Latitudes and Longitudes

AGÊNCIA NACIONALPARA A CULTURACIENTÍFICA E TECNOLÓGICA

This booklet continues the experimentsand activities introduced in Where areyou? Material for observing and

experimenting, and is aimed at children aged tenand over. The experiments described here,together with the instruments described in thefirst booklet can be used to carry out experimentalactivities and observation at a basic educationlevel. You should read the first booklet and carryout the activities and experiments described therebefore you read this one.

Ciência Viva would like to thank Professor Rui Dilão for hisideas from project conception to final product and ProfessorMaurice Bazin and Dr. Elisa Figueira for unwavering supportthroughout the different stages of the project.

Editorial Staff

Text and Instruments: Rui Dilão

Revision and Suggestions: Maurice Bazin, Elisa Figueira, Helena Fonseca,Carlos Rodrigues and the Ciência Viva team.

Comments on the text: Ana Teodoro, Dulce Marcelino, Suzana Andrade andMaria João Mora.

Graphic Design: FPGBdesign

Internet Edition: Simbiose

Pilot testing in schools: E. S. Luísa de Gusmão (Lisboa), E. S. Rainha D. Amélia(Lisboa), E. S. José Régio (Vila do Conde) and EB2,3 D. Manuel I (Alcochete)and Colégio de Quiaios. Our thanks to the teachers and students who tookpart in these tests.

Acknowledgements: The view of the Sun, the Earth and the aerial photographof Lisbon and Setúbal on Pages 2, 3 and 21 courtesy of the NASA Photo Bank.The astrolabe diagram, the sextant and the 1502 planisphere courtesy of theNaval Museum. Some of the Earth pictures are from John Walker's web page.The world map on Page 20 was designed from data 88-MGG-02, Digital Reliefof the Surface of the Earth, NOAA, National Geographic Data Center, Boulder,Colorado, 1988. Our thanks to all.

Printers: Eurodois

Print run: 1.000

Depósito legal: 135929/02

ISBN: 972-97805-8-7

© Ciência Viva - Agência Nacional para a Cultura Científica e Tecnológica, 2002

http://www.cienciaviva.pt

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Index

The Map of the Earth.

The Earth revolves around the Sun!

The Earth’s Rotation.

The North Star.

How to travel on Earth without getting lost.

The Ecliptic.

The GPS.

Measuring latitude and longitude.

2

The Earth around the Sun!

The Earth moves in an almost circular path on its journey around the Sun.The Moon revolves around the Earth, accompanying it in its movement around the Sun.

From a very young age, we get used to seeing that day follows night and night follows day. Why?

Because we see the sun rising, moving across the sky and lighting up the world and, at the end of the day, itdisappears behind the mountains or into the sea. Then the moon and the stars come out,rising and disappearing again in their turn to give way to the Sun.

People who lived long ago thought the Sun revolved around the Earth. Around 450years ago, Nicholas Copernicus proved that it is the Earth that revolves around theSun and day follows night and night follows day because the Earth spins on itsown axis.

• Do you think that the reason we cannot see the stars during the day is because the sunlight is too bright?

• Watch the sky closely at dusk and see how the stars become clearer and clearer.

Nicholas Copernicus was born in Poland in 1473, at the time that the Portuguese had just discovered the AfricanCoast as far as the Gulf of Guinea.Copernicus dedicated himself to the study of medicine, law and astronomy.He was the first to present clear evidence that the Earth revolved around the Sun. He compiled his ideas in thebook On the Rotation of Celestial Bodies, published in 1543 in Nuremburg, Germany. This was the year in whichD. João III was king in Portugal and the Portuguese began their voyages to Japan.

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Today using rockets and space ships we can travel far from the Earth and see that it revolves around the Suntaking 365 days and 6 hours to complete a full circle. From space ships we can photograph the Earth and lookdeeper into the Universe.

A year has 365 days and 6 hours, which is the approximate time it takes the Earth to make a complete circlearound the Sun. Because of this, our calendar has years with 365 days and years with 366 days. A year with 366days is called a leap year. Knowing that 1996 had 366 days and 1997 had 365 days, underline the leap years inthe list below.

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

A space station in orbit around the Earth. The movement of thisstation around the Earth is very similar to the movement of themoon around the Earth. The moon is just further away.

Just as we can see the Earth from the Moon, so also can we seethe moon from the Earth. This picture of the Earth was taken fromthe spaceship Clementine when it was travelling near the moon.

