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Editorial Reviews. About the Author. Jack Case is a retired naval officer and experienced download Astro Navigation Demystified - Full E-book Edition: Read 12 site Store Reviews - raudone.info The publication “A Short Guide to Celestial Navigation“ is owned and copyrighted by. Henning Later, I converted everything to the PDF format. Although this website aims to promote the Astro Navigation Demystified series of books, it is hoped that it will also provide a useful resource for navigators.

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You can download and print pdf files containing sight worksheets as well as the. Almanac They were written by people who know celestial navigation through. Why, I don't know other than celestial navigation has always had a shroud of .. seconds of UT. UTC is the time that you will use for celestial navigation using. Celestial navigation is the art and science of finding one's geographic Each chapter of the manual is a separate pdf file (Adobe Reader™.

Sight Reduction. This is the process of reducing the data gathered from observations of celestial bodies down to the information needed to establish an astronomical position line.

The two essential items of data that we need to begin the process of sight reduction are the azimuth and the altitude of the celestial body in question. Methods of sight reduction usually fall under two categories, tabular and formula. Tabular methods such as Rapid Sight Reduction involve interpolating large tables of data by entering latitude, declination and LHA to extract altitude and azimuth. Formula methods involve mathematically calculating the altitude and azimuth from the same input data.

With spherical trigonometry, we have the tools to quickly calculate the altitude and azimuth of selected celestial bodies at the estimated position without being encumbered by large tables of data. Why Spherical Trigonometry? Why Calculate Azimuth? The true azimuth and the azimuth angle provide exactly the same directional information albeit in different formats. If we measure the azimuth by compass, we can only do so from the true position. At the time of taking the altitude, we would not know where the true position is so our aim must be to find the direction of the true position from the DR position and we can only do this by calculating the azimuth angle at the DR position.

It is said that the crown was given by Dionysus to Ariadne on their wedding day and after the wedding, he threw it into the sky where the jewels became stars which were formed into a constellation in the shape of a crown. Virgo, the Virgin. Virgo lies over the southern hemisphere and is one of the largest constellations in the sky; it is visible between latitudes 80 o N and 80 o S. The brightest star in Virgo is Spica , the 15th brightest star in the sky and a very important navigational star which can be seen during morning nautical twilight from December through to May and during evening nautical twilight from April through to September.

In ancient Greek mythology, Virgo is associated with the goddess Dike, the goddess of justice and the constellation Virgo takes its name from the Latin for virgin or young maiden. Finding Virgo. If, as shown in the following diagram, we continue that curved line by another hand span from Arcturus we will come to the bright bluish-white star Spica in the constellation Virgo. Hydra, the sea serpent. The constellation Hydra, the sea serpent, is the largest constellation in the night sky and it is also one of the longest constellations.

It is best seen from the southern hemisphere, but can be observed in the northern hemisphere between January and May. Hydra contains one navigational star and that is Alphard which, for star sights, is best observed during evening nautical twilight during February, March and May. In Greek mythology, Hydra represents the water snake brought to the god Apollo by the crow Corvus as an excuse for being late from his errand to fetch water.

It may also represent the hydra from the myth of Hercules and his twelve labours. The Hydra was a giant beast with the body of a dog and snake-like heads. It was slain by Hercules on the second of his twelve labours for the king of Mycenae.

As each head was cut off, two more would grow in its place. Hercules burned the roots of the heads to prevent them from growing back. Finding Hydra. Hydra is such a large constellation that it really depends on which part of it you want to see. If you want to see head, then, as the diagram below shows, you should look between the constellations Canis Minor and Leo look for the bright stars Procyon in Canis Minor and Regulus in Leo.

If you the tail, then you should look to the south of Virgo look for the bright star Spica. Cancer The Crab. Cancer is a relatively small constellation in the northern hemisphere and is visible between latitudes 90 o N and 60 o S. Cancer consists of mainly faint stars, none of which is a navigational star and for this reason, it is not a very useful constellation for astro navigation.

However, it does help us in one way: Although astrology has no place in astro navigation, the signs of the zodiac can be very useful to navigators because the order in which they follow one another can tell us the position of one zodiac constellation in the sky with respect to another.

