Chapter 23 I Earth as a Sphere ENHANCE

8/6/2019 Chapter 23 I Earth as a Sphere ENHANCE

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CHAPTER 23: EARTH AS A SPHERE

23.1 LONGITUDE

Great Circles are circles with their centres at the centre of the earth.

Meridians are semicircles connecting the North Pole and the South Pole, running on the

surface of the earth. The longitude of a meridian is determined by

(i) the angle between the plane of the meridian with that of the GreenwichMeridian

(ii) its position to the left or to the right of the Greenwich Meridian.

The longitude of a given point is written asx0E orx0W.

State the longitude for the points given below (NMS is the Greenwich Meridian)

Earth As A Sphere 1

a)

Example:

Longitude for P = 35W

Longitude for R = 60E

Longitude of P =

Longitude of R =

b) Longitude of P =

Longitude of R =

Greenwich Meridian


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The difference between two longitudes:

o If both longitudes are from the same sides of the Greenwich Meridian, (both E

or both W), then the difference between the two longitudes is the difference of

the angles.

o If the longitudes are from different sides of the Greenwich Meridian, (one E

and the other W), then the difference between the two longitudes is the sum of

the angles.

The difference in longitudes = 400 ( - 200) = 600.

Ex. 2 : Calculate the difference between the two given longitudes.

(Note : Sketch a diagram to help you understand better)

23.2 LATITUDE

The Equator is a great circle with its plane that is perpendicular to the axis of the earth.

Parallels of latitudes are circles with planes perpendicular to the axis of the earth and areparallel to the equator.

Earth As A Sphere

Example

1. 25 o E, 135 0 E

Difference : 1350 250 = 1100

2. 40 0 W , 120 0 W 3. 10 0 E , 90 0 E

4. 135 0 W , 20 0 E

Difference : 200 (-1350)=

5. 125 0 E , 60 0 W 6. 15 0 E , 120 0 W

7. 70 0 W , 10 0 E

Difference :

8. 10 0 E , 100 0 E 9. 115 0 E , 5 0 W

2

200 W400 E

600P

N

S

Q

Equator


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Latitude is the angle at the centre of the earth subtended by an arc of a meridian running

from the equator to a parallel of latitude.

The latitude of a point is written as x0 N orx0S.

The latitude of the Equator is O0.

Latitudes ranges from 00 to 900 N ( or S).

All points on a parallel of latitude have the same latitude.

Example 1

1. State the latitude of the given points (EF is the equator).

Exercise 1

1. State the latitude of the given points (EF is the equator).

a) b)

Earth As A Sphere 3

Latitude of K = 45N

Latitude of L = 50 S

Example:

Latitude of K =

Latitude of L =

Latitude of K =

Latitude of L =


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Earth As A Sphere 4


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2. Calculate the difference between the two given latitudes.

Example

1. 10 0 S, 70 0 S

Difference : 700 100 = 60 0

2. 25 0N , 60 0N 3. 75 0N , 45 0 S

4. 50 0 S , 70 0N

Difference : 700 (-500)

=

5. 91 0N , 31 0 S 6. 70 0 N, 400N

7. 55 0N , 10 0N 8. 80 0N , 15 0 S 9. 38 0 N, 120 S

10. 32 0N , 10 0 S 11. 70 0N , 5 0 S 12. 35 0 S, 15 0 S

23.3 LOCATION (POSITION) OF A PLACE

Every place on the surface of the earth is represented by a point on the globe.

Its location is determined by the point of intersection of the relevant parallel of latitude andmeridian.

Ex. The location of X is ( 600 N, 200 W )

The location of Y is ( 600 N, 400 E )

If the longitude of P is 500 W and PQ is the diameter of the earth, then the

longitude of Q is 1300 E. Hence the location of Q is (00, 1300 E)Earth As A Sphere 5

200 W400 E

600 N

P

N

S

Q

The Equator

Y

X

500 W


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Exercise 23.3 A : To determine the location of a place (denoted by a point)

(You need to be able to state the latitude and longitude of the point)

1.

2.

Earth As A Sphere 6

PQ is a diameter of the earth.

Point Location

P ( 00, 1000 W )

Q

A

B

C

D

E


Point Location

P

Q ( 00, 1100 E )

W

X

Y

Z

R

400 E

500N

1000 W

S

N

OQ

BA

C

D

P

E

200 W600N

700

W

S

N

OQ

W

Y

X

Z

P

R


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23.4 Given Point X, To Determine The Location of Y if XY is the Diameter of a given

Parallel of Latitude.

Earth As A Sphere 8

EX. 23.4A 1.


XY is the diameter of the 600 N parallel

of latitude.

Complete the table below :

PointLocationX(600 N, 300 W )YRT

N

X

Y

P Q

S

300 W 600 N

O

T

R

EX. 23.4A 2.


XY is the diameter of the 600 N parallel

of latitude.

Complete the table below :

PointLocationXYRTKL

N

X

Y

P Q

S

150 W 550 N

O

T

R

800 N

K

L


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23.5 Given P, To Determine The Location of Q if PQ is The Diameter of The Earth.

Earth As A Sphere 9

EX. 23.5A 1.