A view of Earth from space at a height of 1000 km on the vertical of Lisbon.

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North Pole

Night

Day

South Pole

21 June Solstice.The beginning of summer in the NorthernHemisphere and the beginning of winterin the Southern Hemisphere.

22/23 September Equinox.The beginning of autumn in the NorthernHemisphere and the beginning of springin the Southern Hemisphere.

21 March Equinox.The beginning of spring in theNorthern Hemisphere and thebeginning of autumn in theSouthern Hemisphere.

The Earth’s Orbit: the path travelled bythe Earth in its journey around the Sun.

During the revolving movement of the Earth around the Sun, the north-south axis always points in the samedirection. If you went on a space voyage for a year, far from the Earth, the Sun and the Moon, you would seethat the Earth moves in the following way:

The revolving Earth. Days, nights and seasons of the year

The Earth spins on an imaginary axis which runs from the North to the South Pole and every twenty four hoursit has turned completely around. This means that every twenty-four hours, there is a day and a night.

The spinning of the Earth on itsnorth-south axis causes day andnight to follow on each other.

21/22 December Solstice.The beginning of winter in the NorthernHemisphere and the beginning of summerin the Southern Hemisphere.

5

Imagine that the Earth’s orbit is on a plane - the plane of the Earth’s orbit - , that the north-south axis is inclined23º and 30’ relative to this plane and that it always points in the same direction. As you can see in the previousdiagram, there is an area along the Earth’s orbit in which the North Pole has no sunlight while the South Pole hassunlight. At these times, it is winter in the Northern Hemisphere and summer in the Southern Hemisphere. Whenthe North Pole is leaning more towards the sun, summer starts in the Northern Hemisphere: this is the JuneSolstice, the longest day of the year in the Northern Hemisphere.

The Earth revolves around the Sun and its axis is tilted relative to the plane of the Earth’s orbit. These facts arewhat cause summer and winter in the areas above and below the Tropics of Cancer and Capricorn. In equatorialregions, the differences between summer and winter are less obvious.

If you looked at the Earth and the Sun from a spaceship at the level of the plane of the Earth’s orbit during thesolstices, you would see the following:

The path of the Earth’s journey around the Sun is roughly circular. Actually there is a time of year when the Earthis closer to the Sun. This is on the 4th January, midwinter in the Northern Hemisphere.

June Solstice December Solstice

• Place a lamp on a table so that it throws light onto your terrestrial globe. Turn the globe slowly on the imaginaryaxis running from the North to the South Pole.

• On which parts of the globe is it day-time and on which is it night-time?

• Try to make a rough estimate of the time in the bright and dark areas of the globe.

• Move the globe around the table trying to copy the movement of the Earth around the Sun, always keeping thenorth-south axis pointing in the same direction. When is it summer and when is it winter in Lisbon?

• What is the position of the Earth (globe) relative to the Sun (lamp) when it is midday in Lisbon on the following days:

21st of December, 21st of March, 21st of June and 22nd of September.

6

Little Dipper

North StarBig Dipper

Cassiopeia

Now let’s take a deeper look at the Universe.

If we look at the sky at regular intervals during the night, we see that the stars move slowly around the NorthStar. In the Southern Hemisphere, all the stars move around a very dark area called the Coalsack.

Nowadays, the North Star always shows the north and is only visible in the Northern Hemisphere. The Coalsackshows the south and is only visible in the Southern Hemisphere.

The North Star

• In which direction does the Earth spin on its north-south axis?

• Why do the stars move around the North Star?

Constellations are groups of stars which form imaginaryfigures and which always seem to be in the sameposition relative to each other. The North Star is one ofthe tail stars of the Little Dipper constellation.

You can see the Big Dipper, Cassiopeia and the LittleDipper, among others, in the Portuguese sky. If youwatch the night sky from a dark spot, you will see themeasily. The most difficult one to find is the Little Dipperbecause the light of its stars is weaker. Start by findingthe Big Dipper and Cassiopeia. Then try to find theLittle Dipper by using the position of the threeconstellations as seen in the diagram.If you have your nocturnal with you, you will be ableto tell what time it is.

If you look at these constellations again an hour later,you will see that they have revolved around the NorthStar. Now you can check the time on your nocturnalagain and you will see that one hour has gone by.