The Tropic of Cancer. These days, the Sun passes through Cancer in late July; however, in the time of Ptolemy, around years ago, this occurred during the summer solstice when the Sun reached The latitude In Greek mythology, Cancer is associated with the crab in the story of the Twelve Labours of Heracles. The goddess Hera sent the crab to attack Heracles while he was fighting the Lernaean Hydra but Heracles kicked it all the way to the stars where it formed the constellation Cancer.

In another version of the story, Hera placed the crab in the sky in gratitude for its efforts even though it was killed by Heracles. Heracles is the Roman name for the Greek god Hercules. Taurus is one of the most prominent constellations in the northern winter sky. It passes through the night sky from November to March and is visible at latitudes from 90 o N to 65 o S. Taurus is most visible in January and for the benefit of navigators, it is always on hand for star sights during morning and evening nautical twilight throughout that month.

The star at the tip of the northern horn of Taurus, Al Nath sometimes spelled El Nath is the second brightest star in the constellation and is also a navigational star. In earlier times this star was considered to be shared with the constellation Auriga, forming the right foot of the Charioteer as well as the Northern horn of the bull.

Taurus is associated with several mythological beliefs. In Greek mythology, Zeus was said to have disguised himself as a bull to abduct Europa, the daughter of king Agenor. Finding Taurus. If we imagine a line from Phad to Meral in Ursa Major and extend it for a distance of 80 o or roughly 4 hand-spans it will point directly to the star Aldebaran in the constellation Taurus.

Once we have located Aldebaran the remaining stars of Taurus can easily be identified. The Pleiades form a small star cluster close to Taurus; they are visible between latitudes 90 o N and 65 o S and are best seen during the month of January.

Merope is the brightest of these stars but even so, it not considered to be a navigational star. In ancient times, the Pleiades were called the Sailing Stars because Greek sailors would not put to sea unless they could be seen in the sky.

Although Pleione was not one of the seven sisters, she along with her consort Atlas is included in the Pleiades Cluster. The constellation Auriga is in the northern hemisphere and is visible between latitudes 90 o N to 40 o S. Capella is one of the navigational stars; it is the brightest star in the constellation Auriga and the 6th brightest in the northern hemisphere. The diagram below shows the star Al Nath sometimes spelled El Nath forming the right foot of the Charioteer and as has already been explained, it was once considered to be shared with the constellation Taurus where it forms the northern horn of the bull.

When the constellation boundaries were changed in , Al Nath was assigned solely to Taurus. However, if we still think of Al Nath the second brightest star in Taurus and also the second brightest in Auriga as the foot of Auriga, we will have an easy method of finding both Auriga and Taurus as we can see from the diagram below.

In mythology, Auriga is associated with Myrtilus the charioteer because the shape of the constellation was said to resemble a pointed helmet of a charioteer. It is also identified with Hephaestus, the god of the blacksmiths who invented the chariot. The Winter Triangle is an astronomical asterism formed from three of the brightest stars in the winter sky; Sirius, Betelgeuse, and Procyon, the primary stars in the three constellations of Canis Major, Orion, and Canis Minor which are discussed below.

As the following diagram shows, imaginary lines drawn between these stars form an imaginary equilateral triangle drawn on the celestial sphere. Orion is one of the brightest and best known constellations in the night sky it lies straddles the celestial equator and is visible between latitudes 95 o N and 75 o S.

This easily recognized constellation contains 4 navigational stars, Rigel, Belatrix, Anilam and Betelgeuse which, for navigation purposes are best seen during nautical twilight in the month of January. In Greek mythology, this constellaion represents the mythical hunter Orion, who is often depicted in star maps as either facing the charge of Taurus, the bull, pursuing the Pleiades sisters with his two hunting dogs, represented by the nearby constellations Canis Major and Canis Minor.

Alnitak, Alnilam and Mintaka form his belt and from this hangs his sword which is marked by the Orion Nebula. His right thigh is marked by Saiph and Rigel marks his left foot. Canis Major contains Sirius, which is otherwise known as the Dog Star. Sirius is the brightest star in the sky and is a navigational star which for navigation purposes is best seen during nautical twilight during the month of February. In Greek mythology, Zeus sent Laelaps, an alternative name for Canis Major, into the sky when it failed to outrun a fox.

