HEAVEN'S GUIDE MERE MORTALS - Department of Mathematics

Celestial Navigation: Heaven’s Guide for Mere Mortals Page 0

CELESTIAL NAVIGATION

HEAVEN’S GUIDE FOR

MERE MORTALS ===================================================================================

Prepared by

Chan Wee Nee Winnie

Charmaine Ong Heng Lin Chong Jin Wei Martin Jordon Bai Bingren

Nah Wen Bin Ng Bee Jing Wendy

--Group 19--


Table of Contents

Page 1. An Introduction to Stars 1 2. Introduction to Celestial Navigation 10 3. Theory Behind Celestial Navigation 11 3.1 Spherical Triangle 14 3.2 Finding Position 16 4. Evolution of Celestial Navigation 19 5. Sextant 33 6. Celestial Navigation and its impact on history, geography and economics 38 7. Conclusion 46 8. Appendix 9. References


ABSTRACT Celestial Navigation – Heaven’s Guide for Mere Mortals: This report aims to bring forward to people some knowledge of celestial navigation. Today, navigation is made easy due to the introduction of Global Positioning System (GPS). But how many of us actually know how navigation was done in the past? In this report, we will cover in great details of what exactly stars are and how they were formed. This is because stars were a form of navigation aid and they were used extensively in the past to determine the distance and location of people. Furthermore, we will also explore the theory behind celestial navigation and many terminologies will be introduced along the way to allow readers to grasp the whole concept. This report also discusses the evolution of celestial navigation from way back in the ancient time to the present time. One of the most commonly used celestial navigation is the sextant. As such, we have dedicated a section on explaining how the sextant is used. As celestial navigation has a long history and has helped people to navigate successfully, we will also talk about the economics, history and geography of celestial navigation. In this section, we will look at how the world has benefited from seafaring as well as some negative implications to the countries. We hope that readers, after reading this report, will have a better understanding of celestial navigation and appreciate the great discoveries of human mankind.


1. AN INTRODUCTION TO STARS Our planet Earth is part of the Milky Way Galaxy, which is home to many generations of stars. Stars have begun to form even before the first galaxies and there is growing evidence that stars had played an important part in the formation of our universe. One of the most important stars is, obviously, the Sun, which is the nearest star to our planet and is the main source of energy necessary to sustain life on Earth. Furthermore, since ancient times, stars have played a very important role as a navigational guide. Before one can proceed to understand the concepts behind celestial or stellar navigation, one should first be familiar with these heavenly bodies called stars itself. This introduction attempts to answer these questions: What are stars and how are they formed?

Beehive Star Cluster

Scientifically, stars are defined as self-gravitating spheres of plasma in hydrostatic equilibrium, which generate their own energy through the exothermic process of nuclear fusion, specifically by the fusion of hydrogen into helium under conditions of enormous temperature and density. Stars are not spread uniformly across the universe but are typically grouped together in galaxies. The majority of stars are gravitationally bound to other stars to form binary stars while larger groups of stars are known as star clusters. A typical galaxy contains hundreds of billions of stars. Astronomers estimate that there are at least 70 sextillion (7×1022) stars in the known universe. That number is 230 billion times as much as the 300 billion stars in our own Milky Way Galaxy. Many stars are estimated to be between 1 billion to 10 billion years old; some stars are even estimated to be about 13.7 billion years old. Stars range in size from the tiny neutron stars to supergiants like the North Star, also known as Polaris.


The Sun itself has the mass of 333,000 Earths. Stars range in mass from approximately 0.08 times to 100 times the mass of the Sun. The mass of a star determines the rate of energy production, which is the thermonuclear fusion mentioned above, in the star’s core. The rate of energy generation, in turn, uniquely determines the star’s total luminosity. Luminosity is the amount of energy emitted in a second. To calculate a star’s luminosity, the apparent brightness of the star (which is the star’s luminosity from Earth) is measured and then multiplied by the distance of the star from Earth. Stars have different absolute luminosities and the brightest stars in the sky are not necessarily the closest ones. The nearest stars make up what is called a solar neighbourhood (shown below) and are mostly small dim stars. These stars are difficult to see at great distances. On the other hand, the twenty brightest stars are mostly supergiant stars which are rare but very bright.

Solar neighbourhood Stars are made of the same chemical elements as found in the Earth, though not in the same proportions; the chemical compositions are found from the stars' spectra. Most stars are made almost entirely of hydrogen (about 90% by number of atoms) and helium (about 10%), elements that are relatively rare on our planet. About 0.1% of a star, which is leftover, consists of all the other elements found in nature. Of these, oxygen usually dominates, followed by carbon, neon, and nitrogen. Of the metals, iron usually dominates. Nevertheless, there is only one atom of oxygen in the Sun for every 1200 hydrogen atoms and only one of iron for every 32 oxygen atoms. However, within this 0.1% proportion, the proportion of the numbers of atoms in the Sun is rather similar to what we find in the Earth's crust. Other stars can deviate considerably, depending on their states of aging or their position in the Galaxy.


All stars follow a basic series of steps in its lifetime, namely from gas cloud to main sequence followed by red giant, then planetary nebula or supernova and lastly remnant. How long a star lasts at each stage and whether or not a planetary nebula forms or a supernova occurs as well as the type of remnant which will form depends on the initial mass of the star. Basically, the above-mentioned series of stages in which a star undergoes changes during its lifetime is called the stellar evolution. The stellar evolution begins with a giant molecular cloud (GMC) which is also known as the stellar nursery. Most of the empty space inside a galaxy typically contains around 0.1 to 1 particle per cm³, however the typical density of a GMC is usually a million particles per cm³. As a GMC orbits the galaxy, one of several events might occur to cause its gravitational collapse. GMCs may either collide with each other or pass through dense regions of spiral arms. Spiral arms are regions of stars which extend from the centre of spiral and barred spiral galaxies. Sometimes, nearby supernova explosions can also trigger the gravitational collapse of a GMC by sending shocked matter into the GMC at very high speeds. Besides that, galactic collisions can cause massive bursts of star formation due to the compression and agitation, by the collision, of gas clouds in each galaxy. A collapsing GMC fragments as it collapses and breaks into smaller and smaller chunks. Fragment with masses of less than about 50 solar masses are able to form into stars. In these fragments, the gas is heated as it collapses because of the release of gravitational potential energy. The gas cloud then becomes a protostar as it forms into a spherical rotating object. This initial stage of the stellar evolution occurs deep inside dense clouds of gas and dust. These star-forming cocoons can be seen in silhouette against bright emission from surrounding gas and are called Bok globules.

NGC 604, a giant star-forming region in the Triangulum Galaxy Very small protostars never reach temperatures high enough for nuclear fusion to begin; these are brown dwarfs of less than 0.1 solar mass. Brown dwarfs are sub-stellar objects which do not fuse hydrogen into helium in their cores and die away slowly, cooling gradually over the hundreds of millions of years. On the other hand, the central temperature in the more massive protostars will eventually reach 10 megakelvins, at which point hydrogen begins fusing into helium at its core. The star then begins to shine. The onset of nuclear fusion establishes a hydrostatic equilibrium in which energy is released by the core prevents further gravitational collapse; hence the star exists in a stable state.


Brown dwarfs throughout the Orion Nebula’s Trapezium cluster taken by a near-infrared camera in NASA’s

Hubble Space Telescope. A star settles down to spend 90% of its lifetime in the stage known as the main sequence. The main sequence is a description of stars based on their absolute magnitude and spectral type. Stars initially begin their lives near other stars in a cluster. After a few orbits around the galactic centre, gravitational tugs from other stars in the galaxy cause the stars in the cluster to wander away from their cluster and live their lives along or with perhaps one or two companions. The gas and dust around the stars may be residual material from their formation or simply interstellar clouds the cluster is passing through. All stars are different in terms of size, colour and brightness as mentioned in the earlier paragraphs. These characteristics differ due to the stars’ differing mass. Small cool red dwarfs burn hydrogen slowly and may remain in the main sequence stage for hundreds of billions of years while massive hot supergiants will leave the main sequence stage after just a few million years. A mid-sized star like the Sun will remain for about 10 billion years. A star remains at a given spectral type during the entire main sequence; the main sequence is not an evolutionary stage. Only if a star has a very close companion of which there is transfer of gas between the stars in the system that a change may occur. Once a star has expended most of its hydrogen at its core then it will move off the main sequence.


