my work

Calculating Longitude

Last time, we decided that at 16:58:38 GMT, it was Solar Noon at my location. That was the moment the Sun reached its peak in the sky. More importantly, it was the moment that the Sun crossed my meridian -- the line of Longitude that I was standing on at that moment.

In other words, at 16:58:38 GMT, the Sun and I were on the same Longitude. So if we can find the longitude of the Sun at that moment, we will know my longitude. Its that easy.

How do we find the Suns longitude at that exact moment? From the Nautical Almanac, of course.


The Suns longitude at any particular time (GMT, of course), is called its Greenwich Hour Angle, in celestial navigation lingo. More commonly abbreviated as GHA.

The Daily Page of the Nautical Almanac lists the Suns GHA for every hour of the day. Its under the Sun column on the left side, labeled GHA.

We will use the information on the Daily page to find the GHA of the Sun at  the nearest hour: 16:00:00 GMT. If you inspect the table, you will see that, at that time, the Suns GHA was 58° 35.2.

Next we need to look up how far the Sun traveled in the next 58 minutes and 38 seconds. Again, the Nautical Almanac provides the answer.




In the Nautical Almanac, the "Increments and Corrections" pages list how far the Sun (and Moon and planets and stars) move through the sky from 0 seconds, up to 1 hour. Since we want to know how far the Sun moved in 58 minutes and 38 seconds, we turn to the 58 Minute page (click on the above image for a closer look).

The seconds are listed down the left side. The Suns incremental GHA is in the first column on the left.

If you follow the seconds down to 38, you will find the incremental GHA for 58:38. Its 14° 39.5.

If we add the hourly GHA and the minutes/seconds GHA, well find the Suns exact longitude at 16:58:38:


And since that, dear reader, was the Suns longitude at solar noon, it was also my longitude. At least according to my sights and calculations.

So, putting the latitude and longitude together, my fix was:


And 5-20nm accuracy is good enough for actual use.

If you were crossing the Atlantic, say, and were taking daily noon Sun fixes, a 5nm accuracy would be more than you could use on a big Atlantic chart. And by the time you got within 20nm, youd be on deck, scanning the horizon, waiting to say "Land Ho!" as loud as you could.

How could you improve these results?

Youd probably get more accurate sights with a good, metal sextant, like an Astra IIIb. A metal sextant will have a more stable Index Error, a better scope, and more precise vernier.

However, a sextant is only as good as the Navigator. It takes a lot of judgment and skill to line up the Sun with the horizon. Especially when the Navigator is being thrown around the companionway, and the horizon looks like the business side of a saw.

It also takes skill to plot the sights and draw a smooth, symmetrical noon curve -- particularly when the sights are not as neat and clean as you get from dry land.

This kind of skill only comes from months or years of daily practice. The kind of practice youd get on an Atlantic crossing. If youre like me, you only dream of getting that kind of practice, but at least now you know what to do if you ever get the chance!

Bottom line, a sextant is not a GPS. Thats why GPS -- lets not pretend here -- has rendered the sextant obsolete as a navigation instrument.

On the other hand, finding your location using a sextant is a heck of a lot more fun! And thats what this has all been about. A bit of summer fun, learning a new skill.

My goal has been to conduct you through this first fix with as little math and mumbo-jumbo as possible, to show you that Celestial Navigation is not rocket science or black magic. If Ive done my job well, you should be saying to yourself, "Hey, that wasnt so hard, after all!"

I hope its been as much fun for you as its been for me.

Ill try to take another set of sights next week, so you can try to work one on your own. Until then, if you have any questions, please leave them in the comments section below, or email them to john@unlikelyboatbuilder.com.



Speaking of next time... if youd like to be notified when I post a new lesson (erratically, about 3 times a week), you can sign up for my super-sophisticated Automatic Notification Process. Actually, its just an email, but Automatic Notification Process sounds better. I wont spam you, and you can de-sign up at any time.

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