Canis Minor is a small constellation in the northern hemisphere and is visible at latitudes from 85 o N to 75 o S. In another mythological tale, Canis Minor represents Maera the dog which was sent to the sky by Zeus after it died of grief when its master Icarius was killed. As shown in the diagram, there are only two bright stars in Canis Minor, Gomeisa and Procyon which is a navigational star and which, for navigational purposes is best seen during nautical twilight in March.

This constellation is associated with the Greek mythological hero Perseus who, on the orders of King Polydectes, slayed the Gorgon Medusa who had the power to turn people to stone. Polydectes had hoped that Perseus would not return and when he did, he became hostile. Perseus was so angered by this that he took out the head of Medusa and turned Polydectes to stone. The wife of Perseus was called Andromeda and the constellation that represents her lies side by side with the one that represents him.

Finding Perseus. If a line is drawn from Navi to Ruchbah in Cassiopeia, it will point almost directly towards the star Mirfak of the constellation Perseus at about one hand-span as shown in the diagram below. The constellation is associated in, Greek mythology, with the twins Castor and Polydeuces.

Pollux and Castor, the brightest stars in the constellation are said to form the eyes of the twins. We use the Latin name Pollux instead of the Greek name Polydeuces. Gemini is in the northern hemisphere and is visible between 90 o N and 60 o S. Pollux is a navigational star and is best seen for navigation purposes during nautical twilight in February. Finding Gemini.

As shown in the diagram below, a line running from Megrez to Merak in Ursa Major leads to the constellation Gemini. The constellation Aries is located in the Northern Hemisphere and is visible between latitudes 90 o N and 60 o S. Aries is a difficult constellation to see with the naked eye but it can be found about mid way between the Pleiades and the constellation Pegasus which we discussed in part 5 of this series.

Pegasus lies to its west, Pleiades to its east as the following diagram shows. Remember that, in star maps, east and west are reversed. Hamal is the brightest star in Aries and it is a navigational star which, for navigation purposes, is best seen during nautical twilight in the month of December. The First Point of Aries. It is the point at which the Sun crosses the celestial equator moving from south to north at the vernal Equinox in other words. The confusing thing is that, although this point lay in the constellation of Aries when it was chosen by the ancient astronomers, due to precession, it now lies in Pisces.

Stars For All Seasons — Part 1. Stars For All Seasons — Part 2. Stars For All Seasons — Part 3. Stars For All Seasons — Part 4. Stars For All Seasons — Part 5. During early autumn in the northern hemisphere, as the Earth continues to orbit the Sun, the last of the summer stars such as Altair, Vego, Deneb, Nunki and Kaus Australis move away to the west. Other stars have taken their place in the night sky including Alpheratz of the constellation Andromeda, Sadalsuud of Aquaries and Markab of Pegasus.

Andromeda is a constellation in the northern hemisphere and is visible between latitudes 90 o N and 60 o S.

Alpheratz is a navigational star which, for navigators, is best seen in the northern hemisphere during nautical twilight in the month of November. How to find Andromeda. Pegasus, which is the 7th largest constellation in the sky, is in the northern hemisphere and can be seen from 90 o N to 60 o S.

It has two navigational stars, Enif and Markab which, for navigators, are best seen during nautical twilight in the month of October. In Greek mythology, the winged horse Pegasus is said to have leaped from the body of the Gorgon Medusa after she had been slain by Perseus. The hero Bellerophon tamed the winged horse and tried to ride it to Olympus. However, Bellerophon fell from Pegasus but the horse made it to Olympus where it was kept by Zeus to carry his thunder and lightning.

This asterism is formed by the stars Scheat, Markab, Algenib and Alpheratz which is also in Andromeda. It is visible between latitudes 90 o N and 65 o S; it is best seen in November. The brightest star in Pisces is Alpherg or Kullat Nunu but this is not a navigational star; in fact, this constellation contains no navigational stars. The name Pisces is derived from the Latin for fish and is said to depict two fish, swimming in opposite directions, held together by a piece of string connecting their tails.

