Celestial Navigation: Altitude

And the wheel's kick and the wind's song and the white sail's shaking

--John Masefield--

The next line, which most people have never heard. Such a pity!

Should you wish to read the poem in its sublime entirety, it is named Sea-Fever and is available in anthologies such as Mary Sanford Lawrence's Best Loved Poems to Be Read Again & Again.

The Compass Rose takes you to the top page...just in case a Search Engine dropped you in the middle of all this!

Position by the Altitude-Intercept Method

What?

There is that peculiar and archaic language already. In celestial navigation, "altitudes" have absolutely nothing to do with jets cruising the skies, and "intercepts" have nothing to do with football...Rather than list a lengthy glossary which no one will read, I prefer to explain words as they are needed. Right now, these are just a title, so keep interested as the explanation is forthcoming.

Is that like finding your position with a sextant?

Now we have that first misconception coming in. Actually, the altitude-intercept method involves observations with a sextant, but is much more work since a sextant cannot, by itself, "tell you your position." In this method, we must have data from both the sextant and also a very accurate clock. (Formerly this was an uncommonly accurate mechanical clock known as a chronometer). You see, taking a sextant observation is entirely worthless unless we know precisely when that observation was made. And even then, for technologic reasons at least two such observations on two different objects are required to yield your position, known as a fix. In practice, a prudent mariner would not care to stake the safety of the vessel on a 2-point fix. The recommendation was always use at least three observations, and prefer to use more.

At best, a sextant without a clock can help you determine your Latitude. To do this invokes a method that predates the altitude-intercept method by many years, and to avoid breaking the chain of thought, I will not discuss it further here. I invite you to read about it later in the Appendix on Latitude by the Noon Sight though, because it is a simple method that actually makes some astronomical concepts very clear.

Well just what does a sextant tell you?

A sextant is a very refined instrument for measuring angles. Most of us are familiar with those plastic protractors from the discount store for measuring angles in high school geometry or trig. These have one division each degree, and most of us would agree that the one degree divisions are pretty small. Now consider taking each of those degrees and dividing it into 60 equal parts. Each of these we call one minute, denoted with an apostrophe mark. A marine sextant can easily measure angles down to the minute.

If we then divide each of these into 60 parts, we have created 3600 arc seconds in only one degree. That is pretty fine division!

A marine sextant subdivides minutes, but not quite as finely as one second. Instead, it takes each minute of arc and divides it into fifths (but marked in tenths) as 0'.0, 0'.2, 0'.4, 0'.6, and 0'.8

Now we see another complication which is a little confusing to the beginner; namely, mixing sexagesimal notation (that is, degrees-minutes-seconds) with decimal notation. So what a Navigator gets from a sextant is a measurement of an angle, which will be reported in degrees, minutes and tenths of a minute. The data look something like: 45^o 52'.2 or 18^o 02'.8.

Since this Web Page is focusing on the concept of how celestial navigation works, all the exact details of how one uses a sextant, checks its operation, and maintains it are not the subject of this page. (Maybe another Appendix one day?)

Where do these angles come from?

They are angles between the sea horizon and objects in the sky. Here is a key definition for you: In celestial navigation, "angles" are referred to as "altitudes".

As an aside, let me add a little about that. I've heard it said: "There are no straight lines in nature." My answer to this statement is: "You obviously have never seen the sea horizon." Through the sextant, which has a 4X or 6X telescope as part of its optics, the horizon appears absolutely straight and has no thickness. It is the one physical example of my acquaintance of the mathematical concept that a line extends only along itself and is "infinitely thin." Similarly, a star viewed through the sextant is a bright source of light which has no physical extent at all--the mathematical notion of a point.

Do the altitudes then tell us our position?

Not directly, but they are a critical part of the whole system. The altitude at which a body appears in the sky is related to three conditions:

The location of the body in space
The exact time of the observation
The position of the observer on the Earth

Do you now see a hint of where this is going? This is like a high school algebra problem where you are given enough information to allow you to solve for that one bit you don't know. From the viewpoint of the sailor, here is where you get the data you need:

The location of bodies in space is compiled into a book called the Nautical Almanac.
The time is measured. Formerly this was done using a chronometer, but today the typical digital quartz wristwatch is more accurate than the very best chronometers of only two generations ago.
The altitude of a star, a planet, the Moon or the Sun is measured using a sextant.

Now 3 things of 4 are known, and the final item of interest can be solved for; namely, the position of the observer on the Earth. That is the theoretical framework. If it were a perfect world, this would be all we need; but owing to technologic reasons hinted at earlier, there will be many complications to the complete solution of the altitude-intercept problem, so be patient and keep interested.

You may notice that we could rearrange this game and play another way if we want, and indeed, we do!

Some astronomers use the precisely-known locations of their observatories, and measure time and altitudes to solve for the locations of objects in space. Computer simulations such as Voyager II or Dance of the Planets ask you to pick a location and time, then use the known positions in space to compute the altitude of everything in the sky and draw it for you on the screen, just as the sky would appear. To work the altitude-intercept method, mariners must also compute the altitude at which an object would appear, but fortunately this isn't required for the entire sky. Lastly, other astronomers use known locations of both their observatories and celestial bodies, measure altitudes and determine the precise time.

Determine time!!??

Yes, it is really true. This is the basis of our notions of "noon" and "time zones", and the reason why our "year" has the length it does; as well as the source of those famous "leap seconds" you read about in the newspapers every so often. By the end of these Pages, I hope you will understand clearly how the motion of celestial bodies is tied to time. In fact, the motion of one particular body, the Sun, actually defines our concept of time.

But for right now, let us continue on in explaining where the "intercept" comes from in the altitude-intercept method...