PQ, XY and AB are diameters of the

earth.

State the location of each of the

following points:

PointLocationP( 00 , 1000 E )QABXY

Y

P

A

750N

1000 E

S

N

O

B

Q

800 E

X

EX. 23.5 A 2.

PQ, XY and AB are diameters of the

earth.


following points:

PointLocationP( 00 , 600 E )QABXY

Y

Q

A

700N

600 E

S

N

O

B

P

800 E

X


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23.6 To Determine the Location of a Point Given the Difference in Longitudes.

Earth As A Sphere 10

B

Q

A EX. 23.6 A1.



following points:

PointLocationA( 750 N , 300 E )XYB

750N

S

N

O

Y

P

300 E

X

400

A

Q

B EX. 23.6 A 2.


State the location of each of thefollowing points:

PointLocationA( 750 N , 300 B )YXB

750N

S

N

O

Y

P

300 B

X

500


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23.7 To Determine The Location of a Point Given the Difference in Parallels of Latitudes.


B

Q

A EX. 23.7 A1



following points:

PointLocationA( 35

0

N , 42

0

E )BYX

350N

S

N

O

Y

P

420 E

X

500

180 W

B

Q

A EX. 23.7 A2.


State the location of each of thefollowing points:

PointLocationA( 550 N , 660 E )BXY

550N

S

N

O

Y

P

660 E

X

600

100 E


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Questions Based on the Examination Format (Paper 1)

1. In Diagram 1, N is the North Pole, S is the South Pole and NOS is the axis of the earth.

2. P(150N, 100E), Q and R are three points on the earth surface. Q is due south of P. The

difference in latitude between P and Q is 650. R is due west of Q. The difference inlongitude between Q and R is 800. The position of R is

A ( )80 ,90S E C ( )50 ,70S E

B ( )80 , 70S W D ( )50 ,70S W

3. In Diagram 3, N is the North Pole, S is the South Pole, NOS is the axis of the earth and

PR is a diameter of the parallels of latitude.


Find the position of point R.

A ( )50 ,50N W

B ( )50 ,130N W

C ( )50 ,50N E

D ( )50 ,130N E Diagram 3

600

60000

N

S

CO

GreenwichMeridian

D

A

B

Considering the four points A, B, C and

D, which of these is (600 N, 00 E) ?

Diagram 1

500

500

0

0

S

O

P RN

Greenwich

Meridian


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4. Diagram 4 shows the position of five towns, A, B, C, D and X, on the surface of the

earth.

5. In Diagram 5, N is the North Pole, S is the South Pole, NOS is the axis of the earth.

(For the questions below you are strongly advised to sketch a diagram!)

6. The shortest distance in nautical miles from P(60 N, 120 W) to Q(50N, 120W) viathe north pole is

A 600 B 3600 C 4200 D 6600


The position of point P is

A ( )10 ,80N W

B ( )10 ,100N W

C ( )80 ,80N W

D ( )80 ,100N E

800

1000

S

O

P

Diagram 5

N

Greenwich

Meridian

Equator

100N

A

Which of the town, A, B, C orD, is located east of X with

difference in longitude of 600 ?

500N

S

N

D

B

400 E

C

600 W

200 W

600 E

X

Diagram 4


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15. P(25 N, 50 W), Q and R are three points on the earths surface. Q is due south of P

and the difference in latitude between P and Q is 60. R is due west of Q and the

difference in longitude between Q and R is 80. The location of R is A (35 S, 30 W) C (85 S, 30 W)

B (35 S, 130 W) D (85 S, 130 W)

16. M(50 N, 110 E) and N are two points on the earths surface. Given that MN is the

diameter of a great circle, find the position of N.

A (40 S, 70 W) C C (50 S, 70 W)

B (40 S, 110 E) D (50 S,110 E)

17. F (80 N, 42 W) and G are the two points on the earth surface . Given that FG is the

diameter of the great circle , the position of G is

A (80N , 138 E) C (10N, 138 E)

B (80 N, 42 W) D (10 N, 42 W)

18. U (0 N, 0 E) and V is the two points on the surface earth . V is 40 due east of U.The position of V is

A (0 N, 40 W) C (40 N, 50 W)

B (0 N, 40 E) D ( 40N, 40 E)

19. J(30 N, 80 E) , K and L are three points on the earth surface. J is due to north K. The

difference in the latitude between J and K is 50. L is due west of K and the differencein longitude K and L is 60. The position of L is

A (50 N, 60 E) C (20 S, 140 W)

B (80 N, 140 W) D (20 S, 20 E)

20. P and Q are two points on the equator. The shortest distance between P and Q is 4320

nautical miles. Q is due east of P and the longitude of Q is 80 E. The longitude of P is

A 8 E C 72 W

B 8 W D 152 E

21. M (5 S , 87E) and M(63 S, 87 E) are two points on the surface earth. Calculate the

distance in nautical miles , between the two points measured along the meridian

A 3480 C 4080

B 3780 D 5220

22. J and K are two points on the equator of the earth. Given that the distance between thetwo points is 1440 nautical miles measured the equator. Find the different in longitude

of two pointsA 14 C 36

B 24 D 66



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23. P(0N , 20 E), Q and R are three points on the surface earth. Q is due west of P and R

is the midpoint of PQ The distance between P and R is 3000 nautical miles. Find the

longitude of Q.

