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™.
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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 Kindle Store Reviews - ronaldweinland.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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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.
There is also the point that, unless you are in the fortunate position of having a gyro compass, you must take magnetic compass readings and these have to be corrected for variation and deviation; so you might just as well calculate the azimuth in the first place.
Using Spherical Trigonometry To Calculate the altitude and azimuth of the star Alioth at the estimated position at the planned time of observation using the data provided in the scenario. Calculate LHA.
Before he can do this, he needs to locate Alioth in the sky. This he does this by using the WTL method to calculate its approximate azimuth angle and altitude as demonstrated below: He bases his calculations on the following data:.
Body is above western celestial horizon if: Body is above eastern celestial horizon if: The LHA of Alioth is 11 o W and so we can conclude that it will be above the celestial horizon to the west. DR Position of observer: Step 4. Estimate Azimuth Angle. In the drawing, we have plotted the position of Alioth in terms of its LHA and declination which are as follows: LHA 11 o W, Dec. If we draw a line joining the position of Alioth to the position of the observer, we will see that the approximate azimuth angle is: N15 o W which, in terms of true azimuth, is: Of course, as discussed earlier, we cannot find an accurate solution to a spherical problem with a straight-line, two dimensional drawing such as this which does not take account of the fact that the Earth is not a perfect sphere and does not allow for phenomena such as refraction and parallax.
It is also stressed that the drawing above is for illustrative purposes only and therefore, it is not drawn to scale and angles are not accurately drawn. The formula for calculating approximate altitude is: Reminder of data gathered to date: Approx alt. Summary of the Demonstration Example Results.
Secondly, we used the method to calculate the approximate azimuth and altitude of Alioth as follows: Approx Az. Full Explanation of the Method. To find if a star or planet will be above the horizon at our position at the time of the planned observations, we need to take two things into account, its local hour angle and its declination.
Suppose that point A in the diagram represents the position of a celestial body whose LHA is 40 o and that point B represents the position of another celestial body whose LHA is o. Since the LHAs of these bodies is either less than 90 o or greater o , they will be visible above the celestial horizon to the west and the east respectively. Bodies whose LHAs are greater than 90 o but less than o would be below the celestial horizon and therefore would not be visible. LHA of A Star. The following method can be used to calculate the LHA of a star.
We will use three celestial bodies, stars X and Y and planet V to demonstrate the method outlined above: DR Position of Observer: Since the LHA of Y is between o and o it will be visible above the celestial horizon to the East. Unlike the stars, the positions of the planets in the celestial sphere are not fixed and for this reason the four navigational planets are listed in the daily pages of the Nautical Almanac by their GHA and declination instead of by their SHA.
The Navigational planets are: Mars, Saturn, Venus and Jupiter. The method used to calculate the LHA of a planet is the same as that for a star except that because the GHA is given in the Nautical Almanac, we do not need to calculate it. The following calculations for planet V demonstrate the method. Azimuth and Azimuth Angle. The difference between azimuth and azimuth angle is demonstrated in the following diagram.
In astro navigation, when we calculate the azimuth of a celestial body, the result is expressed as an azimuth angle. If the observer is in the northern hemisphere, the azimuth angle is measured from north and if in the southern hemisphere, it is measured from south.
If the observer had been in the northern hemisphere, the azimuth angle would have been N o E. In the drawing below, we have added to the LHA diagram by plotting the positions of X and Y in terms of their LHA and declination which are as follows:. If we join the positions of X and Y to the position of the observer, we will see that the approximate azimuth angles are as follows:. Star X: Star Y: Summary of data relating to stars X and Y which are represented in the diagram: Once you have become familiar with this diagram, there will be no need to draw it every time you wish to calculate the approximate azimuth.
Of course we cannot find an accurate solution to a spherical problem with a straight-line, two dimensional, drawing such as this which does not take account of phenomena such as refraction and parallax or the fact that the Earth is not a perfect sphere. It is stressed that the diagram above is for illustrative purposes only, it is not drawn to scale and angles are not accurate. As well as the LHA, we have to take into account the declination of a celestial body.
