Latitudes and Longitudes - Ciência Viva

Latitudes and Longitudes
AGÊNCIA NACIONAL
PARA A CULTURA
CIENTÍFICA E TECNOLÓGICA

This booklet continues the experiments
and activities introduced in Where are
you? Material for observing and
experimenting, and is aimed at children aged ten
and over. The experiments described here,
together with the instruments described in the
first booklet can be used to carry out experimental
activities and observation at a basic education
level. You should read the first booklet and carry
out the activities and experiments described there
before you read this one.
Ciência Viva would like to thank Professor Rui Dilão for his
ideas from project conception to final product and Professor
Maurice Bazin and Dr. Elisa Figueira for unwavering support
throughout 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 and
Maria 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 took
part in these tests.
Acknowledgements: The view of the Sun, the Earth and the aerial photograph
of 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 the
Naval 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 Relief
of 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

Index
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.
The Map of the Earth.
Measuring latitude and longitude.
1

2
The Earth 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, it
disappears 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 450
years ago, Nicholas Copernicus proved that it is the Earth that revolves around the
Sun and day follows night and night follows day because the Earth spins on its
own axis.
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.
• 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 African
Coast 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 the
book On the Rotation of Celestial Bodies, published in 1543 in Nuremburg, Germany. This was the year in which
D. João III was king in Portugal and the Portuguese began their voyages to Japan.

Today using rockets and space ships we can travel far from the Earth and see that it revolves around the Sun
taking 365 days and 6 hours to complete a full circle. From space ships we can photograph the Earth and look
deeper into the Universe.
A space station in orbit around the Earth. The movement of this
station around the Earth is very similar to the movement of the
moon around the Earth. The moon is just further away.
A view of Earth from space at a height of 1000 km on the vertical of Lisbon.
Just as we can see the Earth from the Moon, so also can we see
the moon from the Earth. This picture of the Earth was taken from
the spaceship Clementine when it was travelling near the moon.
A year has 365 days and 6 hours, which is the approximate time it takes the Earth to make a complete circle
around the Sun. Because of this, our calendar has years with 365 days and years with 366 days. A year with 366
days is called a leap year. Knowing that 1996 had 366 days and 1997 had 365 days, underline the leap years in
the list below.
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
3

4
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 hours
it has turned completely around. This means that every twenty-four hours, there is a day and a night.
Night
North Pole
South Pole
Day
During the revolving movement of the Earth around the Sun, the north-south axis always points in the same
direction. If you went on a space voyage for a year, far from the Earth, the Sun and the Moon, you would see
that the Earth moves in the following way:
21 March Equinox.
The beginning of spring in the
Northern Hemisphere and the
beginning of autumn in the
Southern Hemisphere.
21 June Solstice.
The beginning of summer in the Northern
Hemisphere and the beginning of winter
in the Southern Hemisphere.
The Earth’s Orbit: the path travelled by
the Earth in its journey around the Sun.
The spinning of the Earth on its
north-south axis causes day and
night to follow on each other.
22/23 September Equinox.
The beginning of autumn in the Northern
Hemisphere and the beginning of spring
in the Southern Hemisphere.
21/22 December Solstice.
The beginning of winter in the Northern
Hemisphere and the beginning of summer
in the Southern Hemisphere.

Imagine that the Earth’s orbit is on a plane - the plane of the Earth’s orbit - , that the north-south axis is inclined
23º and 30’ relative to this plane and that it always points in the same direction. As you can see in the previous
diagram, there is an area along the Earth’s orbit in which the North Pole has no sunlight while the South Pole has
sunlight. At these times, it is winter in the Northern Hemisphere and summer in the Southern Hemisphere. When
the North Pole is leaning more towards the sun, summer starts in the Northern Hemisphere: this is the June
Solstice, 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 are
what cause summer and winter in the areas above and below the Tropics of Cancer and Capricorn. In equatorial
regions, 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 the
solstices, you would see the following:
June Solstice December Solstice
The path of the Earth’s journey around the Sun is roughly circular. Actually there is a time of year when the Earth
is closer to the Sun. This is on the 4 th January, midwinter in the Northern Hemisphere.
• Place a lamp on a table so that it throws light onto your terrestrial globe. Turn the globe slowly on the imaginary
axis 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 the
north-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.
5

