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Celestial/Astro Nav Notes for students










Using the sun and stars to find our way is a very old art. It is known the Vikings used the sun and the pole star to sail a line of latitude on their voyages to North America. However until the mid -18th century there was no certain method of fixing a ships position. Ocean navigation remained a hit and miss affair with explorers dying of thirst sailing to and fro along lines of latitude looking for islands. 

In 1714 a Board of Longitude was set up in Britain and a prize of £20000 was offered to encourage the discovery of a means of accurately determining longitude at sea. Between 1735 and 1760 John Harrison, a Yorkshire man, clockmaker and genius developed clocks and watches (chronometers) that worked at sea. Thus seafarers could take Greenwich time with them around the world. Captain Cook used a copy of Harrison's chronometer on his second world voyage returning in 1775 to pronounce it to be a very accurate method of establishing longitude. Harrison eventually won the prize. The full story is told in the very readable book, Longitude by Dava Sobel.

How did time solve longitude? Having Greenwich time enables seafarers to time their local noon in Greenwich time. (rather than local time which would just tell you is was local noon!) The time of noon at Greenwich is found from tables (Almanac) as it varies slightly daily. The time difference between the local and Greenwich noon can be converted to longitude. The sun travels 15 degrees around the earth every hour. Therefore if your local noon occurred one hour later than Greenwich noon you would be 15 degrees west. 

By the end of the 18th century celestial navigation had taken off. The navigator was now armed with a copy of Harrison's accurate time piece, a sextant,  (invented in 1757, a development of the earlier quadrant,) and tables giving the accurate positions of the heavenly bodies. These items along with increasingly accurate charts surveyed by the likes of Captain Cook meant that the navigator was able fix his position out in the ocean with a fair degree of accuracy.        

The modern method of celestial navigation was developed by the French navel officer Captain (later Admiral) Marcq St. Hilaire in 1875. This is known as the Intercept Method does not depend on a noon altitude of the sun. This is very handy when the sun is not out all day.

The RYA Ocean Course follows the Marcq St Hilaire Intercept method, as do most modern text books. 

Finally, why do we need to use the celestial bodies when we have the GPS? Some navigators, perhaps because of an interest in the history of navigation, will just want to know. Some may have a healthy mistrust of electronic gear and want a reliable backup out there in the ocean.. Others, perhaps aiming for higher qualifications, need to have the RYA Ocean Yachtmaster qualification..

Celestial navigation can be straightforward. Using the Air Navigation Sight Reduction tables and pro-formas it requires only simple arithmetic. A knowledge of the night skies is not necessary

This is important, buy the smallest book you can find.  I recommend Tom Cunliffe's Ocean Sailing. Master the basics, then if you want know more, buy a thick book.

Ian Crowson May 2002



GMT   Greenwich Mean Time 

In 1880 international agreement accepted Greenwich as the prime meridian from which all time at sea should be measured. 

GMT is based on the 'average time' the sun takes to go around the world. i.e. one day (solar time)   In fact noon, (when the sun it at its highest altitude due south) at Greenwich varies daily . Whilst the sun is not an accurate time keeper it is predictable. The time of the sun's meridian passage (noon) at Greenwich is given in the Nautical Almanac for each day of the year.

GMT is also known as Zulu time (mostly by the services)

Most British tide tables and Almanacs use GMT (UT). But take care Reeds for example uses, for example, French Standard Time (1 hour ahead of GMT) for times of tides at French ports.


Between the last weekend in March and last weekend in October we add an hour to GMT (or UT) for daylight saving.

BST   British Summer Time  (Now called DST - Daylight Saving time.)

DST - Daylight Saving Time) UT plus one hour. 

The name can be confusing as the French also have DST which is 1 hour on French Standard Time, perhaps we should call ours BDST - British Daylight Saving Time.


Remember to add an hour to tide times in Reeds during daylight saving time.


UT  Universal Time

Same as GMT.

Nothing new, actually introduced in 1928 but GMT continued to be used for navigational publications and radio communications until recently. 

UT is based on the spin of the earth. It is the mean solar time and the time scale needed for celestial navigation.


UTC   Co-ordinated Universal Time

This is the time that time signals worldwide are co-ordinated to.  

For practical purposes it can be regarded to be the same time as GMT and UT.