Once the core’s ready supply of hydrogen is depleted, the nuclear processes within will cease, all the hydrogen will be converted into helium and the outer layers of the star begin to collapse inward on the core. This inward collapse is due to the lack of outward pressure generated by the core’s nuclear reactions to counteract the force of gravity. As the outer layers collapse, the helium compresses and heats up. Eventually, the layer just outside the core, called the shell layer, gets hot and dense enough for fusion to start. The fusion in the shell layer, which is called shell burning, is very rapid because the shell layer is still compressing and increasing in temperature. The luminosity of the star then increases from its main sequence value. The gas envelope surrounding the core puffs outward under the action of the extra outward pressure. As the star begins to expand, it becomes a subgiant and subsequently a red giant. The helium burning phase lasts for a few million years.

An image of the M10 globular cluster taken by the Hubble Space Telescope. The cluster is known for its large number of red giants.

An image of a red giant star taken by the Chandra Space Telescope


Once a mid-size star (between 0.4 – 3.4 solar masses) has reached the red giant phase, its outer layers will continue to expand. The core will contract inwards and heat up, and when its temperature reaches 100 million Kelvin, the helium nuclei begins to fuse into carbon and oxygen. The resumption of fusion reactions stops the core’s contraction. Helium-burning soon forms an inert core of carbon and oxygen, with a helium-burning shell surrounding it. Helium-burning reactions are very sensitive to temperature leading to great instability; huge pulsations build up which eventually give the outer layers of the star enough kinetic energy to be ejected as a planetary nebula. The core of the star remains in the centre of the nebula and will cool down to become a small but dense white dwarf.

Planetary nebula NGC 7009, observed by the Hubble Space Telescope


The planetary nebula NGC 2440 containing a new white dwarf

White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy of the star’s electrons. The electrons prevent further collapse of the core. With no fuel left to burn, the star radiates its remaining heat into space for millions of years. In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarf stars to exist.

On the other hand, rare high-mass stars (more than 5.0 solar masses) will go the explosive supernova route. When a massive star’s iron core implodes, the protons and electrons will fuse to form neutrons and neutrinos while the core becomes a stiff neutron star. The inward collapse of the outer layers hit the core and heat up to billions of degrees from the impact. The huge number of neutrinos produced as a result when the core collapses interact with the gas in outer layers, helping to heat it up. During the supernova outburst, elements heavier than iron are produced while free neutrons produced during the explosion rapidly combine with heavy nuclei to produce heavier nuclei such as gold and uranium. The superheated gas is blasted into space carrying a lot of the heavy elements produced in the stellar nucleosynthesis process. This explosion is a supernova.

The Crab Nebula, the shattered remnants of a star which exploded as a supernova almost 1000 years ago.


If the core has a mass of 1.4 – 3.0 solar masses, the neutrons will bump up against each other to form a degenerate gas in a neutron star. The neutrons prevent further collapse of the core. Nothing can prevent the higher mass cores (greater than 3.0 solar masses) from collapsing to a point. On the way to total collapse, it may momentarily create a neutron star and the resulting supernova rebound explosion. It is widely believed that not all supernovae form neutron stars. If the stellar mass is high enough, the neutrons themselves will be crushed and the star will collapse and become a black hole.

There are different classifications of stars ranging from type W which are very large and bright, to M which is often just large enough to start ignition of the hydrogen. Some of the more common classifications are O, B, A, F, G, K, M, and can perhaps be more easily remembered using the mnemonic "Oh, Be A Fine Girl, Kiss Me" invented by Annie Jump Cannon (1863-1941). Each letter has 9 sub-classifications. Our Sun is a G2, which is very near the middle in terms of quantities observed. Most stars fall into the main sequence.

Below is a table of classification of stars according to spectra (the elements which they absorb) and temperature:

STAR TYPE

COLOUR APPROXIMATE SURFACE TEMPERATURE

AVERAGE MASS (THE SUN=1)

AVERAGE RADIUS (THE SUN=1)

AVERAGE LUMINOSITY (THE SUN=1)

MAIN CHARACTERISTICS

O Blue > 25000 K 60 15 1 400 000 Singly ionized helium lines (H I) either in emission or absorption. Strong UV continuum.

B Blue 11000-25000 K 18 7 20000 Neutral helium lines (H II) in absorption.

A Blue 7500-11000 K 3.2 2.5 80 Hydrogen (H) lines strongest for A0 stars, decreasing for other A's.

F Blue to White

6000-7500 K 1.7 1.3 6 Ca II absorption. Metallic lines become noticeable.

G White to Yellow

5000-6000 K 1.1 1.1 1.2 Absorption lines of neutral metallic atoms and ions

K Orange to Red

3500-5000 K 0.8 0.9 0.4 Metallic lines, some blue continuum.

M Red < 3500 K 0.3 0.4 0.04 Some molecular bands of titanium oxide.

Stars can also be classified according to size by dividing them into main sequence stars, giant and supergiant stars, faint and virtually dead stars and variable stars.

Under the main sequence, there are 2 types of stars namely the yellow dwarf and red dwarf. In general, dwarf stars are relatively small, up to 20 times larger than the Sun and up 20 000 times brighter. In addition to being small, red dwarf stars are cool, very faint and have surface temperatures of less than 4000K. Red dwarf stars are the most common type of stars. An example of a red dwarf is the star Proxima Centauri. The Sun, on the other hand, is a yellow dwarf star.

Meanwhile, the giant and supergiant group consists of red giant stars, blue giants and supergiants. A red giant is a relatively old star, which has become cooler (surface temperature is under 6500K), with a diameter about 100 times bigger than it originally was and is frequently orange in color. A blue giant star is a huge, very hot blue star which burns helium and falls under the post-main sequence stage. The third type of stars in this group is the supergiant which is the


largest known type of star and can rarely be found. When supergiant stars die, they undergo a supernova explosion and become black holes.

Besides that, under the faint and virtually dead stars group, there are four other sub-groups namely white dwarfs, brown dwarfs, neutron stars and pulsars. A white dwarf is a small, very dense and hot star which is made mostly of carbon. As mentioned in the earlier paragraphs, the faint-looking white dwarf is what that remains after a red giant star loses its outer layers. The white dwarf will eventually lose its heat to become a cold, dark black dwarf. The neutron star, however, is a very small, super-dense star composed of mostly tightly-packed neutrons with a thin atmosphere of hydrogen. A pulsar is a rapidly spinning neutron star that emits energy in pulses while brown dwarfs are sub-stellar objects which does not have enough mass to ignite any nuclear fusion in its core.

The last group of stars which can be observed in the sky is known as variable stars; stars that vary in luminosity. There are two types of variable stars namely the Cepheid variables and the Mira variables. The Cepheid variables are stars that regularly pulsate in size and change in brightness. As the star increases in size, its brightness decreases; then, the reverse occurs. Cepheid variables may not be permanently variable; the fluctuations may just be an unstable phase the star is undergoing. Polaris and Delta Cephei are examples of Cepheids. A Mira variable star is a variable star whose brightness and size cycle over a very long time period, in the order of many months. Mira variables are pulsating red giants that vary in magnitude as much as a factor of many hundred (by 6 or 8 magnitudes).

Most stars are identified only by catalogue numbers; only a few have names as such. The names are derived from traditional names (mostly from Arabic), Flamsteed designations, or Bayer designations. The only body which has been recognized by the scientific community as having competence to name stars or other celestial bodies is the International Astronomical Union (IAU).