For a celestial body to be visible above the horizon, its declination must be within 90 o of the latitude of our position. If our latitude is north, then the declination must be within the range 90 o north to 90 o — latitude south.
If the latitude is south, then the declination must be within the range 90 o south to 90 o — latitude north. We can explain the reason for this rule with the aid of another diagram which shows the positions of the bodies X and Y from the previous example in terms of their declinations. Please note that the diagram is for illustrative purposes only; for this reason, it is not drawn to scale and angles are not drawn accurately.
C is the center of the Earth and the line CZ is perpendicular to both the celestial horizon and the visible horizon. Y is the position of the star Y in the celestial sphere and Y 1 is its geographical position.
Because of the vast distances of the stars from the Earth, we can assume that, in their cases, the celestial horizon and the visible horizon correspond with very little error. Calculating Approximate Altitude. Angle BCZ is equal to 90 o and is the angle between the celestial horizon and the zenith of the observer. Calculating approximate altitude of star Y. We can confirm the validity of the formula by calculating the approximate altitude of star Y by the same method as above. Testing the Formula for star Y.
The formula previously derived for calculating the approximate altitude is: Does the formula work for stars in the opposite hemisphere? In each of the two cases above, the declination of the celestial bodies have been in the same as the latitude of the observer. The latitude of the observer is 50 o N; therefore, in the diagram, angle, ECZ is equal to 50 o. The declination of star Z is 10 o S; therefore, measuring from the centre of the Earth, the angle between East and the direction of star Z is 10 o.
The angle between star Z and the celestial horizon is 30 o and the angle between star Z and the visible horizon is also 30 o so we can conclude that the approximate altitude of star Z is 30 o see note below. The formula previously derived for calculating the approximate altitude is Approx. If we apply this formula to the example of star Z we have:.
The answer agrees with our findings from the diagram so we can conclude that the formula works in cases where the latitude of the observer and the declination of the celestial body are contrary.
There is no great problem here because sextant measurements of bodies which are close to the horizon are not very reliable anyway because pronounced error due to refraction is likely to occur when the altitude is below 20 o.
Overall Conclusion. The Astronomical Position Line. When a position line is derived from an observation of a celestial body, it is known as an astronomical position line.
The Observed Position. The position of a vessel can be established by the intersection of two or more position lines; such a position is known as a position fix. For this reason, the accuracy of an observed position derived from only two astronomical position lines cannot be relied upon and therefore, it is generally accepted that at least three position lines are required in order to obtain an accurate fix. Daylight Fixes. During the hours of daylight, we are mainly restricted to obtaining fixes from just one celestial body, the Sun.
Sometimes, we can achieve a two point fix from the Sun and the Moon but mostly, all we can do is obtain two time-separated astronomical position lines using the Marcq St. Hilaire method to give us a two point fix. Stars and Planets. There are 59 navigational stars and 4 navigational planets which we can use to achieve position fixes derived from three or more position lines but there are only two short periods during the day in which we can do this because we need it to be dark enough to see the bodies in the sky yet light enough to see the horizon.
Twilight Time. In general, the optimum conditions for taking observations of stars and planets occur during the times of civil twilight and nautical twilight when it is likely to be light enough for the horizon to be seen yet dark enough for those celestial bodies to be visible. Civil Twilight. During civil twilight, the horizon is clearly visible and the brightest stars as well as Venus, the brightest of the navigational planets, can be seen as long as they are above the horizon at that time.
Nautical twilight is so named because it is when navigators are able to take reliable sights of stars and planets using a visible horizon for reference. Unlike the Sun and the Moon which are easily identified, the approximate positions of stars and planets need to be established before observations can be made.
The times of rising and setting of the Sun and Moon can be found in the daily pages of the Nautical Almanac so we know when they will be visible above the horizon.