6
The North Star
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 North
Star. 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 Coalsack
shows the south and is only visible in the Southern Hemisphere.
• 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 imaginary
figures and which always seem to be in the same
position relative to each other. The North Star is one of
the tail stars of the Little Dipper constellation.
You can see the Big Dipper, Cassiopeia and the Little
Dipper, among others, in the Portuguese sky. If you
watch the night sky from a dark spot, you will see them
easily. The most difficult one to find is the Little Dipper
because the light of its stars is weaker. Start by finding
the Big Dipper and Cassiopeia. Then try to find the
Little Dipper by using the position of the three
constellations as seen in the diagram.
If you have your nocturnal with you, you will be able
to tell what time it is.
If you look at these constellations again an hour later,
you will see that they have revolved around the North
Star. Now you can check the time on your nocturnal
again and you will see that one hour has gone by.
Big Dipper
Little Dipper
Cassiopeia
North Star

How to travel on Earth without getting lost
By looking at the horizon and knowing the direction of sunrise and sunset, we can tell in which direction we are
moving. 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 the
opposite 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 cardinal
points lie.
But it is also possible to find your way without a compass, because for instance, in Portugal the midday sun is
always in the south.
Sunrise or East
The position of the Sun throughout the day
The position of the noon Sun in
the Northern Hemisphere above
the Tropic of Cancer.
Sunset or West
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 North
Star, 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 North
Star 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 no
longer see the North Star. But the Coalsack will always show us the way south.
7

8
• Find Cape Verde on the globe. Why do the inhabitants of Cape Verde sometimes see the midday sun in the
north 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 slightly
towards the light so that the area around the North Pole, outlined by the Arctic Circle, is lit up. Place a pencil
against 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 globe
and 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 surface
of 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 move
the pencil towards the sun, its shadow will point south because the midday sun is to the north.
North Pole
Winter
Summer
Tropic of Cancer
South Pole
Equator
Tropic of Capricorn
• But if you tilt the axis in the opposite direction so that it is winter in the Northern Hemisphere, the pencil shadow
will 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 between
the 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 of
the 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 of
Alexandria in Egypt, he noticed that on the June solstice in the Northern Hemisphere, a vertical stick in the city of Siena, 800 km
to the south of Alexandria, cast no shadow at midday. Then based on experiments with stick shadows, he calculated the length
of the Equator and began to include leap years in the Greek calendar.

By observing the regularity of the Earth’s movement around the Sun, astronomers and geographers were able to
find practical ways to determine our position on Earth.
Paralels
Equator
25ºN
0ºN
Latitudes
50ºN
25ºS
Locations to the north and south of the Equator are
marked along circular parallel lines drawn around
the Earth. These lines are called the parallels and
their positions are measured in degrees: the Equator
is the Zero Degree line, the North Pole is at a 90º N
angle to the Equator and the South Pole lies at a 90º S
angle to the Equator. The measurement of the northsouth
position is called latitude.
The latitude of the Tropic of Cancer is 23º 30’, exactly
the same as the Earth’s tilt relative to the plane of
its orbit around the Sun!
To determine the latitude of a location during the day, in addition to knowing the angle of the midday sun above
the horizon, the date, your approximate position on Earth, you also need to know if you are in the Northern or
Southern Hemisphere and your position relative to the tropics. In the Northern Hemisphere the angle of the North
Star 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.
North Star
• Measure the angle of the North Star above the horizon with your quadrant. This angle is the latitude of the
place you are in.
• Use your protractor to measure the angle of your sundial straw above the horizon. This angle should be roughly
the same as the latitude of your position.
30º
30º
The horizon
Latitude:
30ºN
Equator
9

10
17 th century Portuguese astrolabe.
• Use your quadrant and your protractor to measure
the height of the noon sun. Compare the values
obtained. You can calculate the noon sun time with
the aid of your sundial.
Based on experiments with stick shadows and much observation of the Sun and the North
Star, 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 north
or 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 ocean
voyages from the 15th century on. They enabled sailors to return to
their point of origin as well as allowing them to make other voyages
along the same routes.
It was during the 16th century that Portuguese mathematician Pedro
Nunes developed instruments which allowed navigators to draw
accurate charts of their sea routes.
The modern version of the astrolabe
and the quadrant is the sextant,
which is still used today by all boats
that sail the seas.
Pedro Nunes was born in Alcácer do Sal in 1502. He lived at the height of the Portuguese Discoveries and in 1529 he was appointed
Royal Cosmographer by D. João III.
In order to resolve some of the difficulties of navigation, Pedro Nunes invented several astronomical instruments, such as the
universal ringdial, the solar compass and the nonius, nowadays called vernier. The first two calculate the height of the Sun in
the 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 astronomy
have been the basis of the modern description of planet movement since the end of the 16th century.