2. INTRODUCTION TO CELESTIAL NAVIGATION

Celestial Navigation is the art and science of navigating by the stars, sun, moon, and planets, and is one of the oldest of human arts. With the rise of radio and electronic means of finding location - especially with the increasingly popular GPS, based on satellite transmissions that can tell us our latitude and longitude within feet - knowledge of celestial navigation has experienced a precipitous decline. Early humans also realized that the fixed pattern of stars, together with to time-keeping, could be used as navigational aids. Before the wide-spread use of compasses and the advent of clocks that could keep time on the oceans, knowledge of how to use the stars and the planets for orientation, a skill or art that we now call Celestial Navigation, was essential for long distance land travels (particularly in the vast desert-like regions along the trade routes in Asia for example, the Silk Route as well as for travel on open waters out of sight of land. Navigation instruments are designed to measure direction and distance, determine speed, measure the depth of water, and observe the elements of the weather. Sometimes various instruments are used simultaneously in order to yield the required information.

Navigation, in its simplest form, means to find your way to a point and back again. For sailors, navigation means guiding a ship through water without the help of road signs. Early sailors navigated in inland rivers and waterways which was simple. When sailors ventured out into the sea, they remained close to the coastline, using towns and the shoreline to mark their journey. A sailor's feel for the sea, the directional guidance of the sun, landmarks, and oral directions framed the earliest navigational aids.

Later, sailors looked to the heaven for a more reliable means of navigation. The development of the compass and the quadrant allowed sailors to move with some certainty on the sea. Using the North Star as a landmark, sailors sighted the star with a quadrant, measured the angle from the horizon and identified the latitude. Once the ship reached the correct latitude, it sailed east or west to reach its destination. Sailors could tell how far they were going in either direction by locating the lines of longitude. Nautical direction was determined by the magnetic needle of a compass. In the days of sail, courses and bearings were given in points around a compass.

In the 20th century navigation became more reliable and sophisticated. During World War II, sailors used different types of radio wave navigation to help planes and ships find their locations, as well as find enemy ships. Today, sailors on most large ships use satellite and computer technology, such as GPS (Global Positioning System), to guide them on the seas.


3. THEORY BEHIND CELESTIAL NAVIGATION Before going into the basic mathematics of celestial navigation, an understanding of the celestial sphere is necessary. Here, we will look at some of the astronomical terms commonly used and the fundamental concept in celestial navigation. CELESTIAL SPHERE To an observer in the Earth, the sky has the appearance of an inverted bowl, so that the stars and other heavenly bodies, irrespective of their distance from the Earth, appear to be situated on the inside of a sphere of immense radius described about the Earth as centre. This is called the celestial sphere. Figure 1 illustrates the sky as a great, hollow, sphere surrounding the Earth. However, it should be noted that the figure is not proportionate and the celestial sphere is in fact infinitely huge.

CELESTIAL EQUATOR This is the great circle where the plane of Earth’s equator, if extended, would touch the celestial sphere.

South Celestial Pole

North Celestial Pole

Axis of Rotation Celestial

Equator

Figure 1


CELESTIAL POLES They are the two points at which the Earth’s axis of rotation, if extended, would intersect the celestial sphere. The North and South celestial poles are the points in the sky directly above the geographical North and South poles, respectively.

OBSERVER’S ZENITH This is the point straight overhead on the celestial sphere for any observer. It is where a straight line from the Earth’s centre passing through the observer’s position cuts the celestial sphere. In figure 2, we take the observer’s point of view and put his zenith, Z, at the top, where O is the observer’s geographical position. CELESTIAL HORIZON This is the arc on the celestial sphere, where every point of which is 90˚ from the observer’s zenith. OBSERVER’S MERIDIAN It is the semi-great circle passing through the north celestial pole, the observer's zenith and the south celestial pole. The north and south points, N and S in figure 2, are the points at which this meridian cuts the celestial horizon. The north point being the one nearer the North Pole. The observer’s meridian is also known as the local meridian.

Figure 2

O

Z

W

Celestial Horizon S

N

E

Observer’sMeridian


HOUR CIRCLE It is the great circle passing through the celestial poles, perpendicular to the celestial equator. COORDINATE SYSTEMS In positional astronomy, the 2 main coordinate systems are (1) the horizon and local meridian, and (2) the celestial equator and local meridian. These values essential for drawing of the position line can easily be obtained with a sextant (altitude), or the Nautical Almanac (azimuth, declination, local hour angle). (1) THE HORIZON AND LOCAL MERIDIAN ALTITUDE

This is the angular distance of the body above the celestial horizon, measured along the vertical circle through the body and the observer’s zenith.

AZIMUTH

This is the angle at the zenith between the observer’s meridian and the vertical circle through the heavenly body, and it is measured eastward.

(2) THE CELESTIAL EQUATOR AND LOCAL MERIDIAN

DECLINATION It is the angular distance north(+) or south(-) of the celestial equator to some object , measured along an hour circle passing through the object.

RIGHT ASCENSION (RA)

It is the angular distance along the celestial equator eastward from the vernal equinox, or the First point of Aries, to the hour circle of the heavenly body.

SIDEREAL HOUR ANGLE (SHA)

The Nautical Almanac gives the angular distance, measured westward, between the vernal equinox and the star instead of the right ascension. Thus, it is also given by 360˚ - RA.

GREENWICH HOUR ANGLE (GHA)

It is the angle, measured westward, between the observer’s meridian and the hour circle of the heavenly body if the observer were to be on the meridian of Greenwich. Thus,

GHA body = GHA Aries + SHA body

LOCAL HOUR ANGLE* (LHA)

The angle, measured westward, between the observer’s meridian and the hour circle of the heavenly body. It depends both on time and the observer’s position. Thus,


LHA body = GHA Aries ± Longitude + SHA body

Note: Longitude is added if observer is to the east of Greenwich meridian and subtracted if he is to the west.

3.1 SPHERICAL TRIANGLES Now that we have understood the concept of the celestial sphere and the coordinates systems used in celestial navigation, we look into the basic mathematics of using spherical triangles to find our position. Why spherical triangles? This is because in order to work with the information we can obtain (altitude) and the information we have or can calculate (LHA, azimuth, declination), we form a spherical triangle PZX on the celestial sphere as shown,

with: P – celestial pole X – heavenly body with declination δ Z – observer’s zenith with latitude Ø Angle ZPX - LHA Angle PZX - azimuth a – zenith distance b – co-declination of the heavenly body c – co-latitude of the observer at Z In spherical trigonometry, the relation between the angles and sides of the spherical triangle PZX above may be written as: cos a = cos b cos c + sin b sin c cos P & (sin a / sin P) = (sin b / sin Z) = (sin c / sin X) sine formula

δ Ø

a Zd

b c

P

ZX

Figure 3


We can write, cos a = sin (90 – a) = sin (alt) cos b = sin δ cos c = cos (90- Ø) = sin Ø Therefore, our fundamental relation becomes, sin (alt) = sin δ sin Ø + cos δ cos Ø cos (LHA) Using the sine formula, sin (Az) = ( sin (LHA) cos δ ) / cos (alt)


3.2 FINDING POSITION Finally, we look at the steps taken to plot our position on a chart: 1. Find the altitude of a selected star by a sextant and note the exact GMT. 2. Apply the necessary corrections to the sextant reading H. 3. Make an estimate of the observer’s own position. Latitude Ø, Longitude L. 4. From the Nautical Almanac, find the star’s LHA using the estimated longitude.

LHA body = GHA Aries (at time of observation) ± Longitude + SHA body 5. Look up the star’s declination δ. 6. Calculate what the altitude of the star Hc would be if it were actually observed from the

estimated position. Using,

sin Hc = sin Ø sin δ + cos Ø cos δ cos (LHA) 7. Intercept = H – Hc

This shows how much nearer, or further away from the star the observer is as compared to the estimated position.

8. The direction is the azimuth obtained from,

sin (Az) = ( sin (LHA) cos δ ) / cos (alt) 9. Draw a line of bearing on the chart through the estimated position towards the star, i.e. with

azimuth found in 7. 10. Draw a position line perpendicular to that in 8 at a distance H – Hc away from the estimated

position. 11. Repeat the steps for another 1 or 2 other stars and the actual position can be found by

intersecting the lines.