The position of the Sun throughout the day

The position of the noon Sun inthe Northern Hemisphere abovethe Tropic of Cancer.

Sunset or WestSunrise or East

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By looking at the horizon and knowing the direction of sunrise and sunset, we can tell in which direction we aremoving. To turn back, you simply turn around and go back in the opposite direction.

This is easy when we are on land. We only need to take a fix on one or two points on the horizon and go theopposite way, changing the reference points on the right to the left and the points on the left to the right.

Of course, if you have a compass you can tell which direction is north, which is south and where the other cardinalpoints lie.

But it is also possible to find your way without a compass, because for instance, in Portugal the midday sun isalways in the south.

How to travel on Earth without getting lost

Finding our way at night, in the desert, or at sea is more difficult as we cannot see any reference points on the horizon.

In the Northern Hemisphere, the North Star is always in the north and is visible at night. So if we turn to the NorthStar, the Sun will always rise on our right and set on our left.

If you live in Cape Verde, which lies between the Tropic of Cancer and the Equator, you can still see the NorthStar in the north. But, depending on the season, the midday sun may be north or south of your position.

If we travel to the Earth’s Southern Hemisphere like Portuguese navigators from the 15th century on, we can nolonger see the North Star. But the Coalsack will always show us the way south.

8

Equator

Tropic of Capricorn

Tropic of CancerSummer

Winter

North Pole

South Pole

• Find Cape Verde on the globe. Why do the inhabitants of Cape Verde sometimes see the midday sun in thenorth and at other times in the south?

• Find the Equator and the north-south axis on the globe. Light up the globe with a lamp and tilt the axis slightlytowards the light so that the area around the North Pole, outlined by the Arctic Circle, is lit up. Place a pencilagainst the globe and move it vertically on the globe.

• As you can see, there is a point where the pencil casts no shadow. Now find the Tropic of Cancer on the globeand place the pencil against it. Tilt the axis so that there is no shadow when the pencil is on the Tropic of Cancer.The axis of the globe is now inclined 23º 30’ relative to the vertical. For anyone who is standing on the surfaceof the Earth at the point where the pencil meets the globe and who can see the sun in the position of the lamp,it is midday on June 21st.

• If you move the pencil to the north, its shadow will point north and the Sun will be to the south. If you movethe pencil towards the sun, its shadow will point south because the midday sun is to the north.

• But if you tilt the axis in the opposite direction so that it is winter in the Northern Hemisphere, the pencil shadowwill still point north in Cape Verde and in Lisbon.

• So those who can see the midday sun to the north or to the south at different times of the year live betweenthe Tropic of Cancer and the Tropic of Capricorn.

• The answer to our question is simple. As the north-south axis of the Earth is inclined relative to the plane ofthe Earth’s orbit, the midday sun on the first day of summer south of the Tropic of Cancer will be in the north.But in the autumn, between the Equator and the Tropic of Cancer, the midday sun will be in the south.

Eratosthenes was born 2274 years ago in the city of Cyrene in present day Libya. While he was running the famous Library ofAlexandria in Egypt, he noticed that on the June solstice in the Northern Hemisphere, a vertical stick in the city of Siena, 800 kmto the south of Alexandria, cast no shadow at midday. Then based on experiments with stick shadows, he calculated the lengthof the Equator and began to include leap years in the Greek calendar.

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• Measure the angle of the North Star above the horizon with your quadrant. This angle is the latitude of theplace you are in.

• Use your protractor to measure the angle of your sundial straw above the horizon. This angle should be roughlythe same as the latitude of your position.

By observing the regularity of the Earth’s movement around the Sun, astronomers and geographers were able tofind practical ways to determine our position on Earth.

Locations to the north and south of the Equator aremarked along circular parallel lines drawn aroundthe Earth. These lines are called the parallels andtheir positions are measured in degrees: the Equatoris the Zero Degree line, the North Pole is at a 90º Nangle to the Equator and the South Pole lies at a 90º Sangle to the Equator. The measurement of the north-south position is called latitude.

The latitude of the Tropic of Cancer is 23º 30’, exactlythe same as the Earth’s tilt relative to the plane ofits orbit around the Sun!

To determine the latitude of a location during the day, in addition to knowing the angle of the midday sun abovethe horizon, the date, your approximate position on Earth, you also need to know if you are in the Northern orSouthern Hemisphere and your position relative to the tropics. In the Northern Hemisphere the angle of the NorthStar above the horizon is the latitude of your location.