Ian Crowson April 2008



The world is divided into 24 time zones each spanning 15 degrees of longitude. Time zone Z or 0 goes 7.5 degrees each way from Greenwich. Many larger countries group areas together into one zone for domestic reasons.

New York is in Time Zone +5. This means to work out Greenwich Time 5 hours must be added. e.g. if it is 0500 hours in the morning in New York, add 5 hours to discover it is 1000 hours in London.

A good book is Greenwich Time And the Longitude by Derek Howse.

Even better may be a visit to the Old Royal Observatory at 0 degrees longitude, Greenwich.



GPS uses atomic time (TAI time scale). GPS time was identical to UTC on 6th January 1980. Since that date corrections have been made to UTC for leap seconds (atomic time being more accurate) but not to GPS time. Therefore a difference of over 13 seconds has built up between UTC and GPS time. 

A correction is given in the navigation messages transmitted by GPS every 12.5 seconds to automatically correct the time difference and allow UTC to be obtained from the GPS accurate to +/- 1 second.

However it is possible to get a time from the GPS receiver that is not accurate enough for celestial navigation where the correction has not been made for various reasons. 

A chronometer or good quality quartz watch should used for celestial navigation.

Ian Crowson April 2008

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What follows is intended as an overview. I cover the practice in more detail on the workings page.


To get started lets look at the equipment required. A sextant (for measuring the angle of celestial objects above the horizon,) an accurate clock or watch that can be reato hours, minutes and seconds (four seconds error can put you off a mile) and, finally, a copy of the Nautical Almanac for the current year. The almanac contains the exact positions of the sun, moon, planets or stars for every second of the year. Sight Reduction tables will normally also be required, more later. 

I cover corrections required to be made to sextant readings on my Astro workings pages. 


The noon sight for latitude where the navigator observes the sun while it is passing through its highest point for the day is a good place for us to start. The angle of the sun above the horizon at its highest point is measured with the sextant and easily (using declination from the Nautical Almanac) converted to latitude. The time when the sun reaches its highest point can be converted to longitude with reference to the exact time of noon at Greenwich (using the Meridian passage time at Greenwich from the almanac). The RYA syllabus does not include noon sight for longitude. In practice several sights would be required as it is difficult to precisely time noon from just a noon sight. So, if you stick to noon sights there’s not that much to it. An hour or so of instruction, a few hours of practice, and you're on your way. However don’t rely on this method to cross the North Sea in winter!



The angle of Polaris in the sky is roughly equal to your latitude. Therefore you can  measure the altitude (note the time of observation) of the north star (Polaris) and calculate your latitude easily. After the normal sextant corrections (don't forget to use the star altitude correction) four easy Polaris corrections are required.  The corrections page can be found in the Nautical Almanac. The LHA of Aries is required in order to enter the corrections table. Take the GHA of Aries for time of observation from the NA and apply longitude (- west, + east) to get LHA.


Actually Polaris moves around a little and can be nearly 2 degrees away from true north. Take this into account when using it for compass checking. Corrections are in the Nautical Almanac.



You can also measure the altitude (angle above the horizon) of the sun at other times during the day. For the moon, stars, and the planets you need to stick to brief periods of twilight around sunrise and sunset when both stars and horizon are visible. These sights are a little more involved, but their reduction requires only more simple arithmetic

What follows is intended as an overview. I cover the practice in more detail below.


Read the next paragraphs carefully, this is the heart of the matter. This is the standard approach (attributed to Admiral Marcq Saint Hilaire) and is called the intercept method of sight reduction. This is the method the RYA Course is based on and is the one used in modern text books such as Tom Cunliffe’s excellent Ocean Sailing.

Firstly a sight (measured with the sextant) is taken of the celestial body to get an observed altitude (Ho). Note: the exact UT time of the sight must be recorded. Various corrections are applied to the sextant altitude (Hs) to get Ho. (covered later)                    

Secondly you work out the calculated altitude (Hc) of the body from an assumed position. Your assumed position is based on your DR or EP but ‘doctored’ slightly to allow you to enter the sight reduction tables in whole numbers. To do this, use the Nautical Almanac to find the position of the body at the time of observation. Then you take the bodies position and use the sight reduction tables to obtain the altitude (Hc) (angle above the horizon) and azimuth (Zn) compass bearing) that the body would have had if it had been sighted from your assumed position.