OBTAINING A POSITION LINE MARCQ ST HILAIRE (or INTERCEPT) METHOD This method is a comparison between the ship’s known distance from a geographical position and the calculated distance of some arbitrary position from the same geographical position. First distance: True Zenith Distance (TZD) Second distance: Calculated Zenith Distance (CZD) Difference: Intercept Line of bearing is a line drawn from an estimated position or a DR in the direction of the heavenly body. With this information, a position line can be drawn, as shown in Fig. 1, with the position line perpendicular to the line of bearing at the intercept distance away from the estimated position or the DR.

Line of Bearing

DR

CZD

TZD GP

Figure 3

Intercept


A position line is one that connects all the possible positions of a ship or aircraft, as determined by a single observation. A fix can thus be obtained by intersecting two or more positioning lines. Often, the position lines do not intersect exactly at one point. They form a small triangle, or a ‘cock-hat’, and the centre of a circle drawn in the cock-hat is where the fix is as shown in Fig. 2.

·

Fix is in the centre of the circle Figure 4


4. EVOLUTION OF CELESTIAL NAVIGATION Now that we have introduced to you what stars are, the theory behind celestial navigation as well as some important terminologies, which are the building blocks of understanding celestial navigation, we will know explore the different types of celestial navigation used by people in the past.

The navigator who was planning to sail out of sight of land would simply measure the altitude of Polaris as he left homeport, in today’s terms measuring the latitude of home port. To return after a long voyage, he needed only to sail north or south, as appropriate, to bring Polaris to the altitude of home port, then turn left or right as appropriate and "sail down the latitude," keeping Polaris at a constant angle.

The earliest attempt at navigation was undoubtedly simple coastal piloting. Mariners would venture no further than the sight of land. The limitations of such navigation held trade and exploration to a minimum for thousands of years, while open water sailing was reserved for the incredibly brave or foolhardy.

The earliest practical form of celestial navigation was probably what was known as "Running Down The Line." When a ship departed homeport the navigator knew its latitude. At sea, the navigator could also ascertain his vessel's latitude by observing the height of Polaris the North Star. When it was time to return to port, the vessel was steered on a northerly or southerly track until the altitude of Polaris matched that of the homeport. Then course was altered east or west to "sail down the line" of latitude. Improving on the “Running Down The Line” celestial navigation was the kamal which was the next form of celestial navigation. The subsequent pages will introduce to you the other various forms of celestial navigation that had evolved throughout the century ending with the latest invention the Global Positioning System (GPS).


Description In perfecting the method of “Running Down the Line, the Arabs developed a

very simple device called a Kamal which, by means of a knotted cord, indicating the height of the pole star at various latitudes. However, the obvious implications of having to take an indirect course home stirred navigators and astronomers to find a better way.

How it works The kamal consists of a rectangular wooden card about 2 inches by 1 inch, to

which a string with several equally spaced knots is attached through a hole in the middle of the card. The kamal is used by placing one end of the string in the teeth while the other end is held away from the body roughly parallel to the ground. The card is then moved along the string, positioned so the lower edge is even with the horizon, and the upper edge is occluding a target star, typically Polaris because its angle to the horizon does not change with longitude or time. The angle can then be measured by counting the number of knots from the teeth to the card, or a particular knot can be tied into the string if travelling to known latitude.

The knots were typically tied to measure angles of one finger-width. When held at arm's length, the width of a finger measures an angle that remains fairly similar from person to person. This was widely used (and still is today) for rough angle measurements, an angle known as issabah in Arabic, or a chih in Chinese.

Limitation Due to the limited width of the card, the kamal was only really useful for measuring Polaris in equatorial latitudes. This explains why it was not common in Europe because for the higher-latitude regions. Thus it needed somewhat more complex devices and this led to the development of the Astrolabe

Kamal Unknown (Ancient Time)


Description The first part of its name comes from the same Greek word that gave us

"astronomy" - aster, or star - and the second derives from a Greek word meaning take, grasp, or determine. So the name can be translated as "star-finder" or "star-taker." The astrolabe is an instrument that provides a picture of how the sky looks at the observer's latitude and time. It was also the first of the versatile scientific instruments used by navigators.

How it works The astrolabe was invented by the Arabs and it’s about 3 and one-half inches in

diameter. The astrolabe was a highly artistic and multi-purpose device that had a planeishpere on the reverse side made up of an ornamental fretwork plate called the rete, engraved with the names of important stars. Each star had a fixed pointer marking its relative position on the celestial sphere. The rete turned on the mater, a removable holding plate inscribed with elliptical lines showing declination and azimuthal coordinates.

Different plates were inserted at every other degree of latitude and the rete was rotated to the day and hour of observation so that the navigator would know where to look for the key stars.

Three men were required when taking sights. The first would brace his back against the mainmast while holding the instrument aloft. Another would sight the star and the last would read the angular height from the degree scale.

The astrolabe was popular for more than 200 years because it was reliable and easy to use under the frequently adverse conditions aboard ship.

Astrolabe 10th Century


Limitation Despite its popularity, the astrolabe needed three men to take sight and gave a very low precision. It was used to determine latitude by the sight of Polaris or the meridian passage of the sun. Thus, the quadrant was an improvement of the Astrolabe.


Description The astronomer's beautiful, intricate and expensive astrolabe was the

grandfather of the much simpler, easy to use mariner's quadrant and astrolabe. The mariner’s quadrant—a quarter of a circle made of wood or brass--came into widespread use for navigation around 1450, though its use can be traced back at least to the 1200s.

How it works The mariner’s quadrant was a major conceptual step forward in seagoing

celestial navigation. Like the knots-in-a string method of the Arab kamal, the quadrant provided a quantitative measure, in degrees, of the altitude of Polaris or the sun, and related this number to a geographic position—the latitude--on the earth’s surface.

Limitation The quadrant had two major limitations. Firstly, on a windy, rolling deck, it was hard to keep it exactly vertical in the plane of a heavenly body. Secondly, it was simply impossible to keep the wind from blowing the plumb bob off line.

Quadrant 11th Century


Description The next step of the evolution in the celestial navigation was the cross-staff but it was hardly any improvement over and above the astrolabe and quadrant. The cross-staff consisted of a long staff with a perpendicular vane which slides back and forth upon it. The staff is marked with graduated measurements -- calculated by trigonometry and the angles can then be measured by holding it so the ends of the vane are level with the points to be measured.

How it works Originally the staff had only one vane and was very long. Therefore, it was very

difficult to manage on a rocking ship. The mariners added more vanes in order to reduce the length of the staff to about 2 1/2 feet. The long, medium and short vanes on the staff were about 15, 10 and 6 inches in length. The staff was then calibrated directly into degrees for use on board a ship.

For the most part, the cross-staff was used to find the latitude by measuring the altitude of the Pole Star above the horizon. This, of course, was useless in cloudy weather. It could also be used to determine the altitude of the sun, but this required the observer to look directly into the blinding sun.

Cross-Staff 14th Century


Limitation For the cross-staff, although it involved only one person, he had to align simultaneously and hence viewed simultaneously on one end of the cross-staff with the horizon and the other with the sun or other celestial body. Thus, this proved highly impractical as it was prone to error from ocular parallax

Another problem was that the observer had to stare directly at the sun which might cause blindness. He could wait for cloudy day but the horizon might be obscured.

In addition, due to the restriction of the angles between two objects that the human eyes can see at the same time, the angle that can be measured by the Cross-staff is restricted from around 20° to 60°. In addition, the smallest graduation on the staff is around 3°, therefore it is impossible to use the Cross-staff in low latitude regions.

Due to these problems, the back-staff was developed in the late 16th Century

Just For Fun (1)

1) Have you heard of the phrase “shooting the stars,”? Do you know where it came from?