The latitude of a location is the measurement of the angle if you

travel from the Equator to the parallel which passes through this

location, perpendicular to the Equator. At any time of night, this

angle is equal to the angle of the North Star above the horizon.

Measuring latitude is easy, because in the Northern Hemisphere,

the North Star is always visible in the night sky.

Latitudes

50ºN

25ºN

0ºN

25ºS

Equator

Paralels

North Star

Equator

Latitude:30ºN

30º

30ºThe horizon

10

Based on experiments with stick shadows and much observation of the Sun and the NorthStar, instruments were devised to calculate our position on the surface of the Earth.

With the astrolabe and the quadrant, we can find out if we are closer to the northor to the south by measuring the angle of the North Star above the horizon or

by measuring the angle of the sun above the horizon.

It was these instruments that enabled the beginning of the great oceanvoyages from the 15th century on. They enabled sailors to return totheir point of origin as well as allowing them to make other voyagesalong the same routes.

It was during the 16th century that Portuguese mathematician PedroNunes developed instruments which allowed navigators to drawaccurate charts of their sea routes.

17th century Portuguese astrolabe.

The modern version of the astrolabeand the quadrant is the sextant,which is still used today by all boatsthat sail the seas.• Use your quadrant and your protractor to measure

the height of the noon sun. Compare the valuesobtained. You can calculate the noon sun time withthe aid of your sundial.

Pedro Nunes was born in Alcácer do Sal in 1502. He lived at the height of the Portuguese Discoveries and in 1529 he was appointedRoyal Cosmographer by D. João III.In order to resolve some of the difficulties of navigation, Pedro Nunes invented several astronomical instruments, such as theuniversal ringdial, the solar compass and the nonius, nowadays called vernier. The first two calculate the height of the Sun inthe sky and the third, when fitted to a quadrant can measure to fractions of a degree and accurately establish the height of a star.Some of these instruments were tried out successfully by D. João de Castro on his voyages to Goa and the Red Sea.The nonius was used and adapted by the astronomer Tycho Brahe to build two quadrants. Brahe's observations on astronomyhave been the basis of the modern description of planet movement since the end of the 16th century.

Equator

The GreenwichMeridianZero degreeslongitude

0º

20ºE40ºW

20ºW

Meridians

11

We now know how to determine locations further north or further south on the Earth, in other words, we candetermine the latitude of a location. To pinpoint our position on Earth, we need to know if we are further eastor west. This means that we need to know the longitude. Now the Sun and the stars cannot help us.

The idea of establishing our east-west position originated in Egypt with the Greek astronomer Ptolemy, who wasborn about 2170 years ago. Ptolemy decided to draw vertical circles around the North and South Poles and callthem meridians. The position of these meridians was measured relative to the Prime Meridian (Zero Degrees),which passed through a chosen point on the Equator. For Ptolemy, the Prime Meridian passed through the CanaryIslands. This, however, is largely a matter of choice and kings and ministers over the years have changed the PrimeMeridian to pass through the Azores, Cape Verde, Rome, Paris, Philadelphia and London. Today, it passes throughthe Greenwich Observatory which is to the east of London.

Defining the meridians, however, is not enough to determine the longitude of a location, we also need instruments.One possibility is to measure time with the aid of a clock.

Determining the longitude of a location is based onthe fact that the Earth spins full circle on its north-south axis approximately every 24 hours. We needto know the time difference between the noon sunof our position and that of a reference position.These times are determined by the maximum heightof the sun at both locations. As the Earth spinsa complete circle (360 degrees) every twenty-fourhours, for every hour of difference between noonat our location and that of our reference location,the Earth moves 15 degrees east or west.

For example, to determine longitude at sea,we need to sail with an accurate time-keeper.Then when it is noon at your current location,establish what time it is at your port of origin.With the aid of navigation tables which shownoon times for the port of origin for each dayof the year, pilots can calculate the time differencesbetween noon at their current location andat the port of origin.

For each hour of difference, they are roughly15 degrees east or west relative to their port of origin.

As we can determine our latitude by looking at

the angle of the sun above the horizon at midday,or at night by the angle of the North Star abovethe horizon, we know which parallel we are on.Knowing the parallel and the meridian, we can nowpinpoint our position on the terrestrial globe.

