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Celestial Navigation - Lunar Distance

Updated: Jan 17, 2022

Sometimes sailing is very technical. This post is an example of one of those technical subjects. If your eyes are about to glaze over, the result of this whole post is that we used a sextant to find that our watch was 15 seconds off. So now you don’t have to read the rest, but if you’d like more details they are below!

A clear night provided a great opportunity for some celestial navigation practice. Traditional navigation is a skill, you have to use it or you will lose it! Monika and I practice our skills regularly to stay sharp. Tonight, we took a lunar distance sight.

A lunar distance sight is used to determine time by measuring the the angle between the moon and a star or planet. The moon moves relatively quickly compared to other stars and planets which makes it possible to tell the time using a sextant. We used the angular distance between the moon and Jupiter. This is one of the most difficult tasks performed by a navigator because it requires the utmost precision. Any error is magnified 27 times! The outside temperature tonight was 12°F, which made things even more difficult due to thermal expansion of the sextant frame. I always use an insulated glove in cold weather so that the heat from my hand does not interfere with the sight. Because it is so cold outside, I took the sextant sights and Monika recorded them so I didn’t have to keep removing my gloves to write the data down.

The method is as follows:

  1. Determine the sextant error (index correction).

  2. Measure the angular distance between the moon and Jupiter and record the time (lunar distance observed).

  3. Measure the altitude of the moon (moon Hs).

  4. Measure the altitude of Jupiter (body Hs).

  5. Mathematically find the angular distance (D) between the Moon and Jupiter for a time before (D1), and after (D2), your observation.

  6. Mathematically reduce the sextant sight (clear the lunar distance).

  7. Compare the cleared lunar distance to the mathematical times before and after your observation (determine what time corresponded to the measured angle).

It is imperative to pay attention to the small details when taking lunar distance sights. The sextant was acclimatized to the cold temperatures by putting it outside, the temperature and barometric pressure was recorded for abnormal atmospheric refraction, and the sextant micrometer drum was only advanced in one direction to avoid instrument backlash. There are a few other details to get things just right. If we had been at sea, on a rolling vessel, we would have taken multiple sights and averaged them to gain more accuracy. Since we were on land where everything is stable, just one lunar distance and sight was taken.

The results of our sights are shown below on a special worksheet I made for this task. In summary, the worksheet I used for the observation shows that my wristwatch is 15 seconds slow. My wristwatch is synced with the US Naval Observatory master clock so the results actually show that my sextant measurement was off by about 0.1’ of angle. That’s a good result because the sextant is only accurate to about 0.1’ of angle and the mathematics used in the form are quick, but result in a loss of resolution. There are other methods to solve the problem, but the formulas usually take me about two hours. This took about 35 minutes for the sight and complete solution.

Lunar Distance Method
Lunar Distance Worksheet Front

Lunar Distance Method
Lunar Distance Worksheet Back

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Lunar Distance Practice Sight 04 Dec 2023

This is a PDF showing the calculations we used for a lunar distance practice sight taken on December 4. The sight showed that our watch was off by 8 seconds...or only 2nm (at the equator).


Jason Hughes
Jason Hughes
Jan 23, 2022

Impressive! As an engineer, I would be tempted to plug the formulas into a scientific calculator (I'm old), or better yet, a smart phone app. It looks as though just measuring and recording all of the data is a large portion of the time required to complete the procedure. Enjoying your blog and following your progress!


Stanislav Repa
Jan 17, 2022

Very impressive, your skill amaze me every time! Good luck!!!

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