The star Alrisha is said to be the knot that ties the strings that hold the two fish together. In ancient Greek mythology, Pisces is associated with the fish that carried Aphrodite and Eros to safety from the monster Typhon. Finding Pisces. If a line is drawn from Scheat to Algenib in Pegasus and extended by about one hand-span, it will point to the star Alrisha in Pisces; however, this constellation is very hard to find because it is so faint.

Aquarius is a constellation in the southern hemisphere and is visible at latitudes between 65 o N and 90 o S; it is best seen during the month of October. Sadalsuud is not a navigational star and in fact, there are no navigational stars in the constellation Aquarius which, like Pisces, is very faint and difficult to see with the naked eye.

The vernal equinox is the point where the Sun crosses the Equator on its northward movement along the ecliptic and heralds the first day of spring in the northern hemisphere on 20 th. In ancient Greek mythology, Zeus transformed himself into an eagle Aquila to carry a young man named Ganymede to serve as a cup-bearer to the gods in Olympus. Finding Aquarius. If we also run a line from Scheat to Markab in Pegasus and extend that line by a palm-width, that too will point to Aquarius.

The small constellation Piscis Austrinus, also called Piscis Australis, lies in the southern hemisphere and is visible between latitudes 55 o N and 90 o S. It contains mostly faint stars except for Formulhaut which is one of the brightest stars in the sky and is a navigational star. For navigators, the best time to see Formulhaut is during nautical twilight is in the month of October.

Piscis Austrinus is associated with the Babylonian myth about the goddess Atargatis who fell into a lake and was rescued by a large fish. Formulhaut is depicted as the toe of Aquarius and this idea provides us with a way of locating both Aquarius and Pisces Austrinus for if we can find Formulhaust, the brightest star in the region, then we can find both of those constellations.

The following diagram shows Pisces Austrinus nestling at the foot of Aquarius with Formulhaut providing the link between them. The Autumn constellations, Pegasus, Andromeda, Pisces, Aquarius and Piscis Austrinus sink into the west after December and waiting in the wings are the winter constellations of Orion, Taurus, Auriga, Perseus, Gemini, Canis Major and Canis Minor; these will be the subject of the next article in this series.

Centaurus is the ninth largest of all constellations and extends from about 30 o south to 61 o south. It is one of the brightest constellations in the sky and contains three navigation stars: Hadar, Menkent and Rigil Kentaurus.

Finding Centaurus. Centaurus is associated with several mythological tales and is depicted as a centaur, half man and half horse. In Ancient Greek mythology, the constellation is associated with Chiron, the centaur who mentored many of the Greek heroes including Theseus, Jason and Heracles.

Crux Latin for cross , it is one of the smallest constellations in the sky but also one of the brightest which makes it useful for astro navigation. This is the brightest star in the constellation Crux; it is a navigational star and is circumpolar south of 28 o south.

Beta Crucis, also known as Mimosa or Becrux, is the second brightest star in the constellation but is not a navigational star; it is circumpolar south of 40 o south.

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Gamma Crucis or Gacrux , is the third brightest star in Crux; it is a navigational star and is circumpolar below 32 o south. Crux is associated with the mythology of several cultures. Finding Crux. The constellation Centaurus contains two bright stars which make excellent pointers to help us find the Southern Cross. The Pointers as they are known, are Rigil Kentaurus and Hadar which are both navigational stars.

The next diagram shows the relationship between the pointers and the Southern Cross. The constellation Centaurus appears to envelope Crux and indeed the ancient Greeks considered them to part and parcel of the same constellation. It is the 34th biggest constellation and it contains two navigation stars, Canopus and Miaplacidus. It is a variable star and was once the brightest star in the sky but currently its apparent magnitude is around 4.

Carina was once part of a larger constellation, Argo Navis which represented the ship on which Jason and the Argonauts sailed to find the Golden Fleece. In , Argo Nevis was divided into three smaller constellations: Carina, the hull , Puppis the stern and Vela the sails. Vela represents the sails of the Argo Navis. Its brightest star, Suhail has an apparent magnitude of 1. It has only two named stars and neither of these are classified as navigation stars.