The aim of the sights is to obtain position lines in order to get a fix. Comparison of this calculated (Hc) and the observed values (Ho) of the altitude gives rise to a position line which when plotted with other position lines gives you a fix. The altitudes (Ho & Hc) give position circles around the geographical position (GP) of the body. The difference between Hc and Ho is the intercept. That is how far from the calculated position (circle) the observed position (circle) lies. The azimuth gives the bearing from the body and shows which part of the circles to use. Because the circle is so large the small part used (as indicated by the azimuth) appears as a straight line. This is the position line on our plot.





To recap and go over the procedure step by step:

You measure the altitude of a celestial body (Ho), noting the exact time. (UT)

You calculate the position of the object at the time of observation using the Nautical Almanac.

You use your assumed position to calculate what the altitude (Hc) would have been and what the azimuth (direction of the object) would have been. (from that assumed position)

Comparison of the altitude you measured (Ho) with the one you calculated (Hc) gives you an offset that can be plotted on a chart as a position line

A fix is then obtained by observing where two or more position lines cross.


SIGHT REDUCTION AND ASSUMED POSITION                                   

Sight reduction is the process used to determine the altitude and azimuth the celestial object would have at your assumed position. Your assumed position is based on your DR or EP but ‘doctored’ slightly to allow you to enter the sight reduction table in whole numbers.

The method of sight reduction used in the RYA Course is straight forward and use’s tables. These are AP 3270 Sight Reduction Tables for Air Navigation Vols. I, II & III. Volume II latitudes 0 – 39 degrees north or south. Volume III latitudes 40 – 89 degrees north or south. Volumes II & III are limited to celestial objects whose declination (angle above or below the celestial equator) is less than 29 degrees. This is good enough for the sun, moon, planets and some stars.

Volume I. Selected Stars is something completely different. Each day a changing set of seven stars (out of the 57 best navigation stars) are presented along with their altitudes and azimuths. Volume I is great, it makes it easy to find the correct star without a knowledge of the night skies.

Why Air Navigation Tables? – although slightly less accurate, fewer and lighter books are required than the 6 books of Marine tables,.

Reeds Astro Tables are cheap and light. They give almanac information plus a method of sight reduction. Instructions in the book.



Sight reduction is the solving of the PZX triangle. This the spherical triangle traditionally solved by using spherical trigonometry. There are various methods of sight reduction including using tables, trigonometry, calculators, and computer software. There are Concise Sight Reduction tables in the Nautical Almanac, these maybe useful in an emergency, but can be difficult to use. The Sight Reduction Tables for Marine Navigation come in six big, heavy and expensive volumes. After using the Air Table these should be straight forward to use.

One way of doing the sight reduction is with an inexpensive hand calculator (that has "sin" and "cos" keys) using two easy, one line formulas from spherical trigonometry These formulas can be found below. There are also a number of pre programmed calculators which include Almanac information. Computers offer not just sight reduction programes but software which includes Almanac information, sight reduction and fix calculators. Just enter the sextants angles from your sights, date/times and your DR/EP, touch a few keys and out comes your fix in lat and long. Fun maybe, but remember did your machine ever pack up at home?



This requires a scientific calculator. It should have sin, cos and tan functions and be able to handle degrees and minutes. The Casio fx-83WA which should cost less than £10 is suitable.

1.  Sun Sights. 

A. To find Hc (calculated altitude) (Do this calculation first as the Hc is required to find Azimuth)

Required:   (a) LHA of body   (b) DR Latitude   (c) Declination of body

sin Hc = 

(cos LHA x cos DR lat x cos dec)  + or - (sin DR lat x sin dec)

Note: use + if lat and dec are same names.

B. To find Azimuth (Zn)

Required:   (a)  DR Latitude   (b) Declination of body   (c) Hc (from first calculation)

cos Az * =  

sin dec +/- (sin Hc x sin DR lat) divided by (cos Hc x cos DR lat)

Note: use + when lat  and dec are of opposite names.

* Remember Az is the azimuth angle. To get Zn (Azimuth) apply the rules:

Northern Lat:  LHA > 180 deg. Azimuth = Azimuth Angle.   LHA < 180 deg. Zn = 360 - Az

Southern Lat.  LHA > 180 deg. Zn = 180 deg. - Az.   LHA< 180 deg. Zn = 180 + Az  

Ian Crowson. April 2008


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