Celestial Navigation, an Introduction.

Having a working knowledge of Celestial Navigation is often put forward as a back up for GPS and all those other electronic aids we rely on theses days.

Ptolemy / Copernicus

For the purposes of celestial navigation on the surface of our planet you don't need to know about any of those crazy Copernican ideas of the universe. 

As far as we are concerned the pre-Copernican, Ptolemaic notions of what we see up there are sufficient. 

Of course it is always good to know what really is going on, but for now all we need is to be aware of what we can see.

And what we see up there are the Sun, Moon, Stars, and Planets marching in step across the sky. 

They all rise to our east and set in the west. 

Now, imagine that all these celestial bodies are on the inside surface of an immense crystal globe which encloses the earth. 

And imagine that this crystal globe has an equator, north and south poles, latitude and longitude which reflect those of the earth.

Our celestial sphere now has a grid system which we can use, just like the lat and long on earth, to locate the position of celestial objects in relation to us.

The Celestial Spheres.

So, now we earth bound navigators have two spheres to consider. 

The first is the surface of the earth, the second is the inside surface of that imaginary crystal globe surrounding the earth. 

On both spheres we use the same imaginary sets of coordinates, latitude and longitude. 

We use this grid system to pinpoint the location of anything on either sphere.

The grid on the celestial sphere is a projection of the grid on the terrestrial sphere. 

So if you were stood at the Earth's North Pole directly above your head would be the Celestial North Pole. 

And by the same token the Celestial equator would be directly above someone stood on the earth's equator.

OK, so far so good, now it starts to get a bit complicated.

The equivalents of the terrestrial latitude lines are called lines of Declination, on the celestial sphere, while longitude line equivalents become Hour Circles, on the celestial sphere.

And where longitude, on the terrestrial sphere is measured through 180 degrees east or west of the Greenwich meridian, on the celestial sphere it is numbered from 0° all the way around to 360°.

And the 0° hour circle known as the Celestial Meridian is known as the First Point of Aries.

There is also quite a bit of strange archaic language used in Astro Navigation but to begin with there are a few terms which are worth understanding.

These are to do with how you or I relate to the celestial bodies.

First is the point directly over your or my head this is known as your or my Zenith, and the bit of the surface you are standing on is your body's Geographical Position or GP.

The imaginary line running, due north or south from my or your Zenith is known as your or my own Meridian.

And the distance of any celestial body above your or my horizon is known as its Altitude, this is the angle which is measured with a sextant.

If you imagine a line from the centre of any celestial body to the centre of the earth where it passes through the surface of the earth is known as that celestial body's Geographical Position or GP.

The GP for a celestial body is measured in degrees of latitude and longitude. 

The latitude measured north or south of the equator is known as its Declination.

Its longitude is measured in degrees westward from the Greenwich meridian and is known as the Greenwich Hour Angle (GHA) .

The Declination and GHA for the celestial bodies which are used for navigation can be found in the Almanac.

The Sun.

Now don't rush out to buy a sextant, you can make a rough measurement of the suns angle using your hand. 

Stretch your arm out towards the horizon, use your clenched fist as a rough measuring device. 

Your fist will give you a rough angle of 10° this can be subdivided by each finger being the equivalent of 2°. 

So if you want to find due east on the morning of the 1st March, (20 days before the equinox) you know that the sun will be rising 5° south of east, so you need to measure half a fist to the north, of where it rises, to find due east. 

OK, so that tells you where east and therefore all the other compass directions are but it doesn't tell you where you are. 

But what we have learned so far is that the GP of the sun and therefore is Declination changes throughout the year. 

And, that this information is predicted for us in the Nautical Almanac.

The Longitude Problem.

The distance of a body's GP from the Greenwich Meridian is its Greenwich Hour Angle (GHA).

So for every hour your local noon is after UT noon you are 15° further west of the Greenwich meridian and conversely every hour your local noon is before noon UT you 15° further east.

Unfortunately the sun isn't a very good time keeper, it can be as much as 20 minutes slower or faster than UT.

And any error in time will give us an error in longitude.

This is why we need that Almanac, it will give us the UT or Greenwich Mean Time that the sun reaches its highest point at Greenwich, for every hour of the day and for every day of the year.

This is the sun's Greenwich Hour Angle (GHA).

We can then use that time as our starting point.

And the need for accuracy is also why the sextant and an accurate watch are so important to celestial navigation.

In practice there are minor corrections which need to be applied but these only require some simple addition and subtraction and there are simple forms which can be used to make it even easier.

For now, it's the concept we are concerned with.

But regardless how accurate you are or how simple it is, having only one coordinate won't tell us where we are, we could be anywhere along that meridian line between the north and south poles.

The lack of an accurate way of telling the time is why sailors in days of yore had problems determining their longitude.