Well, bet you didn’t know what it was assorted with it celestial navigation. It actually came from the practice of holding a cross-staff up to the user's eye with one hand, with the transom grasped in the other hand so that the person looks like an archer taking aim at the star.

2) Have you ever wondered why pirates had the eye-patch on their left eye?

Hint: Defect of one of the celestial navigations. Do you know which one?

Yes! It is the cross-staff. For the cross-staff, navigators may have to look directly into the sun and over time, eyes are damaged. Some people say this is how pirates came to wear their famous black patches – they went blind staring at the sun!


Description The Davis Quadrant was the successor of the cross-staff and the predecessor of

the Octant.

The advantage of this instrument over the cross staff is that an observer doesn't need to observe the sun with the bare eye

In about 1594 John Davis, an English captain, developed a simple back-staff which eliminated the problems of parallax and the glare of sun sights as well as the problems involved in sighting two widely separated objects simultaneously. Davis' back staff was intended to be an improvement on the mariners' quadrants, astrolabes and cross-staves. The Davis back-staff consisted of a graduated staff, a half-cross in the shape of an arc of a circle on the radius of the staff with a fixed vane, and a brass horizon vane with a slit in it at the fore-end of the staff.

How it works The observer placed the staff on his shoulder and stood with his back to the sun.

With the horizon vane lined up with the horizon, he slid the half-cross back and forth until the shadow of its vane fell across the slit in the bottom vane while the horizon was visible through the slit. By doing this the observer was able to sight both the sun and the horizon while his back was towards the sun.

The back-staff immediately gained popularity, and during the seventeenth century it became indispensable to English as well as foreign sailors.

The back-staff eliminated the disadvantages of the cross-staff by allowing the observer to take a sight without looking into the sun. The instrument also simplified the sighting process by allowing the observer to view both the horizon and the shadow of the sun on the horizon vane simultaneously.

Back-Staff 16th Century


Limitation A disadvantage of the back-staff was that it could not be used easily for star

sights. Despite this limitation, the back-staff remained popular between the years 1600 and 1800. It was the first navigational instrument of any kind produced in America.


Description In 1731, John Hadley, an English astronomer, mathematician, and physicist

invented the octant which was the first double reflecting instrument. He added to the simple quadrant, optics, and a reflecting mirror to bring a body in the heavens into coincidence with the horizon, thereby turning the quadrant into a reflecting telescope. At nearly the same time, in Philadelphia, Thomas Godfrey arrived at the same solution. This instrument, the octant, is the predecessor of out present-day sextant.

How it works An octant, as mentioned above, is the successor of the Davis Quadrant. It is

used to obtain measurements of the angular height of a celestial body above the horizon and this is not difficult to achieve, as compared to the early development of the cross-staff, back-staff, and marine astrolabe.

Basically, double reflecting instruments use two mirrors to bring a celestial body’s reflections down level with the horizon. An index mirror mounted on a pivoting index arm reflects the image of a celestial body onto a fixed horizon mirror. Half of the vertically split horizon mirror is silvered to bounce the reflection from the index mirror back to the eye; the other half is clear so the horizon can be sighted. A navigator rotates the index arm until the reflection in the horizon mirror appears to touch or split the horizon, then reads the angular altitude of the body off the arc on the instrumental’s limb. Because the horizon and the reflection are on the same line, ocular parallax – the problem that occurred on cross-staff – is eliminated.

Octant Mid-18th Century


Limitation The real problem lies in being able to achieve this with great accuracy, and under the difficult conditions of being at sea on a small boat.


Description The sextant like the one above is a tool developed in the year 1735. A sextant is

kind of like a fancy astrolabe. It helps navigators figure out the angles between the sun and other heavenly bodies and the horizon then calculate their latitude and their position.

How it works An instrument for determining the angle between the horizon and a celestial

body such as the Sun, the Moon, or a star, used in celestial navigation to determine latitude and longitude. The device consists of an arc of a circle, marked off in degrees, and a movable radial arm pivoted at the centre of the circle. A telescope, mounted rigidly to the framework, is lined up with the horizon. The radial arm, on which a mirror is mounted, is moved until the star is reflected into a half-silvered mirror in line with the telescope and appears, through the telescope, to coincide with the horizon. The angular distance of the star above the horizon is then read from the graduated arc of the sextant. From this angle and the exact time of day as registered by a chronometer, the latitude can be determined (within a few hundred metres) by means of published tables. The name comes from the Latin sextus, or "one-sixth," for the sextant's arc spans 60, or one-sixth of a circle. Octants, with 45 arcs, were first used to calculate latitude. Sextants were first developed with wider arcs for calculating longitude from lunar observations, and they replaced octants by the second half of the 18th century.

Limitation Obtaining precise results using the sextant is a complex process, requiring a

steady hand, access to the nautical almanac plus calculation know how together with a fair knowledge of general astronomy in order to obtain accurate results.

Sextant 18th Century


Starship Description Global Positioning System (GPS) is a space-based navigation system, with 24

satellites, that provides accurate, three-dimensional position, velocity, and time, 24 hours a day, everywhere in the world, and in all weather conditions. Because the user does not communicate to the satellite, GPS serves an unlimited number of users at any given time.

The system is maintained by the United States Department of Defense, the Navstar. GPS began in 1973 to reduce the proliferation of navigational aids. By creating a system that overcame the limitations of many existing navigation systems, GPS became attractive to a broad spectrum of users commercial and private. Since the earliest satellites, it has successfully proven itself in navigation applications. The greatest thing is that its capabilities are obtainable in small, inexpensive equipment.

How it works GPS satellites carry atomic clocks that measure time to a high degree of

accuracy. The time information is placed in the codes broadcast by the satellite so that a receiver can continuously determine the time the signal was broadcast. The signal contains data that a receiver uses to compute the locations of the satellites and to make other adjustments needed for accurate positioning. The receiver uses the time difference between the time of signal reception and the broadcast time to compute the range to the satellite. The receiver must account for propagation delays caused by the ionosphere and the troposphere. With three ranges to three satellites and knowing the location of the satellite when the signal was sent, the receiver can compute its three-dimensional position.

To compute ranges directly, the user must have an atomic clock synchronized to the global positioning system. By taking a measurement from an additional satellite, the receiver avoids the need for an atomic clock. The result is that the receiver uses four satellites to compute latitude, longitude, altitude, and time.

On STARSHIP a variety of different navigational aids are used. The most predominant being the GPS and a computer chart system. In addition, two radars and sonar are used too.

Although there have been major changes in navigation over the past century the fundamentals have remained the same. Navigation by practice is simply

Global Positioning System (GPS) 20th Century (1973)


getting the vessel from one point to the next be it by stars or satellites. With all these different technologies we can only expect and hope for safe passage at sea.


Timeline of the Evolution of Celestial Navigation

Ancient Time

o Costal piloting o Running Down The line o Kamal

Works through means of a knotted cord, indicating the height of the pole star at various latitudes.

10th Century

o Astrolabe

The astrolabe is an instrument that provides a picture of how the sky looks at the observer's latitude and time.

11th Century

o Quadrant

It provides a quantitative measure, in degrees, of the altitude of Polaris or the sun, and related this number to a geographic position - the latitude - on the earth’s surface.

14th Century

o Cross-Staff

It is used to find the latitude by measuring the altitude of the Pole Star above the horizon

16th Century

o Back-Staff

It was invented to eliminate the problems of parallax and the glare of sun sights as well as the problems involved in sighting two widely separated objects simultaneously

18th Century

o Octant

It is used to obtain measurements of the angular height of a celestial body above the horizon

18h Century

o Sextant

It helps navigators figure out the angles between the sun and other heavenly bodies and the horizon then calculate their latitude and their position.

20h Century

o Global Positioning System

A space-based navigation system, with 24 satellites, that provides accurate three-dimensional position, velocity, and time, 24 hours a day, everywhere in the world, and in all weather conditions.