We now know how to determine locations further north or further south on the Earth, in other words, we can
determine the latitude of a location. To pinpoint our position on Earth, we need to know if we are further east
or 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 was
born about 2170 years ago. Ptolemy decided to draw vertical circles around the North and South Poles and call
them 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 Canary
Islands. This, however, is largely a matter of choice and kings and ministers over the years have changed the Prime
Meridian to pass through the Azores, Cape Verde, Rome, Paris, Philadelphia and London. Today, it passes through
the 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 on
the fact that the Earth spins full circle on its northsouth
axis approximately every 24 hours. We need
to know the time difference between the noon sun
of our position and that of a reference position.
These times are determined by the maximum height
of the sun at both locations. As the Earth spins
a complete circle (360 degrees) every twenty-four
hours, for every hour of difference between noon
at 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 show
noon times for the port of origin for each day
of the year, pilots can calculate the time differences
between noon at their current location and
at the port of origin.
For each hour of difference, they are roughly
15 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 above
the horizon, we know which parallel we are on.
Knowing the parallel and the meridian, we can now
pinpoint our position on the terrestrial globe.
40ºW
20ºW
Meridians
0º
20ºE
The Greenwich
Meridian
Zero degrees
longitude
Equator
The longitude scale
is marked along the
line of the Equator
11

12
However, taking a clock on a boat was a tricky business. 15th , 16th , 17th and 18th century clocks did not take
kindly 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, transporting
a clock on board ship was considered the biggest problem in nautical science. Problems caused by ships sailing
off course and shipwrecks were so great that in 1598, King Philip of Spain offered a prize to anyone who could
discover a practical way to determine longitude. Later on, in 1714, the English King George III, by request of
sailors and traders, introduced the Board of Longitude Award for anyone who could come up with the solution
to the longitude problem.
An accurate time-keeping clock was designed by the English carpenter John Harrison in the mid 18th century and
its first sea test was carried out in 1736 on a voyage to Lisbon. John Harrison’s invention was only recognised in
1773, 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 with
many tales of accidents caused by sailing off course. Navigators very often played it safe and followed the same
routes along the parallels, always keeping the noon sun at the same altitude. This was the case with Christopher
Columbus who arrived in America in 1492 by sailing along the same parallel.
Sample latitude and longitude:
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
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, he
left his native village for London, where he presented his sea-clock designs to Edmond Halley, one of the most famous astronomers
of the time, but Halley received the plans sceptically. In the five years that followed, Harrison dedicated himself to building the
first sea-clock prototype. This clock, which may be seen in the Greenwich Museum, still keeps accurate time. It weighed 35 kg
and had four dials which showed the day, the time, the minutes and seconds. It was tried out successfully for the first time on
the H.M.S. Centurion voyage to Lisbon where it kept time to within some seconds a day. John Harrison was about to win the
Board of Longitude Prize. Much to everyone’s surprise, he asked to be given time to perfect his prototype. Harrison was not happy
with either the precision or the size of his clock. Over the following twenty-five years, he built three more prototypes. During
this time, he had the full support of the English Royal Society and developed all of the mechanisms which form part of the working
of 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 the
Board 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 malfunction
in four hundred years’ time!

During the time of the Discoveries, Portuguese navigators succeeded in making charts of undiscovered areas using
just an astrolabe, a magnetic compass, a compass, a globe and an hour-glass. One of these maps is the 1502
Alberto Cantino planisphere.
Tropic
of Cancer
Equator
Tropic
of Capricorn
Longitude
1502 Cantino planisphere showing the meridians and the parallels.
Greenwich Meridian
0º
Present day map showing the same area as the Cantino planisphere.
Latitude
23º 30’N
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 idea
of the shapes of the seas and continents, were of invaluable aid to sailors and traders.
0
23º 30’ S
13

