This document provides information about latitude, longitude, and the coordinate system used to locate positions on Earth. It defines key terms like latitude, longitude, meridians, parallels, and the differences between them. Methods for calculating distances between points and angles subtended at the center of Earth are presented. Worked examples demonstrate how to find latitudes/longitudes of points, distances along meridians/parallels, and the shortest distance between two points on a great circle.

1. Prepared by
Pn Hjh Saripah Ahmad
sahgi63@yahoo.com.my
H/P: 0133759142
SEK MEN SAINS MUZAFFAR SYAH
MELAKA

3. Great Circle is a circle on the
surface of earth through the north
and south poles and its centre is
in the centre of the earth

4. I’ve got an attitude for latitude and longitude.
I’ve got an attitude for latitude and longitude.
The Equator is the center of the world you know
With a latitude number that says zero.
It divides the globe into North and South
In two hemispheres...
...I’ve got an attitude for latitude and longitude.
I’ve got an attitude for latitude and longitude.
The longitude lines travel up and down...
...I’ve got an attitude for latitude and longitude.
I’ve got an attitude for latitude and longitude.
So that’s the story about the map’s strange grid...
...I’ve got an attitude for latitude and longitude.
I’ve got an attitude for latitude and longitude.
I’ve got an attitude for latitude and longitude.
I’ve got an attitude for latitude and longitude.
The Longi t ude / Lat i t ude Rap
Ron Br ownListen this
song

6. LONGITUDE
Longitude lines are made by circles that
intersect with both the North and South Poles.
Each longitude can be thought of as dividing
the Earth in half. Longitudes are measured in
half circles of 0 degrees to 180 degrees East
and from 0 degrees to 180 degrees West from
the Royal Greenwich Observatory in
Greenwich, England. The Royal Greenwich
Observatory was established in 1675 to
advance the art of navigation.

7. The lines of longitude divide
the earth into Eastern and
Western hemispheres.

8. The equator is located at 0 degrees latitude. It
is 24,901.55 miles (40,075.16km) long. The
equator divides the planet into the Northern
and Southern Hemispheres.

9. The vertical longitude lines are also known as meridians. They converge
at the poles and are widest at the equator. Zero degrees longitude is
located at Greenwich, England (0°). The degrees continue 180° east and
180° west where they meet and form the International Date Line in the
Pacific Ocean.
The memory rhyme I use to help remember that
lines of longitude denote east-west distance is:
"Lines of LONGitude are all just as
LONG as one another."
With this saying in my mind, I picture all of the
longitudinal meridians meeting at the poles, each
meridian the same length as the next.

10. Learning Outcomes :
ii) Sketch a great circle through the north and south poles.

12. (ii) State the longitude of a given point
Longitude of a Given Point
150o 160o

13. 80o

14. iii) Sketch and label meridian with the longitude given
37o
E b) 108o
3’ W

17. iv) Find the difference between two longitudes.

20. When looking at a map, latitude
lines run horizontally. Latitude lines
are also known as parallels since
they are parallel and are an equal
distant from each other. To
remember latitude, imagine them as
the horizontal rungs of a ladder
("ladder-tude"). Degrees latitude are
numbered from 0° to 90° north and
south. Zero degrees is the equator,
the imaginary line which divides our
planet into the northern and southern
hemispheres. 90° north is the North
Pole and 90° south is the South Pole.
Longitude slices the long way around.
Latitude dices climb up or down.
Longitude lines go from pole to pole.
Latitude's parallel, that much I know.

21. Sketch a circle parallel to the
equator.
.
parallel

22. State the latitude of a given point.

25. Sketch and label a parallel of latitude.

28. Find the difference between two
latitudes.
(iv).

30. People pinpoint places on the Earth using a pair of
coordinates known as latitude and longitude. Latitude
describes a location’s distance from the Equator.
Longitude describes its relative distance east or west
of a north-south band called the prime meridian,
which runs through Greenwich, England. The latitude
and longitude of any place on Earth’s surface define
its unique global address.
WHERE IS MALAYSIA

31. The diagram shows two points C and D on the
surface of the earth. State their locations.
a) Latitude of C = 72°N
Longitude of C = 75°E
Location of C is (72°N, 75°E)
b) Latitude of D = 80°S
Longitude of D = (180 - 35)°W
= 145°W
Location of D is (81°S,145°W)

33. Marking the Location of a Place
In order to mark the location of a point M (x °N, y °E),
we find the point of intersection of latitude x °N and
longitude y °E.
Mark the locations for the
following points:
a) A (68°N, 145°W)
b) P (71°S, 35°E)
c) C (0°S, 75°E)
A is the intersection point of latitude 68°N
and longitude 145°W(from [180 - 35]°)
P is the intersection point of latitude 71°S
and longitude 35°E.
C is the intersection point of latitude 0°
and longitude 75°E.

