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**Celestial/Astro Nav Notes for students**

**CELESTIAL NAVIGATION**

**A VIEW BY IAN CROWSON**

**1. A LITTLE HISTORY****,**

** 2.TIME - GMT,
UT, DST, BST, UTC & TIM****E
ZONES**

**3. TIME AND GPS**

**4 .****THE
ART OF FIXING YOUR POSITION USING CELESTIAL BODIES**

**5. SIGHT REDUCTION USING A CALCULATOR**

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**A LITTLE HISTORY**

**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**

2. TIME

**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.**

**DST OR BST**

**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**

**TIME ZONES**

**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.**

**3. TIME AND GPS**

**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**

**4. THE
ART OF FIXING YOUR POSITION USING CELESTIAL BODIES**

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

**EQUIPMENT**

**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 **

**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!**

**POLARIS - LATITUDE **

**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.**

**POLARIS - THE NORTH STAR.**

**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.**

**OTHER SIGHTS **

**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.**

**THE INTERCEPT METHOD**

**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.**

**POSITION LINES**

**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.**

**RECAP **

**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.**

**OTHER METHODS OF SIGHT REDUCTION**

**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?**

**5. SIGHT REDUCTION USING A POCKET CALCULATOR**

**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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