What they were able to do, with considerable accuracy, was work out their latitude.

Finding Latitude.

So to plot our position on that line of longitude we need to know our latitude.

The Declination, if you remember, is the celestial spheres equivalent of our terrestrial latitude.

The almanac will tell us the declination of the sun for our particular date and time.

Now if the sun were directly overhead our declinations would be the same and we would have our latitude.

However, that is unlikely, usually we are going to be either north or south of the sun.

So to arrive at our latitude, we begin by measuring the angle between our horizon and the object, the sun, with our sextant.

This angle is the sun's Altitude.

However this angle is one we are measuring on the surface of the earth.

The suns declination is measured from the center of the earth.

To get from altitude to declination we need what's known as the Zenith Distance, this is simply 90° minus the Altitude.

If we now add or subtract the sun's declination, which we got from the almanac, to or from that zenith distance and we have our Latitude!

Why did I say add or subtract?

Well, that will depend on whether declination is north or south.

There are also other corrections, which in practice have to be taken into consideration but for now we are just looking at the concept.

Navigating by the Stars.

Finding your latitude and longitude using Polaris requires a similar process to that of the Noon Sun sight, except that it does require a few more simple corrections because Polaris is never precisely at the North Celestial Pole.

In fact Polaris makes a very small circuit around North Celestial Pole.

But despite that tiny discrepancy Polaris is always more or less on the observers Meridian whereas the sun is only on your Meridian at noon.

All the other stars circle around the Celestial Poles, how they appear to circle and whether or not they set will depend on your latitude.

Travelers from time immemorial have been using the stars to help them find their way.

The Pacific Islanders were especially adept at using star patterns for navigation.

And they are just as useful for today's navigator, fortunately for us we do not have to keep all the relevant information in our heads as did those Polynesians, all we need is in the Almanac.

However, if the Almanac were to give us the GHA of every star, the book would be too large and heavy for the average cruiser.

So, what the Almanac gives us is its Sidereal Hour Angle (SHA).

The SHA is the star's distance from the First Point of Aries, (represented by the sign of the ram) which using simple worksheets and some simple maths we can then convert.

So, the almanac only needs to tabulate the movement of this one position then by giving us the angular distance to all the navigational stars, we can easily calculate the GHA for any star at any time.

So, what is this First Point of Aries?

It is a point on the celestial sphere which is used as a reference point, it is in fact where the 'Ecliptic' and the Celestial Equator cross one another.

However, the relevance for celestial navigation is that, as far as we are concerned, all the stars remain in the same relative positions to it and each other through out the year.

The Planets.

The advantage of using the stars for navigation is that as they revolve around the celestial sphere they remain in the same relationship to each other, which is why they used to be known as the 'Fixed Stars'.

The planets however move, but their movements are predicted in the almanacs so we can tell precisely where each body is for any second throughout year, these used to be called the 'wandering objects'.

While the astronomers using their telescopes can count innumerable planets the ones we are interested in are those which are easily visible to the naked eye.

Venus, Mars, Jupiter, and Saturn plus of course the Sun are the only ones used for navigation unless we include the Moon with this group.

The method used to reduce an observation of a planet is similar to taking a sun sight, except that as you also need to see the horizon to measure the altitude this must be done at twilight.

The Moon, if I can be forgiven for including it here under Planets, can also be used for navigation.

However because it is so much closer to the earth than the other object we use, many more 'corrections' have to be made when reducing the sight.

Anyone who has read Joshua Slocum's account of his sail around the world will know that he used Moon sights as his main way of telling the time, his only clock was an old wind up alarm clock with no minute hand.

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The Sextant.

A reasonable quality sextant such as the one I bought years ago will cost about the same as four or five hand held GPS sets.

There are some much cheaper plastic sextants on the market which I am led to believe are just as accurate.

I am also led to believe (never having used one) that care must be taken over the storage of the plastic ones as they are much more susceptible to developing errors, so might need adjusting more often.

The sextant as I'm sure you are aware by now is used to measure the angle between the horizon and a celestial body.

It can also be used to measure the any sighted angle, such as the angular distance between two landmarks or the height of a lighthouse, when coastal sailing.

Like any good magic trick it's all done with mirrors.

It is called a sextant because the calibrated arc is one sixth of a circle 60° , however because of the mirrors it can actually measure angles up to 120° .

The frame of the sextant looks a bit like a slice of pizza.

How reflecting instruments -- like sextants -- work
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View my Flipboard Magazine.

• Polaris
• Southern Cross
• Marine Charts
• Passage planning
• Pilotage
• Rule of Twelfths

Thanks to the GPS you know where you are, you can check your position against the sextant, see the difference, note any little errors, gradually correct them and become almost as good s the GPS itself.
 (Bernard Moitessier)

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