34. Sketching and Labelling the Latitude
and Longitude of a Given Place
If the latitude and longitude of a place is given, we can sketch the
meridian and the parallel of latitude on a sphere. The location of the
given point is the intersection point of the latitude and the longitude
and this can be represented by a point on the sphere.

35. Follow the steps given below to sketch and label the point for Q
(40°N,50°W)
STEP 1
Sketch a circle to represent
earth with its polar axis NOS.
Sketch the equator and
the Greenwich Meridian NGS.
STEP 2
Mark angle GOH = 50° on the
equator. Sketch and label
the longitude 50°W.
∠
Step 3
On the meridian plane of
50°W, mark angle QOH = 40° from the
equator to the north. Sketch and label
the parallel of latitude that passes through
Q, which is 40°N.
Mark the intersection point as N Q.

37. DISTANCE ON THE SURFACE OF THE EARTH
Finding the length of Arc of a Great Circle in Nautical Mile
Two places A and B lie on the equator,
with longitude 23°W and 24°W
respectively. The angle subtends at the
centre of the earth, O, is angle AOB and
has a value 1°. The distance from A to B
on the surface of the earth is equivalent to
60 nautical miles. Since 1° = 60',
then 1' = 1 nautical mile.
The nautical mile is defined as the length
of arc of a great circle on the earth’s
surface which subtends an angle of 1' at
the centre of the earth.

38. Figure above shows a great
circle through the plane cutting
across the polar axis NOS
Figure above shows a globe
with WABCED as the equator.
F
Arc Angle subtends
at earth’s centre
Distance
computation
Distance in nautical miles
DE 15O
15 x 60 900.n.m.
EF 45o
45 x 60 2700.n.m.
Arc Angle subtends
at earth’s centre
Distance
computation
Distance in nautical miles
AB 20O
20 x 60 1200.n.m.
BC 90o
90 x 60 5400.n.m.
CD 50o
50 x 60 300.n.m

39. The distance along the equator
between J and R is 1234
nautical miles. Find the angle
subtended by the arc JR at the
earth’s centre, O.
Distance between J and R = 1234
nautical miles. =JOR = 1234'
= 20°34'
The angle subtended by the arc JR
at the earth’s centre is 20°34'.

40. Finding the length of an arc of a great circle in nautical mile,
given the subtended angle at the centre of the earth and vice versa.
Convert the angle to ‘minutes’ and hence you can determine the
distance between the two points along the meridian in nautical miles.
Points A and B on
longitude 35°W.
The difference in latitude
between A and B
= (70 - 35)°
= 35° x 60 = 2100'
The distance between A
and B along the meridian
is 2100 nautical miles.
Points A and B on
longitude 123°E.
The difference in latitude
between A and B
= (65 - 15)°
= 50 °x 60 = 3000'
The distance between A
and B along the meridian
is 3000 nautical miles.
Points A and B on
longitude 93°W.
The difference in latitude
between A and B
= (73o
54’ + 47o
16’)°
= 121° 10’
= 121X 60 + 10’
= 7270’
The distance between A
and B along the meridian
is 7270 nautical miles.

