Celestial Navigation 101: Lesson 3, the Navigational Triangle

Here's another topic where you don't have to take notes. You will not actually ever do any of what I'm about to demonstrate. You will have logarithmic tables or calculators to do all of this for you. But, pay attention anyway. This is the cornerstone of all traditional celestial navigation; everything else we do is based on this.

We begin with three known pieces of information.

From the Nautical Almanac or other similar source, we know the latitude and longitude of the geographical position of the celestial body at the moment we observed it. We call the latitude of an object in the sky Declination, or Dec. We call the longitude of an object in the sky Greenwich Hour Angle, or GHA.

We know our own Assumed Position (AP). This may be our dead reckoning position, it might be our GPS position, or, depending on the method we intend to use to reduce the observation to a line of position, it may be something rather more arcane than this. It really doesn't matter, we just need something to use as a baseline to compute and compare the actual observation to.

Our Assumed Position can be broken down into two parts, Assumed Latitude (aLat) and Assumed Longitude (aLon).

So, in essence, we know both the latitude and longitude of both our own assumed position, and the geographic position of the celestial body.

The latitude (declination, really) of the Geographic Position of the body is a distance from the equator. We know that the total distance from the equator to the pole is 90°. So the latitude of the GP of the body, subtracted from 90°, is the distance in degrees from the pole to the GP of the body. This number is called CoDeclination. The same is also true for the latitude of our Assumed Position. This number is called CoLatitude. You don't need to worry about CoDeclination or CoLatitude, the logarithmic tables will take care of them for us. But it's good to understand the principle.

The difference between the longitude (really GHA) of the celestial body and our own Assumed Longitude is an angle centered on the pole. This angle is called the Local Hour Angle (LHA) of the celestial body.

Once we know the length of our CoLatitude, the length of the CoDeclination of the body, and the angle (LHA) between them, we have only to calculate a side-angle-side triangle using the principles of spherical trigonometry to determine the length of the remaining side of the triangle, and the angle between our own longitude and this leg.

Going back to Lesson 1 on Circles of Equal Altitude, we know that 90° minus the height of the celestial object (in degrees above the horizon) equals the distance from ourselves to the Geographic Position of the object. So, conversely, 90° minus the computed distance to the GP equals the height of the celestial object above the horizon.

And going back to Lesson 2 on the Azimuth Intercept Method, the difference between our Computed Height (Hc) and our actual Observed Height (Ho) of the object is the difference in nautical miles between our assumed position and our actual position.

That's it. Everything else we do in this course will be anchored on this principle.
Understand this lesson, and everything else which follows will fall magically into place.

If you don't understand this lesson, don't sweat it. Lots of people don't, and still manage to navigate across oceans safely with just a sextant and a chronometer. The whole purpose of the various tables we're going to use is to eliminate the need to understand this lesson.

What you do need to understand is this. Whatever method you choose to use to reduce your observations to a line of position, you will first need to determine three things:

1) Your own Assumed Latitude

2) The Declination of the celestial body

3) The Local Hour Angle (LHA) between the body and your own assumed Longitude.

Latitude, Declination, Local Hour Angle.

"Lat, Dec, LHA."

Say it over and over again until it becomes a mantra. Really.

That's one of them Very Important Concepts.