14
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 uses
his 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. Then
he 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 the
equator: as the North Star is at a 90º angle relative to the Equator, latitude would be calculated at 90º minus the
angle of the Sun above the horizon. On the other hand, since I left Lisbon several days ago, the midday sun has
always 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:
Because the midday sun is on the Equator during the equinox
and the Equator is at a 90º angle relative to the North Star,
the latiude measured from the Sun’s angle at midday is equal
to 90º minus the angle of the Sun above the horizon.
The Sun during the Equinox
Height of the Sun
The North Star
Lat.
Lat.
The horizon
N
S
Cancer
Equator

If it was during the solstice, the position of the Sun would be like this:
The Sun during
the solstice
23º 30’
Height of
the Sun
If today were June 21 st , the midday sun would be on the vertical of the tropic of Cancer and
would no longer be at a 90º angle with the North Star. But as the latitude of the Tropic of Cancer
is 23º 30´ from the height of the Sun in my current location to determine the height of the Sun
relative to a point on the Equator. With this new angle, I could calculate latitude as if it were a
day during the equinox.
North Star
Lat.
23º 30’
The horizon
N
Lat.
S
Tropic
of Cancer
Equator
As there are 92 days between the solstice and the equinox, the height of the midday sun relative to the equator
varies 15’ 20” per day. I got this figure by dividing 23º 30’ by 92 days. So, on July 22nd , 61 days before the equinox
the 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 angle
from 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 my
location. With the aid of the navigation tables drawn by the astronomers of my port of origin, I know that the noon
sun in Lisbon was at 12:43. The noon sun at my location was 45 minutes later than in Lisbon. As the Earth spins
15º per hour, a time difference of 45 minutes corresponds to an angle of 11º 15’. So, as the Earth spins from West
to 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 see
that 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.
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The Ecliptic
Over two thousand years ago, while Egyptian and Greek astronomers were watching the night sky, they realised that
there 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 Sphere
and the set of stars the heavens. Today we know that this is not the case. The stars in the heavens move but they are
so 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 same
position in the heavens. But what happens in relation to the Sun?
If we mark the position of the midday sun in the Celestial
Sphere every day for a year, it will show a
circumference with a 23º 30’ incline relative to the
equator of the Celestial Sphere. The apparent
orbit of the Sun in the Celestial Sphere is
called the ecliptic. The incline of the
ecliptic is the same as the north-south incline
relative to the plane of the Earth’s orbit.
It is approximately midday on March 21st at the point where the Equator meets
the Greenwich meridian that the Sun in
its apparent movement around the Earth, 23º 30’
intersects the Celestial Equator. It is from Winter
Solstice
this moment that clocks which show days,
nights and seasons are set. To maintain the
regularity of the Sun’s apparent movement
around the Earth, we need to adjust the calendar
Celestial Sphere
Ecliptic
Celestial
Equator
Summer
Solstice
23º 30’
every leap year and less often we need to put the clocks
back or forward a few seconds. For example, under the Papal
Decree of 1582, the 5th of October became the 15th of October. On the eve of the year 2000, the final seconds should
have 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 determine
latitude and longitude. The International Astronomy Union meets periodically to present average figures of the incline
of the ecliptic and year length. Knowing that the Earth spins an average 15º every hour and that on 21st March 1999
at 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 on
the Earth. For instance, in the year 2000 the ecliptic is at an angle of 23º 26' 21" to the Celestial Equator. The Earth
spins an average of 15º 2' 28" every hour and the year is approximately 365 days, 5 hours, 58 minutes and 54 seconds.

It is by using data on the apparent movement of the Sun in the Celestial Sphere that astronomers draw up maritime
charts for navigators. For instance, to determine the latitude of a location on any given day of the year, a navigator
needs to know the height of the noon sun on the ecliptic. So astronomers draw up charts of the incline of the
Sun throughout the year, as shown in the chart below. According to the chart, on 22 nd May, for example, the
midday sun is on the vertical of the 16º N parallel. On the 7 th November, the midday sun is on the vertical of the
12º parallel. The negative values in the chart refer to latitudes south of the Equator.
0º
5º
-5º
10º
-10º
Angle of correction used in determining latitude
15º
EMBER AUGUST
-15º
JULY
20º
23º30’ 20º
JUNE
-20º -23º30’-20º
MAY
MARCH FEBRUARY JANUARY DECEMBER NOVEMBER OCTOBER SEPT
15º
-15º
APRIL
10º
-10º
5º
-5º
0º
17