42. Finding the latitude of a point given the latitude of another
point and the distance between the two points along the same
meridian.
If you are given the distance between two points and the latitude of any
one of the points, then the latitude of the second point can be determined.
a) A and B are both located north of the equator.
The distance between A and B along the meridian
is 600 nautical miles and the location of B is
(15°N, 101°E) Difference in latitude = 600 ÷ 60
= 10°
Since A is north of B, latitude for A is (15 + 10)°N
= 25°N
• A is north of the equator and B (23°10'S, 50°W)
is south of the equator.
Distance A from B along the meridian is 240nautical miles.
Difference in latitude = 2400 ÷ 60
= 40°
Since A is north of the equator, latitude for A is
(40° - 23°10')N = 16°50'N

43. The distance between 2 points A and B along a great
circle = 60 x θ nautical miles, where θ is an angle
subtended by the arc AB at the center of a great circle.
N
S
W E
O
θ
A B
60° E40° W
θ = 40° + 60°
= 100°
The distance between
A and B along the
equator
= 60 x 100
= 6000 nautical miles
Great Circle
(equator)
Horizontal

44. N
S
W EO
A
40° N
θ = 40° + 70°
= 110°
The distance between
A and B along the
meridian
= 60 x 110
= 6600 nautical miles
Great Circle
(meridian)
B
70° S
Vertical

46. Finding the distance between two points measured along
the equator, given the longitudes of both points.
The only parallel of latitude which is a great circle is the Equator. The
distance between two
points on the equator is the ‘difference in longitude in minutes’.
The globe shows 4 points P, G, R and T on the
equator. NGS is the Greenwich Meridian. The
diagram below the globe is the cross-sectional
view of earth through the equatorial plane.
The distance PG = 56 x 60
= 3360 nautical miles.
The distance GR = 20 x 60
= 1200 nautical miles.
The distance RT = (52 x 60) + 12
= 3132 nautical miles.

48. Finding the longitude of a point given the longitude of
another point and the distance between the two points along
the equator.

51. Stating the relation between the radius of the earth and
the radius of a parallel of latitude
As we know, the radius of the equator is the radius of the earth, R. As
we move northward or southward, the radius of the parallel of latitude
becomes shorter and shorter until the North or South Pole when the
radius becomes zero.
Observe the point P with latitude X °N, and Q is the centre of the
parallel of latitude on which P lies. Since angle OPQ and angle POT are
alternate, angle OPQ = Xo
.
T

52. Find the relationship between the radius of the parallel of latitude
60°N, r, and the radius of the earth, R.
Radius of parallel of latitude 60°= Radius of earth x cos 60°
r = R cos 60°
r = R x 0.5
:. r = 0.5 R

53. Stating the relation between the length of an arc on the
equator between two meridians and the length of the
corresponding arc on a parallel of latitude.
If R = radius of earth and r = radius of a parallel of
latitude ø°, then we can obtain the ratio.

54. Find the distance of AB measured along parallel of latitude
a) A (28o
N, 18o
E), B (28o
N, 107o
E) b) A (37o
S, 108o
W) , B (37o
S, 5o
W)

55. The distance between 2 points A and B along the circle
of latitude x° N or x° S = 60 x θ x cos x nautical
mailes, where θ is the angle subtended by the arc AB at
the centre of the circle latitude.
θ
A B
50° E40° W
O
N
S
50° N
θ = 40° + 50°
= 90°
And x = 50°
The distance between
A and B along
latitude 50° N
= 60 x θ x cos x
= 60 x 90° x cos 50°
= 3471 nautical miles

56. Find the distance of AB measured along parallel of latitude
c) A (63o
N, 23o
E), B (63o
N, 74.5o
W) d) A (42o
5’S, 37o
14’W),B(42o
5’S, 94o
50’
E)

57. Finding the longitude of a point given the longitude of
another point and the distance between the two points along
a parallel of latitude.

60. Finding the shortest distance between two points on the
surface of the earth.
The shortest distance between two points on the surface of the
earth is along the great circle which passes through both points.

62. solving problems involving
a) distance between two points,
b) travelling on the surface of the earth.

65. P(61o
N,10o
E) and Q are two points on the surface of the earth such
that PQ is the diameter of a parallel of latitude
(b) Find the longitude of Q [ 1 mark ]
(c) PR is the diameter of the earth, On the diagram mark the position
of Q and R , Hence, state the position of R [ 4 marks]
(d) Calculate the shortest distance, in nautical mile, from Q to the
North Pole.[ 2 marks ]
(e) An airplane took off from P and flew due west a long its parallel of
latitude with an average speed of 500 knot. The airplane took 9
hours to reach a point M.
(f) Calculate
(i) the distance, in nautical miles, from P to M
(ii) the longitude of M
N
S
P
Equator