5. SEXTANT

From the previous section, we can see that the GPS holds numerous advantages over its predecessors rendering them almost obsolete. However, many traditional navigators have refused to fully adopt this new technology and continue to depend on their trusty sextants and their nautical almanac. Their claim is that nothing beats the feeling of satisfaction of reading a star, and making the calculations to determine where you are. Furthermore, the modern day sextant provides a dependable backup in the case of GPS equipment failure or lack of power. With that, so let us take a more in-depth look at our trustworthy workhouse, the sextant.

Evolution of the sextant In 1731, John Hadley, a London instrument maker and mathematician presented a paper to fellow members of the Royal Society describing the use of a double reflecting device. This discovery was almost simultaneously repeated in America by Thomas Godfrey, an associate of Benjamin Frankin. Hadley' octant at that time period was undoubtedly a major advancement over all other previous designs and is still the basic design of the modern sextant. An octant measures angles up to 90 degrees. However, greater range is needed for lunar distance observations. In 1759, John Bird came up with the first sextant by simply enlarging Hadley's octant, an eighth of a circle, to a sixth of a circle, that could measure up to 120 degrees. The purpose of the device Use the principles of light reflection; a celestial body’s reflection is brought down level with the horizontal. The index mirror (A) mounted on the pivoting index arm reflects the image of a celestial body onto a fixed horizontal mirror (B). This fixed horizontal mirror is half silvered so as to be able to allow the horizon to be sighted as well as to bounce the reflection from the index mirror into the eye. The altitude of the celestial body then can be read from the vernier scale. Components of the sextant A Sextant consists of a frame together with an arc (C), an index arm (D), a fully reflecting index mirror (A), a fixed half silvered horizontal mirror (B), and an eyepiece (E). Modern sextants feature a micrometer drum vernier scale for increased reading accuracy, sunshades for daytime readings, plus a telescope in place of the eyepiece for better clarity.


Principle The angle that the 2 mirrors make with each other, ∠CGB is half that of the altitude of the celestial body ∠ADC. ∴∠2CGB = ∠ADC How do we determine this? Principle 1 - The angle of incident always equals to the angle of reflection. Principle 2 - An exterior angle of a triangle equals to the sum of the two non adjacent interior angles.


Hence from principle 1, ∠a=∠b and ∠c=∠d From principle 2, ∠ABC=∠ADC+∠BCD and ∠EBC=∠BFC+∠BCF ∠a+b = ∠e + ∠c+d ∠b = ∠f + ∠c Rearranging, we get ∠e =∠a+b - ∠c+d and ∠f = ∠b - ∠c Substituting ∠e = ∠2b - ∠2c = 2(∠b - ∠c) = 2∠f Angles ∠f and ∠g are equal because their sides are mutually perpendicular. Hence, ∠e = 2∠g The altitude of the celestial body ∠ADC is twice the angle that the two mirrors make with each other. ∴∠ADC = ∠2CGB This relationship allows the altitude of the celestial body to be easily read off a vernier scale. Types of Sextants There are 2 main types of sextants available on the market today. Namely, traditional and whole horizon. Traditional Sextants feature the half-silvered index mirror as highlighted in previous sections. It divides the field of view into half. On one half (clear glass), you can see the view of the horizon. On the other half (silvered mirror), you can see the celestial body. Whole Horizon Sextants feature a full-view mirror that works by using specially coated optics to split the light spectrum into half. This allows both the horizon and the image of the celestial body to be superimposed on a single surface.


Pros and Cons Beginners will find the whole horizon easier to handle since the superposition of the images makes obtaining readings more intuitive and faster in ideal conditions. However, due to the filtering effect of the coated glass, light transmission through it is reduced. This makes it difficult to locate the horizon in the night and hazy conditions. Thus, whole horizon sextants easy sights easier and hard sights harder. Sextant errors explained Sextants are prone to errors which need to be taken into consideration to ensure accuracy. Index error It is an instrument error, the equivalent to the zero error on a vernier scale. It

occurs when the index and horizon mirrors get slightly out of adjustment. To check for this error, we need to align the actual horizon with the reflected image of the horizon. If index error is present, rather than attempt to adjust the mirrors, it is recommended to apply an index correction to your reading by simply adding or subtracting the index error in order to compensate.

Dip This error is due to the fact that the horizon is not level with the height of the eye

above sea level. This results in a reading larger than it actually is. This effect is known as "The dip of the sea horizon". The correction is always subtracted.

Dip is the correction in minutes of arc

Refraction Refraction refers to the change in direction of a wave due to a change in

velocity in the wave as it passes between mediums of different refractive indexes. This error is the same error as why the sun appears just on the horizon when in reality it has already dipped below the horizon. It is the bending of light rays as it passes through the atmosphere. It makes the reading larger than what it actually is. The correction can either be obtained from the Nautical Almanac, or through the following approximation.

Where the correction is always subtracted and is in minutes of arc. P = Atmospheric pressure in millibars T = Air temperature in degrees Kelvin Altitude is measured in degrees

(refractive index of a material is the factor by which the phase velocity of electromagnetic radiation is slowed relative to vacuum)

metersineyetheofheightDip 753.1=

)028.0)(

10848.4(

267.02

+×

+=Δ −

altitudeTanaltitudeTan

TP


Semi-Diameter When taking readings using the sun or the moon, this correction needs to be taken into account. It is due to the discernible diameter of those two heavenly bodies. Depending on personal preference, the upper or lower edge of the body is made to touch the horizon. This edge is known as the upper or lower limb in technical terms. The table in the Almanac applies to the center of the body. Thus if the lower limb was selected, you need to add half of the diameter of the body to compensate.

Parallax Parallax is the error that occurs as a result of the altitude reading being taken

from the surface of the earth rather than the center of the earth. Since the error has to do with the radius of the earth, it is only applicable for heavenly bodies relatively near to the earth such as our sun, moon and visible planets. This error is published in the Almanac under the name “Horizontal Parallax” or HP.

This error is always added to the altitude reading since the reading obtained at the surface (apparent altitude) will always be lesser than the true altitude obtained from the center of the earth. In addition, we can also see that this error is naturally larger for lower altitudes and is zero for bodies at zenith.


6. CELESTIAL NAVIGATION AND ITS IMPACTS ON HISTORY, GEOGRAPHY AND ECONOMICS

Throughout human history, Navigation has played a major part in the development and the evolution of a civilization. From the early Greeks to the 17th century European nations, great civilizations have recognized the importance of celestial navigation. Its applications have directly and indirectly affected the prosperity and development of nations in terms of wealth, knowledge and power. Wealth, obtained through the gains of trade. Knowledge, through the discovery of new lands and unknown civilizations, and finally power, which is basically the extension of influence of territory - both land and sea. The Phoenicians - Pioneers of Celestial Navigation The Phoenicians and Greeks were the first of the Mediterranean sailors to navigate beyond the sight of land and to sail at night. In fact, the Phoenicians were said to be the best ship builders and seafarers of the ancient world. The Phoenician civilization was characterized a rather innovative and enterprising maritime trading culture that spread right across the Mediterranean during the first millennium BC. They produced primitive charts and practiced a rudimentary form of dead reckoning. They were capable of making observations of the sun and the North Star in order to establish their bearings, and were also able to judge distances from the time needed to traverse that distance. In the centuries following 1200 BC, they were characterized by their remarkable seafaring achievements and have dominated trade by being the major naval power of that region.

Rock carvings of Phoenician Seahorses

Due to their lack of a compass (only invented in China ---yrs later), navigation was dependent upon the Ursa Minor and the North Star. Of which the latter was termed 'The Phoenician Star' by the Greeks. According to the Greek historian Herodotus, the furthest voyage ever undertaken by the Phoenician sailors was the circumnavigation of the African continent, accomplished around 600 BC. The voyage is said to have taken 3 years. The fact that the sun was to their right as they passed the tip of Africa is proof that the journey was made. Herodotus writes (4.42): The Phoenicians took their departure from Egypt by way of the Erythraean sea, and so sailed into the southern ocean. When autumn came, they went ashore, wherever they might happen to be, and having sown a tract of land with corn, waited until the grain was fit to cut. Having reaped it, they again set sail; and thus it came to pass that two whole years went by, and it was


not till the third year that they doubled the Pillars of Hercules, and made good their voyage home. On their return, they declared - I for my part do not believe them, but perhaps others may - that in sailing round Libya they had the sun upon their right hand. In this way was the extent of Libya first discovered. When it comes to ship design, the Phoenician came up with the “round boat", a broad-beamed ship that depended principally on sails rather than oars was revolutionary for its time. This allowed for much larger cargo storage compared to the narrower galleys. This illustrated the advances in seamanship (which is the art of handling a ship) which complemented the large strides in navigational techniques made at that time.