The longitude scaleis marked along theline of the Equator

Lisbon: 38º 44’ N, 9º 8’ W

Oporto: 41º 8’ N, 8º 22’ W

Faro: 37º 1’ N, 9º 5’ W

Bragança: 41º 49’ N, 6º 45’ W

The Azores: 38º N, 25º W

Madeira: 33º N, 17º W

Sample latitude and longitude:

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However, taking a clock on a boat was a tricky business. 15th, 16th, 17th and 18th century clocks did not takekindly to the ship’s roll, the humidity and temperature differences.

From the end of the 15th century, when Columbus discovered America, to the end of the 18th century, transportinga clock on board ship was considered the biggest problem in nautical science. Problems caused by ships sailingoff course and shipwrecks were so great that in 1598, King Philip of Spain offered a prize to anyone who coulddiscover a practical way to determine longitude. Later on, in 1714, the English King George III, by request ofsailors and traders, introduced the Board of Longitude Award for anyone who could come up with the solutionto the longitude problem.

An accurate time-keeping clock was designed by the English carpenter John Harrison in the mid 18th century andits first sea test was carried out in 1736 on a voyage to Lisbon. John Harrison’s invention was only recognised in1773, when he was awarded the Board of Longitude Award Prize.

Only after 1773 was it possible to accurately determine longitude at sea. Until then navigation was very risky withmany tales of accidents caused by sailing off course. Navigators very often played it safe and followed the sameroutes along the parallels, always keeping the noon sun at the same altitude. This was the case with ChristopherColumbus who arrived in America in 1492 by sailing along the same parallel.

John Harrison was born in rural England in 1693 and by the time he was 18, he had already built a wooden clock. In 1730, heleft his native village for London, where he presented his sea-clock designs to Edmond Halley, one of the most famous astronomersof the time, but Halley received the plans sceptically. In the five years that followed, Harrison dedicated himself to building thefirst sea-clock prototype. This clock, which may be seen in the Greenwich Museum, still keeps accurate time. It weighed 35 kgand had four dials which showed the day, the time, the minutes and seconds. It was tried out successfully for the first time onthe H.M.S. Centurion voyage to Lisbon where it kept time to within some seconds a day. John Harrison was about to win theBoard of Longitude Prize. Much to everyone’s surprise, he asked to be given time to perfect his prototype. Harrison was not happywith either the precision or the size of his clock. Over the following twenty-five years, he built three more prototypes. Duringthis time, he had the full support of the English Royal Society and developed all of the mechanisms which form part of the workingof modern-day clocks.

The fourth clock was only finished in 1759 and it weighed 1.5 kg. After navigation tests to India, John Harrison received theBoard of Longitude Prize in 1773 and died three years later.

Today his wooden clock and his three sea-clocks are still in working order. It is forecast that the last one will start to malfunctionin four hundred years’ time!

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If we compare both maps, we can see that the latitudes of the Tropics and the Equator are well-positioned.Longitude is not well-positioned owing to the inexistence of good clocks. These maps, which gave a rough ideaof the shapes of the seas and continents, were of invaluable aid to sailors and traders.

During the time of the Discoveries, Portuguese navigators succeeded in making charts of undiscovered areas usingjust an astrolabe, a magnetic compass, a compass, a globe and an hour-glass. One of these maps is the 1502Alberto Cantino planisphere.

1502 Cantino planisphere showing the meridians and the parallels.

Present day map showing the same area as the Cantino planisphere.

Tropicof Cancer

Equator

Tropicof Capricorn

Longitude

Greenwich MeridianLatitude

23º 30’N

0

23º 30’ S

0º

Because the midday sun is on the Equator during the equinoxand the Equator is at a 90º angle relative to the North Star,the latiude measured from the Sun’s angle at midday is equalto 90º minus the angle of the Sun above the horizon.

Lat.

The North Star

Lat.

Height of the Sun

N

S

Equator

Cancer

The Sun during the Equinox

The horizon

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How a navigator determines latitude and longitude

A navigator sails from Lisbon with a clock that keeps time with another clock at the port of origin.

After several days, when the Sun is at its highest in the sky (noon) he sees what time it is in Lisbon and then useshis astrolabe, quadrant or sextant to calculate the angle of the Sun above the horizon.

With the aid of a compass the navigator establishes whether the midday sun is in the north or in the south. Thenhe writes down the following information about the noon sun at his location:

Height and direction of the Sun at noon: 62º south

Lisbon time: 13:28

Date: 22 July

Latitude and longitude of Lisbon (port of origin): 38º 44´ N, 9º 8´ W.