Triangulum Australe The Southern Triangle. This is a small constellation located over the southern hemisphere. Atria is the brightest of the three and the only navigation star in the constellation. Finding Triangulum Australe.

If we line the pointers up in the opposite direction, that is pointing from Hadar to Regel Kentauri and extend that imaginary line by about 15 to 20 degrees it will point to Betria in Triangulum Australe. The diagram below demonstrates this. This is the last constellation that we will visit in this article although there are many more that we could discuss. Another method is to imagine a line from the star Peacock to the star Delta Pavonis, the third brightest star in Pavo, and as shown in the diagram above, this line will also point to the Celestial South Pole.

Michael Punk. The Revenant. In article one of this series this article, we briefly touched on the topic of circumpolar stars and here we continue with that discussion.

A circumpolar star is one that, from a given latitude on Earth, never rises or sets because it is always above the horizon. If the angular distance of a star from the nearest pole is less than the latitude of the observer, then that star will be circumpolar to the observer.

The angular distance of a star is the complement of its declination so if its declination is S57 o then its angular distance from the South Pole will be 33 o.

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Ursa Major. The best known and easily recognisable constellation in the northern hemisphere is the constellation Ursa Major which is also known by various names such as the Great Bear, the Big Dipper and the Plough.

Ursa Major contains 3 navigational stars named Dubhe, Alioth and Alkaid and is circumpolar from about 42 o North the angular distance of Alkaid is 41 o. Ursa Minor. The Little Bear also known as the Little Dipper. Polaris is only the 45th brightest star in the sky; however, it has always played an important role in navigation; not only because it indicates the direction of north but also because it is useful for position fixing in the north polar-regions.

Finding the Pole Star. Ursa Major contains a reference line known as the line of pointers. The line joining Merak to Dubhe, when extended will point to Polaris in the constellation Ursa Minor as illustrated in the following diagram. Ursa Major and Ursa Minor are associated with several mythological stories.

How to find Cassiopeia. Cassiopeia can be located along a line of reference from the Pole Star at an angle of o to the line of pointers in Ursa Major, as the diagram below shows. The constellation Cassiopeia is associated with Queen Cassiopeia in Greek mythology. Taurus, The Bul l. Taurus is a constellation in the northern hemisphere and is visible at latitudes from 90 o N to 65 o S; for navigators, it is best seen during nautical twilight in January.

Al Nath is circumpolar from 60 o N. Auriga, The Charioteer.

Capella is the brightest star in the constellation Auriga and the 6th brightest in the northern hemisphere. It is circumpolar at latitudes above 45 o North. However, if we still think of Al Nath as the foot of Auriga as well as the northern horn of Taurus, we will have an easy method of finding both Auriga and Taurus as we can see from the diagram below.

The easiest way to locate the stars in which we are interested is to locate the constellations to which they belong.

One method of doing this is to establish reference lines in known constellations and from these, memorise the directions in which other constellations lie. The Summer Triangle. The diagram below shows how the triangle is formed by imaginary lines drawn between those stars.

Lyra contains Vega, which is the second brightest star in the northern hemisphere and is a navigational star. In Greek Mythology, when Orpheus died, he dropped his lyre into a river from where it was retrieved by an eagle sent by Zeus.

Zeus then sent both the lyre and the eagle into the sky as the constellations Lyra and Aquila. Aquila contains Altair, the 12 th brightest star in the sky and also a navigational star.

In Greek mythology, Aquila, the eagle, carried thunderbolts for Zeus and as explained above, later rescued the lyre of Orpheus from the river. As with Lyra, Cygnus is visible between latitudes 90 o N and 40 o S.

For navigators it is best seen during nautical twilight in late summer and autumn. Cygnus contains an asterism formed by the brightest stars in the constellation which is named the Northern Cross. In Greek mythology, Orpheus was said to have been turned into a swan by Zeus and sent into the sky as the constellation Cygnus along with Aquila and Lyra. Finding the Summer Triangle. In the diagram below, if we join the star Meral in the constellation Great Bear Ursa Major to a point midway between the stars Alioth and Dubhe also in the Great Bear and then extend this line, it will point to Vega, the brightest star in the constellation Lyra.