A Phoenician trade ship of about 1500 BC.

A later ship dating to around 850 BC.


The Adventurous Polynesians While the Phoenicians ruled the seas in the Mediterranean, on the other side of the globe, from islands south of the Pacific Ocean, Polynesians were know as the finest seafarers of the vast Pacific, and were making great strides with their own version of navigation. In Greek, poly equals many and nesos refers to islands. Hence, the Polynesians were people who populated large number of islands. Being surrounded by endless seas, the early Polynesians developed a close relationship with the ocean. Over-population on many of these tiny islands of Polynesia was a push factor which led to these oceanic migrations. So the question is, how did the Polynesians manage to populate the Pacific Ocean 2,000 years ago without the use of charts or navigation instruments? The answer, comfort zone navigation. This is essentially navigating by gut feel or intuitive forces. Captain William Bligh (of Mutiny on the Bounty fame), successfully demonstrated this technique some 200 years ago by being able to travel 3,600 miles in an open lifeboat, without the use of navigational equipment, to the Dutch colony, Timor, near Java. Eventually, this race of Seafarers came up with detailed, elaborate maps made out of palm twigs and cowrie shells. These charts denoted everything from the position of islands to the prevailing direction of the swell. Our First Map In second century A.D, an Alexandrian astronomer, Claudius Ptolemy made tremendous strides in the field of Cartography by creating the first world atlas. This served as a reference for a series of 26 regional maps which documented the various parts of the known world. Written at the height of the Roman Empire, it was essentially a long and detailed guide to drawing a map of the entire world. His magnificent works however, failed to significantly impact the Roman Empire at that time as it became supposedly “lost” for over a thousand years. It was only after it was rediscovered in the 15th century, when the Geographia had an impact on the emerging western European mind, contributing to the exploration being conducted out during the time of the Renaissance.


The Ptolemy world map, reconstituted from Ptolemy's Geographia

Oh Great Compass In 2nd Century BCE, the Chinese discovered that a certain type of magnetized metal would always point north when balanced on a fulcrum. By the 1400s, the Chinese were using it as a navigational aid in their voyages. (Think Zheng He, who made seven historical ocean voyages between 1405 and 1433). This invention also contributed to the Chinese Empire’s dominance as a trading empire in the early 15th century. Europeans soon obtained this device thru silk road trading, and by the 1500s, was widely adopted as a navigational aid by the European sailors.

A working model of the early compass.

The spoon is crafted from magnetic loadstone, and the plate is made of bronze. The Age of Discovery 12th and 13th century during the Middle age period in Europe saw many important discoveries, namely the astrolabe and the quadrant by the Arabs. In addition, the invention of mechanical clocks and new ship designs such as the caravel during the period of the Renaissance made possible the Age of Exploration. The origins of the astrolabe come from classical Greece by Appolonius in 225BC. The astrolabe was introduced to the Islamic world in eighth and ninth century through translations of Greek text. The astrolabe moved together with Islam through North Africa into Spain (Andalusia) where it was introduced to European culture through Christian monasteries in northern Spain.


The astrolabe, as seen is previous section, is an ancient astronomical computer for solving problems relating to time and the position of the Sun and stars in the sky. Astrolabes are used at that time to show how the sky looks at a specific place at a given time. This is done by drawing the sky on the face of the astrolabe and marking it such that positions in the sky are easy to find. This allows a great many astronomical problems to be solved in a very visual way. Typical uses of the astrolabe include finding the time during the day or night, finding the time of a celestial event such as sunrise or sunset and as a handy reference of celestial positions. The Age of Exploration Early 15th century saw the dawn of a new age of navel exploration, fuelled by the recent advances in navel and navigation technology. Their motivations included economic incentives as well as religious zeal. Curiosity to explore during the age of the Renaissance was another factor. The age of exploration began with a legendary man known as Prince Henry the navigator. Prince Henry the Navigator (Dom Henrique) was the son of King João of Portugal, born in 1394. He is most famous for the voyages of discovery that he organised and financed, which eventually led to the rounding of Africa and the establishment of sea routes to the Indies. He set up a base at Portugal’s lands end, called Sacred Promontory by Marinus and Ptolomy (from which the name Sagres derives). From there he made his base for sea exploration, making it a centre for cartography, navigation and shipbuilding. There were 6 other explorers who contributed significantly to exploration worldwide. Five of these European explorers were Spanish, namely, Ferdinan Magellan, Vasco da Gama, De Soto, Ponce de Leon, and Christopher Columbus. Sir Frances Drake was an Englishman. The First Explorers Initially the Europeans started their explorations with a geographical picture of the world largely based on Ptolemy’s knowledge brought forward from the ancient world. In the 15th century, advancements in naval knowledge further improved methods of navigation. Mariners relied on charts called "portolans" to assist them on their voyages. Portolan comes from the Italian word portolani, which were medieval pilot books. The portolans contained maps of coastlines, locations of harbors, river mouths, and manmade features visible from the sea. They were a compilation of centuries of seafarer observations. Portuguese chart makers further added the meridian line, a point useful for latitude sailing as well as for navigating solely by compass. A geographic feature could now be located through the use of its distance in degree of latitude from a ship's point of departure.


A 15th century map used by Portuguese navigators

A 16th century invention, “Cross-staff”

A picture of a cross-staff

The Portuguese Cross-staff was invented in the early sixteenth-century as an instrument for measuring the altitude of a heavenly body. It consists of a square shaft and a sliding cross-piece set at right angles to the shaft. The shaft end is held at the observer's eye and the cross-piece positioned to line up with the sun and the horizon. The cross-piece marks a point on the shaft that is referred to in a table of degrees and minutes. This instrument was important as it made it possible for navigators to obtain latitude of the ship through celestial sightings. This was a great improvement in determining the ship’s position and navigation as a whole. Effects of navigation Navigation has played a crucial role in many of events that have taken place throughout history. The first effect was of course, trade. Once upon a time, people thought the world was flat and if anyone ventured past the horizon he would drop down and never been seen again. Thankfully this theory was proven wrong and people starting taking to the seas as a mode of transportation.


Transportation meant two things; transportation of people and transportation of goods. With exploration, those who took to the seas first stumbled upon either inhabited or uninhabited lands. Some places which were discovered had many raw materials that their native countries did not have. Things such as rubber in Malaya (present-day Malaysia) and spices from the Spice Islands (present-day Indonesia). With the ability to navigate the seas, the notion of trade between different countries became feasible. The difference in who benefited most from trading was usually quite obvious. The countries who had at that time the best seafaring ability usually won the battle, getting on the favorable end of trade. This meant the Europeans managed twist the arms of their trading partners, which in this case were usually the Asians, for unfair terms of trade. With navigation, came along the battle for power. As European countries began to see the potential of sea trade, there came a need to protect their investments. The Portuguese started taking newly discovered lands as their colonies and assumed the responsibility of protecting their colonies, mostly using naval ships. But naval aggression did not start from there. The famous Vikings from Sweden were to be the first Europeans who passed the winter in Labrador and New foundland. They populated Greenland, Iceland, the Faroe Islands, the Shetland Islands, Orkney, the Hebrides and the Isle of Man. They founded states in Ireland and in Britain. They conquered Normandy in France and founded a dynasty which lived and ruled far into the Middle Ages. They built merchant towns in Birka (Sweden), Hedeby (Denmark) and Kaupang (Norway). They even founded the first colony in America long before anyone else in Europe even though that there existed land that were far westwards. All this happened during the age of the Vikings back in 793 till 1066. Another major impact of navigation and exploration was that it changed the way people around the world lived. The biggest aspect of this change deals with the exchange of people, plants, animals, ideas, and technology. This is known as the Columbian Exchange, because it started with Columbus. While many aspects of this exchange had positive effects, such as the exchange of foods between Europe and America, there were also negative effects, such as the exchange of diseases between Europe and America.