From this information, the navigator uses the following methods to establish his position:

Calculating latitude would be very easy if it was during one of the equinoxes when the midday sun is on theequator: as the North Star is at a 90º angle relative to the Equator, latitude would be calculated at 90º minus theangle of the Sun above the horizon. On the other hand, since I left Lisbon several days ago, the midday sun hasalways been to the south so I must be north of the Equator.

Let’s see what the Sun’s position is during the equinox when I can see the midday sun in the south:

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If today were June 21st, the midday sun would be on the vertical of the tropic of Cancer andwould no longer be at a 90º angle with the North Star. But as the latitude of the Tropic of Canceris 23º 30´ from the height of the Sun in my current location to determine the height of the Sunrelative to a point on the Equator. With this new angle, I could calculate latitude as if it were aday during the equinox.

If it was during the solstice, the position of the Sun would be like this:

Lat.

North Star

Lat.

Height ofthe Sun

Equator

Tropicof Cancer

The Sun duringthe solstice

The horizon

23º 30’

N

S

23º 30’

As there are 92 days between the solstice and the equinox, the height of the midday sun relative to the equatorvaries 15’ 20” per day. I got this figure by dividing 23º 30’ by 92 days. So, on July 22nd, 61 days before the equinoxthe Sun is between the equator and the tropic. This means that the height of the Sun relative to the equator is 15’20” multiplied by 61 giving a total of 15º 35’. So to calculate the latitude of a place, I have to deduct this anglefrom what I measured, like I did during the solstice. Therefore the angle to calculate latitude is 62º minus 15º 35’which gives 46º 25’. Finally I can calculate latitude like on an equinoctial day: 90º - 46º 25’ = 43º 35’ N.

To calculate longitude I need to know noon time in Lisbon and compare it with the time of the noon sun at mylocation. With the aid of the navigation tables drawn by the astronomers of my port of origin, I know that the noonsun in Lisbon was at 12:43. The noon sun at my location was 45 minutes later than in Lisbon. As the Earth spins15º per hour, a time difference of 45 minutes corresponds to an angle of 11º 15’. So, as the Earth spins from Westto East, I am west of the point of origin on longitude 9º 8’ + 11º 15’ = 20º 23’ W.

The navigator’s position on Earth is 43º 35’N, 20º 23’ W. If you mark these co-ordinates on the globe you will seethat the navigator is in the Atlantic Ocean, north-west of Lisbon and north-east of the Azores islands.

• Find the place where you live on the globe and determine its approximate latitude and longitude.

It is approximately midday on March 21st

at the point where the Equator meetsthe Greenwich meridian that the Sun inits apparent movement around the Earth,intersects the Celestial Equator. It is fromthis moment that clocks which show days,nights and seasons are set. To maintain theregularity of the Sun’s apparent movementaround the Earth, we need to adjust the calendarevery leap year and less often we need to put the clocksback or forward a few seconds. For example, under the PapalDecree of 1582, the 5th of October became the 15th of October. On the eve of the year 2000, the final seconds shouldhave been counted 5, 4, 3, 2, 1, 1,0.

It is by setting the clock by the approximate regularity of movement of the celestial bodies that we can determinelatitude and longitude. The International Astronomy Union meets periodically to present average figures of the inclineof the ecliptic and year length. Knowing that the Earth spins an average 15º every hour and that on 21st March 1999at 0º N 0º W the noon sun is at 12:06, we can determine quite accurately the time of the noon sun at any point onthe Earth. For instance, in the year 2000 the ecliptic is at an angle of 23º 26' 21" to the Celestial Equator. The Earthspins an average of 15º 2' 28" every hour and the year is approximately 365 days, 5 hours, 58 minutes and 54 seconds.

Over two thousand years ago, while Egyptian and Greek astronomers were watching the night sky, they realised thatthere were sets of stars - constellations - which kept the same approximate positions relative to each other.

Then they imagined that the Universe was an enormous sphere with fixed stars. They called this the Celestial Sphereand the set of stars the heavens. Today we know that this is not the case. The stars in the heavens move but they areso far away that it is very difficult to see them moving, even with more powerful telescopes.

As the Earth lies in the middle of the Celestial Sphere, approximately every 24 hours the stars are seen in the sameposition in the heavens. But what happens in relation to the Sun?