Alphecca , the brightest star in the group, is a navigational star and is best seen during nautical twilight in July. Sagittarius, The Archer. Sagittarius is a large constellation lying over the southern hemisphere and is visible between latitudes 55 o N.

It contains several bright stars including two navigational stars, Nunki and Kaus Australis which are best seen during nautical twilight in August. In ancient Greek mythology, Sagittarius was said to represent the Archer, a beast called a Centaur which was half man and half horse. In the representation below, the Archer has a drawn bow with the arrow pointing to the star Antares, the heart of the scorpion, which had been sent to kill Orion. Finding Sagittarius. The Summer Triangle provides a useful pointer to Sagittarius.

If we draw an imaginary line from the star Deneb through the star Altair in the Summer Triangle and extend that line by about 20 o or one hand-span, it will point to the constellation Sagittarius as the diagram below shows. However, in ancient Greek times, the Sun passed through the constellation Capricornus at this time hence the reason for naming the latitude Scorpius Scorpio , The Scorpion.

The constellation Scorpius lies above the southern hemisphere and is visible between latitudes 40 o N and 90 o S. Scorpius has several bright stars which, between them, form the shape of a scorpion.

The brightest star in Scorpius is Antares which is often mistaken for Mars because of its reddish orange colour. Antares is the 16th brightest star in the sky and is a navigational star.

The second brightest star in Scorpius is Shaula which is said to represent the sting in the tail of the scorpion. Shaula is also a navigational star. For navigation purposes, Antares and Shaula are best seen during nautical twilight in July.

In Greek mythology, Scorpius represents the scorpion that the goddess Artemis sent to sting and kill Orion who had tried to ravish her. The line from Nunki to Kaus Media represents the arrow, the head of which points to Antares in Scorpio. It also helps to remember that the orange star Kaus Media points along the line of the arrow towards the red star Antares.

The bright red glow of Antares further helps us to identify Scorpius.

The angular distance from Kaus Australis in Sagittarius to Shaula in Scorpius is approximately 10 o or roughly equivalent to the width of the palm of the hand when held at arms length. Why do the stars that we see in the night sky change from season to season?

There are two separate reasons for these phenomena, Rotation and Revolution. The Earth rotates about its axis while it revolves around the Sun.

The Earth rotates from west to east about its axis of rotation which is a line joining the celestial poles and if this axis is produced far enough, it will cut the celestial sphere at a point marked by the North Star Polaris as shown in the diagram. Facing north from the Earth, the Pole Star appears stationary, and the other stars appear to rotate from east to west around the Pole Star although in fact the positions of the stars are fixed and it is the Earth which is rotating from west to east.

If the sidereal day were to be exactly 24 hours, as is the Mean Solar Day, then the stars would rise and set at the same times every day. However, the Earth completes each rotation about its axis in 23 hours, 56 minutes and 4 seconds so the stars will take the same amount of time to circuit the Pole Star and that is the length of the sidereal day. In other words, the star in question will rise 3 minutes and 56 seconds earlier each day usually rounded off to 4 minutes. For example, Say that Arcturus the brightest star in the northern celestial hemisphere rises at In the diagram below we see the Earth as it orbits the Sun or to put it another way, we see it as it revolves around the Sun.

The positions of some of the more well known stars in relation to our Sun are also shown and it can be seen that, as the Earth follows its orbital path, different stars will gradually come into and out of view in the night sky.

So, in the Northern Hemisphere, we have our winter stars such as Aldebaran, Rigel and Betelgeuse and we have our summer stars such as Nunki and Kaus Australis; of course, it is the other way round for the Southern Hemisphere. Circumpolar Stars. Depending on the latitude of the observer, some stars will never rise or set because they will always be above the horizon, these are known as circumpolar stars.

The diagram below shows the constellations Ursa Major Great Bear and Cassiopeia which are both circumpolar to observers throughout the Northern Hemisphere and down to 20 o South in the Southern Hemisphere. There are many other circumpolar constellations such as Ursa Minor, Auriga and Perseus in the Northern Hemisphere and Centaurus and Crux in the Southern Hemisphere; we will be looking at these more closely in future articles of this series. Sight reduction methods tend to fall under two categories, Formula and Tabular.

