How celestial navigation works in easy stages – part 2

Last time I promised to say something about how a meridian altitude – or ‘mer alt’ – works.

The mer alt of any heavenly body listed in the Nautical Almanac will reveal your latitude, but usually when people talk about a mer alt they’re thinking of the sun.  So that’s what I’m going to focus on here.  In fact the sun’s mer alt is the commonest observation made with a sextant, and it used to be a key part of the daily routine aboard every ocean-going ship.  Quite simply it is a measurement of the sun’s height above the horizon as it crosses the observer’s meridian.  In other words, when its GP is either due south or due north of him or her.  This is also the moment of local noon – when, in the days of sail, ‘eight bells’ would have rung out to mark the end of one day and the start of the next.

How does a mer alt enable the observer to work out the latitude of the ship?  Let’s start with the simplest case.

If you know that the sun is vertically above the equator (as it is twice every year – on the spring and autumn equinoxes), then its height above the horizon as it crosses your meridian – when subtracted from 90 degrees – is equal to your latitude.  This figure is known as the sun’s zenith distance – literally its angular distance from your zenith.

To find your latitude from a mer alt on any other day of the year, however, you need to adjust the zenith distance to allow for the sun’s varying declination.  See diagram for an example:

The principles of the 'mer alt'
The principles of the ‘mer alt’

As the earth orbits the sun, the sun’s GP moves steadily between the two Tropics  – which is, of course, why there are seasons.  On midsummer’s day in the northern hemisphere the sun’s GP is slightly more than 23 degrees NORTH of the equator, and on midsummer’s day in the southern hemisphere it’s the same distance SOUTH of the equator.  This steadily altering angular distance is the sun’s declination and it is tabulated in the Nautical Almanac for every hour of every day of the year.  At the two equinoxes it is, of course, zero.

In order to find your latitude by mer alt you add the sun’s declination to, or subtract it from, its zenith distance – depending on whether or not the sun’s GP is on the same side of the equator as you.  The result is, once again, your latitude.

So the mer alt is a simple process: 90 degrees minus CORRECTED SEXTANT ANGLE plus/minus DECLINATION = LATITUDE.

It took a long time for astronomers to work out exactly how the sun’s declination varied.  The first reasonably accurate tables of the sun’s declination only appeared in Europe at the very end of the 15th century and they played a vital part in enabling Portuguese and Spanish explorers to find their latitudes when they sailed south of the equator – and lost sight of Polaris.

Next time I’ll start to talk about finding your longitude – the Holy Grail of navigation finally discovered in the mid-18th century.




How celestial navigation works – in easy steps: 1

You may well think celestial navigation is a dark science that calls for a lot of complex mathematics.  In a way that’s perfectly true because it took the work of many brilliant mathematicians to perfect the techniques mariners use to fix their position on the open sea.

But to practice the art of celestial navigation today you really don’t need much mathematical skill.  In fact you only have to be able to add and subtract – and maybe not even that now that we all have access to computers.

To explain the basic principles of celestial navigation let’s start with a crucial concept – the ‘geographical position’ of a heavenly body.

At any given moment every heavenly body is vertically above a precisely defined spot on the surface of the Earth.  So if you imagine a straight line drawn from the centre of the Earth to a star, someone standing where that line passes through the surface of the Earth would see that star directly overhead – or in their zenith.  That person will then be standing at the star’s geographical position (GP).  Its GP can be defined by its latitude (degrees north or south of the equator) and its longitude (degrees east or west of the Greenwich meridian, a line joining the North and South Geographical Poles that happens to pass through the observatory at Greenwich).

Now if the Earth did not rotate about its axis all the stars (though not the sun, moon or planets) would appear to stand still in the sky.  That would of course also mean that their GPs were fixed.  So a very simple way of navigating would be to identify the star whose GP was closest to your goal and then sail (or walk, or fly – or whatever) until that particular star was overhead.

You may say that won’t work because the Earth actually does turn.  But wait.  There are two special places on the Earth’s surface that actually do remain stationary in relation to the sky immediately above them: the North and South Geographical Poles.  So if you want to find your way to either Pole you only need to identify the star whose GP is closest to it and travel until it’s overhead.

We’re lucky that there is a prominent star whose GP currently lies very close to the North Pole – it’s called Polaris, or the Pole Star, or sometimes simply the North Star.  (Unfortunately there is no such star standing over the South Pole.)

If you watch the night sky in the northern hemisphere closely you’ll see that all the stars appear to revolve slowly around Polaris, which itself remains stationary.  Here’s a link that shows how to find Polaris:

As the height of Polaris increases the navigator knows that he or she is getting nearer to the North Pole.  And of course if its height is decreasing he or she must be travelling away from the North Pole.   So the very simplest form of celestial navigation is to measure the height of Polaris above the horizon.  This angle is what you measure with a sextant – in degrees and minutes of arc.  Obviously when the sextant tells you that Polaris is exactly overhead – a height of 90 degrees – you know you’ve arrived at the North Pole (latitude 90 degrees).  Equally if the height of Polaris is zero degrees – when it’s touching the horizon – you know you’re on the Equator (latitude 0 degrees).

The height of Polaris is in fact equivalent to the observer’s latitude.  If you measure the height of Polaris as, say, 45 degrees then you know are in the latitude 45 degrees North.  What could be simpler? (In fact Polaris is not quite vertically above the North Pole so a small correction is usually needed, but that need not concern us here.)

A sailor crossing the North Atlantic who knows the latitude of his or her destination can therefore make very good use of Polaris.  Suppose, for example, you want to enter the English Channel safely all you have to do is sail eastwards keeping Polaris at a height of roughly 49 degrees above the horizon.  That latitude brings you into the Channel roughly mid way between the Scilly Isles on the British side and Ushant on the French side.

This method has been used by mariners for centuries.  Of course it only works in the northern hemisphere as Polaris disappears below the horizon once the equator is crossed.  So another method of finding a ship’s latitude was needed when ships sailed in the southern hemisphere.  The answer was to measure the height of the sun at midday, but, as we shall see, that presented considerable difficulties.

Next instalment: latitude from the sun’s ‘meridian altitude’.