Getting Your Latitude from the Stars while Sailing South to Baja in November

Let’s say you are at San Diego, doing some final provisioning before cruising off to Baja. At about 10 pm in the evening on Nov 1 (or 9 pm on Nov 15) you will be able to see the constellation of Orion just after it rises in the east. The line between its two brightest stars, the redish Betelgeuse to the left of Orion’s belt, and the silver white Rigel to the right of it, will be exactly parallel to the horizon. It will look like this:

Once you get to the latitude of Turtle Bay, though, Orion will look like this after rising:

Because you have been traveling around a curved Earth, the line between Betelgeuse and Rigel just after they have risen is no longer parallel to the horizon. Rigel, the southern most of the two stars, is now higher up. The angle to the horizon of this line, in degrees, is, in fact, equal to the number of degrees of latitude you have sailed south from San Diego. If you are good at estimating angles, or you lay out and cut some wedges of paper to various different small angles, and fairly accurately determine that the line between these two bright stars is now at a 5° angle to the horizon, then you will know you have traveled 5° south from San Diego. (A useful fact to know in estimating this angle is that when the line between Betelgeuse and the middle star of Orion’s belt is parallel to the horizon, the Rigel-Betelgeuse angle to the horizon will be 4.25°.)

Since San Diego is at N 32° 40’ (at Pt. Loma), the Rigel-Betelgeuse-horizon angle being 5° means you must now be at a latitude of about 5° less than this, or at about N 27° 40’, which is, in fact, the latitude of Turtle Bay. Bear in mind, though, that you will probably only be able to estimate this angle to the nearest fourth of a degree (15’), so the latitude you obtain could be up to 15 NM out. (Although this is a useful level of accuracy, Celestial Navigation Without Almanacs does describe a more accurate way of measuring these angles, by timing how long one star rises or sets after the other one. At Turtle Bay Betelgeuse will rise eight minutes after Rigel — 1.5 minutes per degree south of N 33°. Getting accurate star rise and set times does depend, though, on having a clear horizon, free of haze.)

This change in the angle of Orion as it rises is certainly an interesting thing to observe as you sail south in late October or November, a real indication of the curvature of the earth that you can see with your own eyes. But could it ever be useful? Not while you have a working GPS, of course! But let’s say you are sailing a course out to sea of Isla Cedros and the Islas San Benito in order to avoid the land effect and keep in some wind during the night, like I did when I sailed down last November. And let’s say that because of an attempted terrorist attack by a group that could be using GPS to navigate, the US government turns off the GPS for a time (a thing it can easily do, since the US military has its own separate GPS system it can use). Night sets in, and you still can’t see the San Benitos. Of course you can do dead reckoning from your last known position, but variations in the southward current could play havoc with this, especially if the wind is light and you’re travelling slowly. In such a situation it sure would be reassuring to see what angle Orion rises at. If it’s about 4.25° (which it will be when the line between Betelgeuse and middle star of Orion’s belt is exactly parallel to the horizon when the whole constellation of Orion has just risen and you can see all three stars in the belt) then you’re still not quite past the San Benitos, and need to make a little further south before turning SE. If it’s around 5° you are pretty much at the latitude of Turtle Bay already, and need to sail East.

A little later at night, about 11 pm, the bright star Achernar will be seen just above the southern horizon, approaching its highest point. It’s the only bright star in the area at this time, so you can’t miss it. It will be there ahead of you, beckoning you south, getting a little higher in the south each night. It will be at its highest point each night when it is true south (which you can determine using your hand bearing compass, taking variation into account. This will be at 11:40 pm on Nov 1 at the longitude of Pt Loma, 10:40 pm on Nov 15). When it is at this highest point each night, its angle in degrees above the horizon is also equal to how many degrees of latitude you have sailed south from San Diego (or from N 33°, to be precise, in this case). So, say you see Achernar there, a little above the horizon. How can you tell precisely what angle it is above the horizon, in order to determine your latitude? Of course you could always use a sextant to find the angle, if there’s enough moon to make the horizon visible through a sextant. But what if there isn’t a moon or you don’t have a sextant?

In this case you can compare the distance of Achernar above the horizon with the known distance apart of certain other stars. Celestial Navigation Without Almanacs has a table of the distance apart (in great circle degrees) of 28 pairs of bright stars, many of them in very recognizable constellations. At the time Achernar is due south, Sirius, the brightest star in the sky, has just risen in the southeast, and the table in the book shows that Sirius is 5.5° from the closest bright star to it, Mirzam. Knowing these two stars are 5.5° apart provides the comparison we need to fairly accurately estimate the angle of Achernar above the horizon. You can just eyeball the two distances, compare them with the width of three or four fingers at the end of your arm, or view the comparison stars through binoculars, and compare how much they span the field of view with how much Achernar to the horizon spans the field of view. Binoculars used on boats normally have a field of view of about 7° to 8°. After a while you will get a good idea what different angles look like through your binoculars, then see how they compare with the height of a star above the horizon. Here is what Achernar looks like at the latitude of Turtle Bay:

To the left you can see Sirius and Mirzam (β Canis Major), the comparison stars just mentioned, which are 5.5° apart. Orion’s belt, seen at the top left of this picture, is 2.7° across.

As you go further south, to Mag Bay and beyond, the angle Orion rises at, and the angular height of Achernar above the horizon will both get bigger and bigger, but they will always both be equal to how many degrees of latitude you are south of San Diego. At Mag Bay they will be about 8°, at Cabo San Lucas they will be about 10°.

Finding your latitude using these stars can, of course be done at any place in the world between N 30° and the equator, for close to half the year. You could be on the “Puddle Jump” to French Polynesia, sailing to Hawaii, in the Carribean or in Asian waters. And at other times of year, and other latitudes, there are many other stars that can be used for the purpose of finding your latitude. Celestial Navigation Without Almanacs explains how to do this, and has all the star information needed to do it.

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