A 5 E C 5 W

B 70 E D 30 W

24. X( 50 N, 140 E) and Y (60 N, 40 W) are two points on the earth surface. Calculate

the distance in nautical miles between X and Y via North pole.

A 3000 C 4200

B 3600 D 6600

25. P (60 0 S, 90 0 E) and Q (60 0 S, 90 0 W) are two points on the surface of the earth.

Calculate the distance in nautical miles from P to Q measured along the common

parallel of latitude.

A 10800 C 5400

B 7200 D 3600



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Past Year SPM Questions (Paper 1)

1. (2003N, P1, Q15)

In Diagram 8, N is the North Pole, S is the South Pole and NOS is the axis of the earth.

Considering the four points A, B, C and D, which of these is (40 0 N, 00 E)?

2. (July 2004, P1, Q19)

( )40 ,60M N W and N are two points on the earths surface. If MN is a diameter of the

parallel latitude, the position of point N is

A ( )40 ,120S W

B ( )40 ,120S E

C ( )40 ,120N W

D ( )40 ,120N E

3. (November 2004, P1, Q17)

P(150N, 100W), Q and R are three points on the earth surface. Q is due south of P. The

difference in latitude between P and Q is 500. R is due west of Q. The difference in

longitude between Q and R is 700. The position of R is

A (650N, 600E)

B (650N, 800W)

C (350S, 600E)

D (350S, 800W)Earth As A Sphere 17

400

60000

N

S

CO

Greenwich

Meridian

D

A

B

Diagram 8


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4. (July 2005, P1, Q18)

Diagram 10 shows three points P, Q and R on the surface of the earth. P and Q lie on the

equator. NPS is the Greenwich Meridian and O is the centre of the earth.

State the position of point R

A ( )40 ,50N E C ( )40 ,50N W

B ( )50 ,40N E D ( )40 ,50S W

5. (November 2005, P1, Q17)

In Diagram 10, N is the North Pole, S is the South Pole, NOS is the axis of the earth and

PR is a diameter of the parallels of latitude.


Find the position of point R.

A ( )40 ,70N W

B ( )40 ,70N E

C ( )40 ,110N W

D ( )40 ,110N E

400

700

0

0

S

O

P R

Diagram 10

N

Greenwich

Meridian

N

S

P Q

O

R

40o

50O

DIAGRAM 10


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6. (November 2005, P1, Q18)

Diagram 11 shows the position of five towns, A, B, C, D and X, on the surface of the earth.

7. (July 2006, P1, Q18)

In Diagram 9, N is the North Pole, S is the South Pole, NOS is the axis of the earth.


Which of the town, A, B, C or D,is located east of X with difference

of 400 in longitude?

100N

A 500N

S

N

D

B

200 E

C

600

W

200 W

400 E

X


A (600 N, 800 W)

B (600 N, 1000 W)

C (800 N, 600 E)

D (800 N, 1000 E)

600

800

S

O

P

Diagram 9

N

Greenwich

Meridian

Equator


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8. (November 2006, P1, Q18).

In Diagram 10, N is the North Pole, S is the South Pole and O is the centre of the earth. R

is the centre of the circle of latitude 30 N .

DIAGRAM 10


A ( )15 ,20S E

B ( )15 ,140S E

C ( )45 ,20S E

D ( )45 ,140S E


O

P

N

R

S

45o60o

80o E

30o N


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9. (Jun 2007, P1, Q19).

In Diagram 12,Nis the North Pole, Sis the South Pole andNOSis the axis of the earth..

P and Q are two points on the surface of the earth.PQ is a diameter of the earth.

Find the position of point Q .

A ( 40S, 170E)

B ( 40S, 170W)

C ( 50S, 170E)

D ( 50S, 170W)


N

S

Q

O

P

50

10

Equator

Meridian Greenwich

Diagram 12


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10. (November 2007, P1, Q17).

In Diagram 11,Nis the North Pole, S is the South Pole and NOS is the axis of the earth.

Find the position of point Q .

A ( 38N, 15E)

B ( 38N, 65

E)

C ( 52N, 15E)

D ( 52N, 65E)


N

S

O

Q

38

40

Equator

Diagram 11

25W


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11. (Jun 2008, P1, Q18).

P and Q are two points on the surface of the earth and the latitude ofP is 55N.

Given that Q is located 15 south ofP, find the latitude of Q .

12. (November 2008, P1, Q18).

In Diagram 11,NOSis the axis of the earth.PQ is diameter of the parallel of latitude.

Diagram 11

Find the longitude ofP.

A 10W

B 10E

C 170W

D 170E

Earth As A Sphere

A 40S

B 40N

C 70S

D 70N

23

O

P

N

S

10o

Greenwich meridian

Q


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Answers

Past Year SPM Questions

1 2 3 4 5 6 7 8 9 10 11 12

A D D A D B B A D C B C


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Chapter 23 I Earth as a Sphere ENHANCE