If we mark the position of the midday sun in the CelestialSphere every day for a year, it will show acircumference with a 23º 30’ incline relative to theequator of the Celestial Sphere. The apparentorbit of the Sun in the Celestial Sphere iscalled the ecliptic. The incline of theecliptic is the same as the north-south inclinerelative to the plane of the Earth’s orbit.

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The Ecliptic

23º 30’Winter

Solstice

SummerSolstice23º 30’

Celestial Sphere

CelestialEquator

Ecliptic

17

Angle of correction used in determining latitude

23º30’ 20º

15º

10º

5º0º

-5º

-10º

-15º

-20º-23º30’-20º

-15º

-10º

-5º

0º5º

10º

15º

20º

It is by using data on the apparent movement of the Sun in the Celestial Sphere that astronomers draw up maritimecharts for navigators. For instance, to determine the latitude of a location on any given day of the year, a navigatorneeds to know the height of the noon sun on the ecliptic. So astronomers draw up charts of the incline of theSun throughout the year, as shown in the chart below. According to the chart, on 22nd May, for example, themidday sun is on the vertical of the 16º N parallel. On the 7th November, the midday sun is on the vertical of the12º parallel. The negative values in the chart refer to latitudes south of the Equator.

APRIL

MA

RC

HFEBRU

ARY

JANUARYDECEMBER

NOVEMBER

OC

TOBE

RSE

PTEM

BER

AU

GU

ST

JULYJUNE

MAY

18

Noon Sun at thePavilhão do Conhecimento

Lisbon 9º 5’ 42” W

CorrectionsOporto: about 3 minutes earlierBragança: about 10 minutes earlierFaro: the same timeAzores: about 1 hour and 3 minutes laterMadeira: about 31 minutes later

For mainland Portugal and Madeira, add one hourduring the period between the last Sunday inMarch and the last Sunday in October. For theAzores, subtract one hour between the last Sundayin October and the last Sunday in March.

APRIL MARCH

FEBRUARY

JAN

UA

RY

DEC

EMBER

NO

VEMBER

OCTOBERSEPTEMBER

AUGUST

JULY

JUN

E

M

AY

40 42 44 45 47 48 4950

5051

5150

5049

4746

4442

4038

3533

3129

2725

2322

2120

202020212123242627293133353638

39

4041

4242

4242

4241

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In order to determine longitude, the time of the noon sun in a location on Earth is shown in a chart. For example,at the Pavilhão do Conhecimento in Lisbon, the time of the noon sun shown on the clock is calculated by adding12 hours to the minutes shown in the chart. Using these charts, a quadrant, a compass and a clock with a localreference time, it is always possible to know where we are on Earth.

Using these charts, a quadrant, a compass and a clock with a local reference time, it is always possible to knowwhere we are on Earth.

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Nowadays, longitude and latitude can be calculated electronically using man-made satellites. This is a great aidto ships and planes in finding their way on the Earth.

With man-made satellites, it is possible to find out our location on Earth, the time and the average height abovesea-level. All in all, there are 24 satellites 20 200 km high whichorbit the Earth every 12 hours. These satellites continuallytransmit radio waves to Earth, where they are captured byan antennae. Using an apparatus specially designed tocapture these signals, we can immediately discover latitude,longitude and altitude on Earth. The signals from fiveout of eight of these satellites can always be receivedanywhere on Earth.

This system is called GPS - Global Positioning System.

The GPS

The GPS satellite constellation in orbitaround the Earth.

Each of the GPS constellation satellites sends constant radio signals

to Earth, which show its position, latitude, longitude and the time.

Some radio waves arrive earlier and others later, depending on

the distance of each satellite from the antennae. The calculator

of the GPS apparatus is programmed to determine latitude and

longitude with signals from at least four of the satellites.

Nowadays ships and planes are equipped with GPSreceivers. However, reception of GPS signals isdependent on atmospheric weather conditions, soas a precaution, ships always carry a sextant on board.

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• Look at the map or at your globe. Find the mountains on the sea bed. Find the Azores archipelago and noticehow they all form part of a chain which rises out of the sea bed and crosses the Earth from north to south.

• Find the latitude and longitude scales on the planisphere.