However, the risings and settings for stars and planets are not listed so we have to calculate these for ourselves. The Stars. The stars are at such an immense distance from the Earth that the movement of their relative positions in the sky, which is so slow and so small, can be discounted without any great loss of accuracy and we can assume therefore, that they are in fixed positions in the celestial sphere.
The Planets. The planets in the solar system orbit the Sun in an anti-clockwise direction when viewed from the north pole of the celestial sphere. The apparent motions of the planets, when viewed from the Earth, are complicated by the facts that they are at varying distances from the Sun, have different orbital patterns, retrograde motions and orbital speeds.
These are: Venus, Mars, Jupiter and Saturn. So what we need is a method that will enable us to calculate not only which of the navigational stars and planets will be above the celestial horizon during civil and nautical twilight but also what their approximate position in the sky will be during those times.
The Where To Look Method, of which I claim ownership, is particularly advantageous in the close confines of a small-boat chart table and is cost-free. It is emphasised that this is not intended to be a method of accurately pin-pointing the position of a celestial body; it is just a method of locating it so that we can begin the process of using it to calculate an astronomical position line.
Before proceeding with the explanation, I would like to say that Although it will take many words to explain this method thoroughly, it is something which, once fully understood, can be put into practice quickly and easily with just a little mental arithmetic and logic.
Stage 1. Planning which stars and planets will be above the celestial horizon during civil and nautical twilight. Firstly, in the Nautical Almanac, look up the time of nautical twilight for your latitude.
To find out if a star or planet will be above the celestial horizon at your estimated position during nautical twilight, you need to take two things into account, its local hour angle and its declination. For a star or planet to be visible, its geographical position must be within 90 o east or west of our estimated longitude at the time of the planned observations.
We can explain this in the following way: Body is above horizon to the east if: Since the LHAs of these bodies are either less than 90 o or between o and o , they will be visible above the celestial horizon to the west and the east respectively. The following method can be used. Chosen Star: SHA of Arcturus: N19 o from the Nautical Almanac. Estimated Long: If the latitude is north, then the declination must be within the range 90 o north to 90 o — latitude south.
We can formulate the above statements as follows:. The procedure for calculating whether or not a planet will be above the horizon during civil and nautical twilight is the same as that for stars except for one thing. 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:. Stage 2. Calculating Approximate Altitude And Azimuth.
We will discuss stage 2 in part 2 of this series. They will soon join the ever-present circumpolar constellations of Ursa Major and Minor, Cassiopeia, Perseus and Auriga. Leo, The Lion. Leo is one of the largest constellations in the sky and is visible throughout the Northern Hemisphere during the spring months and in the northern regions of the southern hemisphere during the summer and autumn months.
Leo is home to two navigational stars, Denobola and Regulus which are shown in the diagram above. From a navigation perspective, these stars are best seen for star sights during evening nautical twilight during the month of April.
The name Leo means Lion in Latin and the constellation, which is depicted as a crouching lion, is associated in Greek mythology with the lion of Nemea which was killed by Heracles as one of his twelve labours. How to find Leo. When the line of pointers in Ursa Major is produced in the opposite direction to the Pole Star, that is from Dubhe to Merak, it will point to Leo as shown in the diagram below.
Corona Borealis The Northern Crown. Alphecca , the brightest star in the group, is a navigational star and is best seen for star sights during morning and evening nautical twilight in April and May.
The main stars in Corona Borealis form a semi-circle which is associated with the crown of Ariadne in Greek mythology. 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. It is the ultimate authority.
And digital is FREE. A bound volume, even if it is not the current edition, is very handy, easier to flip pages than scroll a mouse or drag a finger. Pre calculate time of Local Apparent Noon, when the sun is exactly on your meridian. Start shooting just before, record times and reading, and watch how the sun goes higher and finally when it is exactly due south or north as the case may be it will seem to hang there for a bit.
From the time it last seems to move until the time it appears to be moving again, height wise, will likely be the best part of half a minute.
Take the average of those two times and see how closely it agrees with your calculation. Should be spot on the money. The height of the observation corrected, subtracted from 90, is your Latitude.