celestial navigation, or astronomical navigation. The
sextant, the
chronometer (nowadays possibly a quartz watch), the
nautical almanac, and navigation tables (now perhaps some form of calculator or computer) in one form or another remain the essential requirements for celestial navigation, by means of which, provided the heavenly bodies themselves are visible, the
navigator can find his position anywhere in the world. For centuries,
navigation by sextant, or one of its predecessors, was the only position-fixing system in the deep ocean and all the great voyages of
exploration by sea have found their way by it. The practice has now largely been replaced by
satellite navigation, in its current (2004) form
GPS (Global Positioning System) or, less frequently, the Russian Glonass. The reason for the present supremacy of GPS is clear. For the first time in the long history of navigation a system exists that will give the navigator a position within a few metres, by day or by night, in any weather and in any part of the world. That astronomical navigation has not yet become obsolete is largely due to the fact that it remains self-contained, is wholly independent of any national or political authority, and is not subject to system failures.
For all the brilliance of its conception and performance satellite navigation as we know it remains for one reason or another vulnerable. As things stand, for example, GPS, which is provided free by the US Department of Defense, is still classed as a weapon-targeting system and could be withdrawn at any time. So a back-up still remains a requirement and celestial navigation remains at any rate one wholly viable alternative.
The practice of celestial navigation at sea remains in principle very much as it was in the days of
Captain Cook. But things have become easier. Time is universally available and the problem of
longitude has long been solved. The
ephemeris is now presented in the nautical almanac in such a manner that only the most elementary mathematics are required to solve the nautical triangle. Perhaps, above all, the concepts of the
position line and the
intercept have illuminated and simplified the whole business of astronomical position finding.
The predicted apparent positions of the heavenly bodies used in navigation, namely the sun, moon, planets, Aries, and the selected navigational stars, are tabulated for hourly intervals in the nautical almanac. The coordinates used are Greenwich
Hour Angle (
GHA) and
declination which are adjusted by interpolation tables to the time of observation. The values extracted are used to enter the reduction tables (or calculator as the case may be). Each sextant observation or sight will produce a position line, somewhere along which the observer's position must lie. Two position lines taken at roughly the same time will indicate just where along the first position line the observer lies, and three sights in a series will normally produce a
cocked hat which gives a more reliable
fix. A single position line can be advanced along the ship's track and crossed with a later observation to give a position. Where the sun is used this is known as a sun-run-sun. The same principle of the transferred position line is of course frequently used in
coastal navigation.
To take a
sight the navigator measures the altitude of the heavenly body with his sextant, taking the time of observation (generally to within a second) since, due to the rotation of the earth, the body will be in constant motion. The
altitude corrections, given in the nautical almanac and elsewhere, are then applied; first
dip for the observer's height of eye, then atmospheric
refraction, then
semi-diameter for the sun or moon, and finally any index error of the instrument.
To work the sight up (to use the time-honoured phrase) the GHA is first of all converted to LHA (local hour angle) at the position from which the sight is being worked (generally the
dead reckoning position or a position that suits the tables) by adding or subtracting the longitude. Nowadays using modern direct entry altitude-azimuth tables, or a dedicated calculator, the declination and local hour angle are converted into
altitude and
azimuth. The altitude is compared with the observed (i.e. corrected) sextant altitude to obtain the
intercept or altitude difference. This whole process is known as sight reduction.
On the
chart or a
plotting sheet a distance on the chart scale equal to the intercept is measured along the azimuth line, towards the assumed or chosen position if the observed altitude is the greater and away from it if it is not. From that point the position line is drawn as a perpendicular, at right angles to the
bearing.
There are many methods of sight reduction, tabular, instrumental, and mechanical. During and immediately following the Second World War (1939–45) logarithmic solutions such as the cosine-haversine method, or longitude by chronometer, held sway. These were later at least temporarily eclipsed by what were generally called the ‘short’ methods. These split the navigational triangle into two parts and lessened the work, but at the expense of introducing special rules for different situations. It was the introduction of large computers that made modern direct-entry tables possible. From these precomputed altitudes and azimuths could be extracted for any value of GMT (Universal Time). Bulky though the tables may be they still represent the most convenient form of tabular sight reduction. There are dedicated calculators, such as the Merlin II, that carry the ephemeris for the sun, moon, and navigational stars for a number of years and dispense altogether with the use of an almanac or reduction tables, or indeed the need to plot in order to establish the observed position. In some ways, given the altered status of celestial navigation, they perhaps represent the best way of reducing sights in the modern navigational environment.
The simplest form of sight is the
meridian altitude taken when the body observed, usually the sun, crosses the observer's meridian and reaches its maximum altitude. The altitude, adjusted by the altitude corrections and with the declination as appropriate taken into account, defines the latitude. The most accurate sight is a four-star fix with the stars in two opposed directions. The accuracy of celestial observations is a matter of some importance which affects not only the accuracy of position at sea but also the precision to which almanacs and nautical tables must be tabulated. The confidence level with which practising mariners are most concerned is the 95% level, which means that out of every 100 observations only five will be expected to exceed whatever the stated value is. In 1957 the Royal Institute of Navigation with the Royal Netherlands Navy and a number of shipping companies conducted an investigation into the accuracy of sextant observations actually achieved in different conditions at sea. The errors in question were position line errors, not errors in position. Some 4,000 observations were received and analysed by HM Nautical Almanac Office. The accuracy achieved by the average observer was 3 minutes of arc (or miles) and by the best observer 2 minutes. The figure, now generally accepted, was substantially greater than had been widely believed. Blewitt, M. ,
Celestial Navigation for Yachtsmen (1990).
Moody, A. ,
Navigation Afloat (1980).
Mike Richey