The Map of the Earth

A map is a simplified representation of populated areas, geographical features, roads, rivers, continents andoceans. As well as maps of the Earth and its countries, there are city plans and ordnance survey charts. These areall maps. In the past they were drawn using a compass, an astrolabe and a tape measure. Nowadays, they arecharted using aerial photography and the GPS.

Maps are used for several purposes.

The world map shows us countries, large rivers and mountains, the position of oceans and deserts, etc.

A country map shows us the larger cities and towns, roads, etc.

Ordnance survey maps show contours, roads, houses, forests, etc.

A city plan shows us streets, monuments, parks, etc.

All maps show the cardinal points as well as a scale.

A world map showing the continents and the sea beds in relief. The blue represents the sea. Dark blue representsthe deeper ocean beds and light blue the shallower beds. The continents are shown in yellow and the darkerareas are the contours. The positions of the Equator, the Greenwich meridian, the Tropics of Cancer andCapricorn, the Arctic and the Antarctic Circles are shown on the map.

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• Here is an aerial photograph of Lisbon and Setúbal. Use tracing paper to copy the picture. Draw a map of thisarea and identify what you think are the relevant features. For example, rivers, bridges, roads, etc. Try to layout your own map. This is how modern maps are made.

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Measuring latitude and longitude

Just before noon, point your sundial to the south with the aid of a compass. But the compass only gives anapproximate indication of the North Pole’s position and your sundial needs to be accurate, so if you are in mainlandPortugal you should turn it about 5º East. In the Azores, this angle needs to be 11º and 8º in Madeira. Theseangles vary only very slightly and up to the year 2007 they will decrease by just 1º.

At noon, that is when the shadow of the straw on your sundial points to 12 on the scale, use your quadrant tomeasure the angle of the Sun above the horizon.

Angle of the Sun above the horizon at noon

To determine latitude from this information, we need to use a table similar to those used by 15th and 16th centuryPortuguese navigators. Look at the circular chart on Page 17 to find out the necessary correction angle for latitudeof the location where the measurement is being taken:

Latitude = 90º - (measured angle) + angle of correction =

Note that the angle of correction may be positive or negative.

It is possible to tell noon time using only a stick shadow. Just before midday place a stick vertically and mark the ends of theshadows it casts with chalk, then check the time. When the shadow is at its shortest then it is noon. In addition, the noon shadowpoints exactly North. Now you can carry out your experiment setting your sundial by the shadow and you don’t even need touse a compass. For example you could determine the direction of the north-south axis one day and measure latitude the next day.

In order to determine latitude we must first determine local noon time, know the longitude of a reference pointand noon time at this point. Let’s use the Pavilhão do Conhecimento in Lisbon, Latitude 9º 5’ 42” W as ourreference point.

Just before noon, point the sundial to the south as described in the above activity. At noon, that is when theshadow of the straw on your sundial falls on 12 on the scale, look at the time on your wristwatch, which mustbe accurate by Lisbon time:

Noon time at my location:

Look at the circular chart on Page 18 to find out what noon time is at your reference point - the Pavilhão doConhecimento:

Noon time at the Pavilhão do Conhecimento:

Now calculate the difference between noon time at your location and at the Pavilhão do Conhecimento:

Time difference = Noon time at my location - noon time at the Pavilhão do Conhecimento =

This number may be positive or negative and should be calculated in minutes. For example: 12.30 - 12.25 = 5minutes; 12.30 - 12.35 = -5 minutes; 12.25 - 13.35 = -70 minutes.

As the Earth spins 15’ every minute, this time difference corresponds to the difference in longitude:

Longitudinal difference = Time difference in minutes x 15’/minutes =

As the Earth spins from West to East, the longitude of your location is:

Longitude = 9º 5’ 42” W + longitudinal difference =

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How many days are there in a year?

How many days are there in a leap year and how often are they?

Does the Earth revolve around the Sun or does the Sun revolve around the Earth?

Which direction is the north, south, sunrise and sunset where you live?

Which days are the solstices and the equinoxes?

Can you point out the Little Dipper, Cassiopeia and the Milky Way?

What is the latitude and longitude where you are?

The Arctic Circle is the parallel which borders the areas of the Earth where there is no night on the21st June. What is the latitude of this parallel?

Draw a map of the streets and paths of your area. Do not forget to include a scale and a compass rosewith north pointing to the North Pole.

You can do lots of activities with your globe. For example, you can draw national borders, the largest riversand deserts on Earth, the sea routes of 15th and 16th century Portuguese navigators and many more.

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