Columbian Exchange

From Old World to New World From New World to Old World

wheat sugar bananas rice grapes horses pigs cattle sheep chickens smallpox measles typhus

corn potato beans peanuts squash pumpkin tomatoes avocados chili pepper pineapple cocoa tobacco quinine (a medicine for malaria)

In the positive light, navigation by sea opened the doors for people to experience a culture totally different from his native culture. They experienced different types of food, sources of entertainment and even spiritual beliefs. Each society had a different way of life and these seafarers managed to experience it firsthand. As such they could then go on to extract the positive practices and bring them back to their own country to influence the others.


There were some who took this as an opportunity to spread their own beliefs to other “barbaric” countries. “Barbaric” as not being enlightened by their culture or religion. An example of such would be in Japan during the Tokugawa Period where Portuguese and Spanish missionaries followed merchant traders to Japan on missions to educate the Japanese on the ways of Christianity. Unfortunately for a couple of these missionaries there were executed by the Tokugawa in the 16th century for “corrupting the Japanese mind”. Negative effects Unfortunately, this mutual exchange may not all be beneficiary. Diseases were unknowingly brought over to Asian countries by the Europeans. The natives lacked the immunity to European diseases and suffered greatly. Inca and Aztecs faced near total destruction of their cultures either through disease brought by the Europeans, or by colonization. This is why even up to this day there exist quarantine procedures for all visiting ships to a foreign port. At some ports, ships are required to fly the Quebec (Q) flag upon entering the port as an indication that the ship has been cleared of all diseases. Another negative effect of maritime navigation was the problem of exploitation of the weaker countries. Africa faced a diaspora, or forced movement of its people, as slavery became the dominant labor force in the Americas. Africans were shipped to America as slaves in the most inhumane conditions possible and were treated as animals. They received little or no pay from their masters and were given little welfare. Because of slavery, many able bodied men were removed from African societies which may have contributed to the relatively slow development of Africa. By early seventeenth century, most European nations caught up with each other in terms of navigational expertise. It became a race to see who could build bigger guns, bigger ships and larger fleets. The ability to navigate was thus no longer a factor for naval dominance.


7. CONCLUSION In this project, we have explored many aspects of navigating by the stars. We have firstly looked at what stars are and how they came about. We then defined some of the key astronomical terms commonly used before exploring the theory behind celestial navigation. We moved on, to look at the evolution of navigational equipment over the years, from the Kamal to GPS, before taking an in depth look at the aspects of the modern day sextant. Finally, we looked at the historical, geographical and economic impacts of celestial navigation from the Phoenicians to the Age of Exploration. The human love affair with the stars has existed since the dawn of human civilization. Although current GPS technology has rendered most traditional methods obsolete, nothing beats the personal satisfaction of reading a star to determine one’s position. Space travel in the distant future may require us to have an intimate knowledge of the heavens as we trek from star to star. But till then, we have to be content with trekking from place to place via the never ending bliss of heaven’s little light bulbs.


JUST FOR FUN (2)

Here are some comics that are related to navigation. Enjoy!



APPENDIX 1 ASTRO-NAVIGATION This is basically what a celestial navigator goes through in his daily business of navigating a ship at sea. MORNING SIMULTANEOUS SIGHTS (OMNIBUS) • Compute time of morning nautical twilight. • Determine which heavenly bodies may be visible. • Select six or seven of them and compute what their altitudes and azimuths will be at the time

he intends to ‘shoot’ them. • At the right time, he shoots each body and notes the exact time of the sight and the sextant

altitude. • After all the observations, he works his sights to obtain a line of position from each

observation. • He advances or retards each line of position to a common time and plots them. This gives

him a fix. Note: Since the time interval between the first and the last sights is short, most navigators consider them simultaneous sights. FIRST SUN SIGHT • Approximately 2 hours after sunrise, he shoots the sun. • Compute the sight and plot the resultant line of position. • About 2 hours later, he may observe the sun again. • After computing and plotting this sight, he advances his earlier sun line to this time and plots

his running fix. • Sometimes the moon and even Venus may be available for observation and obtaining a

nearly simultaneous sight. SUN SIGHT (FORENOON) – SUN-RUN-SUN + GYRO ERROR CHECK • During mid-morning the navigator will take an azimuth of the sun. • Difference between the computed azimuth and the observed one gives the compass error

for the vessel’s heading at that time. MERIDIAN PASSAGE (MERPASS) – SUN-RUN-MERPASS • After plotting the forenoon fix, the navigator will compute the noon DR and the zone time of

Local Apparent Noon (LAN) – merpass. • At merpass when the sun is on the meridian, noon observation is taken. • He reduces it for latitude, and plots the latitude. • He advances his best morning sun line to determine his noon position by running fix.


SUN SIGHT (AFTERNOON) – MERPASS-RUN-SUN • Navigator takes his afternoon sun sights after the sun has changed in azimuth enough to

cross with the noon latitude line. SUN SIGHT (LATE AFERNOON) – SUN-RUN-SUN • After his last afternoon fix, navigator computes the zone time of evening twilight. • Select stars for observation • Plot DR for that time • Pre-compute the altitudes and azimuths of the stars he selects so as to find them readily in

the few minutes of twilight available. EVENING SIMULTANEOUS SIGHTS (OMNIBUS) • ‘Shoot’ the selected stars as soon as they appear. • He works them for lines of position and plots the fix as he did for the morning stars. DEFINITIONS Fix: a. a charted position determined by two or more bearings taken on landmarks, heavenly bodies, etc. b. the determining of the position of a ship, plane, etc., by mathematical, electronic, or other means.

Running fix: a fix made from a moving vessel from observations made at different times, the course and distance run between the observations being considered.

Omnibus: pertaining to, including, or dealing with numerous objects or items at once.


REFERENCES Dennis Fisher, Latitude Hooks and Azimuth Rings: How to Build and Use 18 Traditional Navigational Instruments Ministry of Defence, Nautical Institute, Admiralty Manual of Navigation Vol 2 (Astro Navigation) http://www.celestialnavigation.net/classroom.html http://www.celestialnavigation.net/ http://www.pip.dknet.dk/~pip261/navigation.html http://www.geocities.com/alfgon.geo/cnhist.htm http://www1.minn.net/~keithp/cn.htm http://celestaire.com/page4.html http://en.wikipedia.org/wiki/Celestial_navigation http://www.pbs.org/wgbh/nova/teachers/ideas/sammons/packet.html http://www.space.com/scienceastronomy/brightest_stars_030715-1.html http://www.celestialnavigation.net/instruments.html http://www.nationalgeographic.com/features/97/stars/chart/index.html http://www.tecepe.com.br/nav/inav_c11.htm http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0203-1-10-instruments/home.htm http://www.westsea.com/tsg3/octlocker/octchart.htm http://pwifland.tripod.com/historysextant/ http://images.google.com.sg/imgres?imgurl=http://www.boatsafe.com/kids/crossstaff.gif&imgrefurl=http://www.boatsafe.com/kids/navigation.htm&h=150&w=145&sz=4&tbnid=5bSWvEULFpQJ:&tbnh=90&tbnw=87&hl=en&start=3&prev=/images%3Fq%3Dcross-staff%26svnum%3D10%26hl%3Den%26lr%3D http://users.tpg.com.au/users/vmrg/History%20of%20Navigation.html http://home.earthlink.net/~nbrass1/cardart.htm http://www.geocities.com/Colosseum/Park/8386/cnhist.htm http://www.mat.uc.pt/~helios/Mestre/Novemb00/H61iflan.htm

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