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Editorial Reviews. About the Author. Jack Case is a retired naval officer and experienced Buy Astro Navigation Demystified - Full E-book Edition: Read 12 Kindle Store Reviews - wildlifeprotection.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.

Astro Navigation Demystified Pdf

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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™.

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.

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.

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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.

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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.

An error in the observed altitude will lead to an error in the observed zenith distance. A pronounced error in refraction is likely to occur when the altitude is below 15 o.

Deck-watch error. An error in the LHA will lead to an error in the calculated altitude and this will cause the position line to be displaced. Errors in the D. Errors in the course and distance laid down on the chart may result from a combination of inaccurate plotting, compass error.

An error in the DR position and resultant assumed position will lead to errors in the estimated longitude and hence the local hour angle and this in turn will lead to an error in the calculated altitude. Nautical Almanac. There are accumulative and unavoidable errors caused by the addition and rounding-off of quantities taken from the almanac.

Position lines obtained from two or more astronomical observations are not likely to pass through a common point. The reasons for this are firstly, the observations are not likely to be taken simultaneously since it is not possible to take sextant readings of three several celestial bodies at the same instant.

Secondly, observed altitudes are very seldom correct and therefore, the resultant observed zenith distances will not be correct. For the average yachtsman sailing in the vast expanse of the ocean, an accuracy level of plus or minus 1 nautical mile is probably nothing to worry about but for those engaged in activities that require a greater level of accuracy such as surveying and naval operations, it is obviously a matter of concern.

Wish to learn more? Skip to content. Spring Stars in the Northern Hemisphere. Finding The Stars and Constellations. Measuring the Altitude of the Moon. Why Astro? The Importance of Altitude and Azimuth in Celestial navigation. Bearing, Azimuth and Azimuth Angle.

Learning from the Polynesians Survival — Star Compass 1. Survival — The Daytime Star. Survival — Calculating altitude without an angle measuring instrument. The Survival Sundial. Exercise 4 — Local Hour Angle. Sight Reduction Forms. See the latest article: David Cooper says: July 16, at Posted in Uncategorized. He bases his calculations on the following data: Calculate LHA of Alioth. Calculate whether or not Alioth is above the celestial horizon.

The rules for this are: Step 3.

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Is Alioth above the celestial horizon to the north and south? Latitude North: Latitude South: Step 5. Calculate Approximate Altitude. We can formulate the above statements as follows: NS is the meridian of the observer and in terms of LHA, is 0 o. WE is the celestial equator.

From the nautical almanac daily pages, find the Greenwich Hour Angle GHA of Aries to the nearest degree at the planned time of the observation.

A list of navigational stars can be found on page Calculate your estimated longitude to the nearest degree at the planned time of the observation.

Details of Planet V: 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: LHA 22 o , Dec. LHA o , Dec. 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: PQ is tangential to the circumference of the Earth at point O.

Data previously determined: Angle ECX is equal to 65 o , the declination of star X. Lat of observer: We can formulate this as follows: Data previously determined for Star Y: Angle ECY is equal to 15 o , the declination of star Y. Summary of Data for star Y: Testing the Formula for star Z. If we apply this formula to the example of star Z we have: Reliability of the Formula when for bodies close to the horizon.

Books of the Astro Navigation Demystified Series: Theory and Practice email: Posted in astro navigation , astronomy , celestial navigation , Marine Navigation , navigation Tagged astro navigation , astronomy , celestial navigation , Marine Navigation , navigation.

By Jack Case Introduction. Body is above horizon to the west if: NS is the meridian of the observer and in terms of LHA is 0 o. Using the following scenario, calculate LHA of Arcturus. Date and Time: Civil twilight: 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: GHA Mars: Posted in astro navigation , astronomy , celestial navigation Tagged astro navigation , astronomy , celestial navigation , Marine Navigation , navigation.

Posted on January 22, by Jack Case. From this, it can be seen that Cancer can be an aid to locating both Gemini and Leo.

Posted in astro navigation , celestial navigation , Marine Navigation , navigation Tagged astro navigation , astronomy , celestial navigation , mathematics of astro navigation. Auriga the Charioteer. Orion, The Hunter. Canis Major, The Greater Dog. Canis Minor The Lesser Dog.

Gemini,The Heavenly Twins. Aries, The Ram. Posted in astro navigation , astronomy , celestial navigation , Marine Navigation Tagged astro navigation , astronomy , celestial navigation , navigation. 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. Sweet and simple.Finding Perseus. The height of the observation corrected, subtracted from 90, is your Latitude.

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. 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. Because nautical twilight gives us only a short period of time to make observations, advanced planning is essential.

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