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.




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