opposite to the sun's bearing) and the explanation of why the values are added.