18
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 adding
12 hours to the minutes shown in the chart. Using these charts, a quadrant, a compass and a clock with a local
reference time, it is always possible to know where we are on Earth.
JUNE
JULY
32 33 33 34 35 36 37 39
APRIL
MARCH
Noon Sun at the
Pavilhão do Conhecimento
Lisbon 9º 5’ 42” W
MAY 40 42 44 45 47 48 49 50 50 51 51 50 50 49 47 46 44 42 40 38 35 3331 29 27 25 23 22
Corrections
Oporto: about 3 minutes earlier
Bragança: about 10 minutes earlier
Faro: the same time
Azores: about 1 hour and 3 minutes later
Madeira: about 31 minutes later
For mainland Portugal and Madeira, add one hour
during the period between the last Sunday in
March and the last Sunday in October. For the
Azores, subtract one hour between the last Sunday
in October and the last Sunday in March.
Using these charts, a quadrant, a compass and a clock with a local reference time, it is always possible to know
where we are on Earth.
FEBRUARY JANUARY DECEMBER NOVEMBER OCTOBER SEPTEMBER AUGUST
21 20 20 20 20 21 21 23 24 26 27 29 31 33 35 36 38 39 40 41 42 4242 42 42 41 40 39 38 37 36 35 34 34 33 32 32

The GPS
Nowadays, longitude and latitude can be calculated electronically using man-made satellites. This is a great aid
to 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 above
sea-level. All in all, there are 24 satellites 20 200 km high which
orbit the Earth every 12 hours. These satellites continually
transmit radio waves to Earth, where they are captured by
an antennae. Using an apparatus specially designed to
capture these signals, we can immediately discover latitude,
longitude and altitude on Earth. The signals from five
out of eight of these satellites can always be received
anywhere on Earth.
This system is called GPS - Global Positioning System.
The GPS satellite constellation in orbit
around 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 GPS
receivers. However, reception of GPS signals is
dependent on atmospheric weather conditions, so
as a precaution, ships always carry a sextant on board.
19

20
The Map of the Earth
A map is a simplified representation of populated areas, geographical features, roads, rivers, continents and
oceans. As well as maps of the Earth and its countries, there are city plans and ordnance survey charts. These are
all maps. In the past they were drawn using a compass, an astrolabe and a tape measure. Nowadays, they are
charted 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 represents
the deeper ocean beds and light blue the shallower beds. The continents are shown in yellow and the darker
areas are the contours. The positions of the Equator, the Greenwich meridian, the Tropics of Cancer and
Capricorn, the Arctic and the Antarctic Circles are shown on the map.
• Look at the map or at your globe. Find the mountains on the sea bed. Find the Azores archipelago and notice
how 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.

• Here is an aerial photograph of Lisbon and Setúbal. Use tracing paper to copy the picture. Draw a map of this
area and identify what you think are the relevant features. For example, rivers, bridges, roads, etc. Try to lay
out your own map. This is how modern maps are made.
21

22
Measuring latitude and longitude
Just before noon, point your sundial to the south with the aid of a compass. But the compass only gives an
approximate indication of the North Pole’s position and your sundial needs to be accurate, so if you are in mainland
Portugal you should turn it about 5º East. In the Azores, this angle needs to be 11º and 8º in Madeira. These
angles 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 to
measure 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 15 th and 16 th century
Portuguese navigators. Look at the circular chart on Page 17 to find out the necessary correction angle for latitude
of 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 the
shadows it casts with chalk, then check the time. When the shadow is at its shortest then it is noon. In addition, the noon shadow
points exactly North. Now you can carry out your experiment setting your sundial by the shadow and you don’t even need to
use 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 point
and noon time at this point. Let’s use the Pavilhão do Conhecimento in Lisbon, Latitude 9º 5’ 42” W as our
reference point.
Just before noon, point the sundial to the south as described in the above activity. At noon, that is when the
shadow of the straw on your sundial falls on 12 on the scale, look at the time on your wristwatch, which must
be 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 do
Conhecimento:
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 = 5
minutes; 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 =
23

24
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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 the
21 st 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 rose
with north pointing to the North Pole.
You can do lots of activities with your globe. For example, you can draw national borders, the largest rivers
and deserts on Earth, the sea routes of 15 th and 16 th century Portuguese navigators and many more.

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Fundos Nacionais do MCT