Therefore, in this article, I will discuss the relative merits of these two methods. Sight Reduction. This is the process of reducing the data gathered from observations of celestial bodies down to the information needed to establish an astronomical position line.

The two essential items of data that we need to begin the process of sight reduction are the azimuth and the altitude of the celestial body in question. We measure the altitude at our true position and we calculate the altitude at the DR position or assumed position ; this enables us to calculate the zenith distances at the two positions.

The difference between the two zenith distances will give us the distance from the DR position to the true position measured along the direction line of the calculated azimuth. Measuring the altitude and azimuth at the true position with a sextant and azimuth compass is relatively straightforward but calculating what they would have been at the DR or Assumed position is the real work of sight reduction. Formula Methods. The traditional way of calculating the azimuth and zenith distance at the DR position is by spherical trigonometry.

Before the advent of the electronic calculator, this would have been a very lengthy and time consuming method involving the use of tables of logarithms to make calculations involving the Haversine Formula. However, these days we can still make use of spherical trigonometry with the use of a scientific calculator and with the application of just two formulas derived from the Cosine Rule, one for the azimuth and one for the zenith distance.

With just a little practice, it will be found that this method is quick and easy to apply. We usually refer to these methods as Formula Methods. Accuracy is the greatest advantage of formula methods; calculations are usually made to 3 or 4 decimal places but this can be extended if greater accuracy is required. Of course there is always the risk of human error when making mathematical calculations but with an electronic calculator, it takes very little time to double check.

During the twentieth century, tabular sight reduction methods were first devised and today there is such a proliferation of these methods that choosing one can be very confusing. Tabular methods do not require a knowledge of spherical trigonometry; they involve the use of sets of pre-computed tables of data from which the altitude and azimuth can be interpolated.

The disadvantage of these tables is that they have to be entered with the latitude and Local Hour Angle rounded to the nearest degree so that calculation of the altitude and azimuth depends on interpolation and extrapolation.

This is a position where the latitude and longitude closest to the DR position have the following properties: The assumed latitude is the DR latitude rounded up to the nearest whole degree and the assumed longitude is the longitude closest to the DR longitude that makes the local hour angle a whole degree.

In comparison, when we solve the problem directly by spherical trigonometry, we use the latitude and longitude of the DR or EP position and we make exact calculations without the inaccuracies of interpolation methods.

Of course the greatest advantage of tabular methods is that the navigator does not require a knowledge of trigonometry and the only mathematical calculations needed involve simple arithmetic. Below, we compare the accuracy of calculations made to establish astronomical position lines using two different methods, one a formula method and the other a tabular method.

We use identical input data for both examples. The first example shows the calculations made using the cosine formula method and the second shows those made using the Rapid Sight Reduction Method NP Please note that the sight reduction forms used in these examples are not standard but are designed as learning aids for use with exercises in my books. Cosine Formula Sight Reduction Method.

Rapid Sight Reduction Method. There is a difference of 1. In terms of distance, 1. So how do we decide which method is the more accurate? The arguments above are really inconclusive and it would seem that, from the point of view of accuracy, there is not a great deal of difference between the two methods.

If we are concerned about accuracy in astro navigation, it matters not which sight reduction method we use, the real danger of inaccuracy lies in other areas. Inaccuracy in calculations may be introduced by a number of contributory errors irrespective of the sight reduction method being used; these errors are summarized below. Errors in the observed altitude.

Even when the sextant altitude has been corrected for index error, semi-diameter and parallax, the resultant altitude reading may still be incorrect owing to a combination of other errors such as incorrect calculated values for dip and refraction.We can confirm the validity of the formula by calculating the approximate altitude of star Y by the same method as above. Canis Major, The Greater Dog.

It calls you to be hot or cold, and calls you to examine yourself before its holy pages and before the holy Lord Jesus that it points to and proclaims. Canis Minor The Lesser Dog.

The Little Bear also known as the Little Dipper. Latitude South: Whereas the Nautical Almanac does not list the GHA for stars, it does for planets, so for this reason, the procedure is made simpler as shown below:

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