chapter 23 i earth as a sphere enrich
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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 as x0E orx0W.
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 ofthe 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.
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 are
parallel to the equator. 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.
Earth As A Sphere 1
200 W400 E
600P
N
S
Q
Equator
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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 and
meridian.
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)
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.
Earth As A Sphere 2
PQ is a diameter of the earth.
Point Location
P ( 00, 1000 W )
Q
A
B
C
D
E
400 E
500N
1000 W
S
N
O Q
BA
C
D
P
E
200 W400 E
600 N
P
N
S
Q
The Equator
Y
X
500
W
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Exercise 23.3 B : To MARK the location of given points on the earth.
1. PQ is a diameter of the earth.
Mark on the given diagram, the location of each of the points below.
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 3
Point Location
A ( 00 , 700 E )
B ( 420 N, 100 E )
C ( 420 S, 1000 E )
D ( 00 , 100 E )
X ( 00 , 800 W )
Y ( 420 N, 800 W )
Z ( 420 N, 700 E )
700 E
420N
1000 ES
N
OQ
P
100 E
EX. 23.4A 1.
PQ is a diameter of the earth.
XY is the diameter of the 600 N parallel
of latitude.
Complete the table below :
Point Location
X
Y
R
T
K
L
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 4
EX. 23.5A 1.
PQ, XY and AB are diameters of the
earth.
State the location of each of thefollowing 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.
State the location of each of thefollowing 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 5
B
Q
A EX. 23.6 A1.
PQ is a diameter of the earth.State the location of each of the
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.
PQ is a diameter of the earth.State the location of each of the
following 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.
Earth As A Sphere 6
B
Q
AEX. 23.7 A1
PQ is a diameter of the earth.
State the location of each of the
following points:
PointLocationA( 350 N , 420 E )BYX
350N
S
N
O
Y
P
420 E
X
500
180 W
B
Q
A EX. 23.7 A2.
PQ is a diameter of the earth.
State the location of each of the
following 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 in
longitude 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.
Earth As A Sphere 7
500
500
00
S
O
P R
Find the position of point R.
A ( )50 ,50N W
B ( )50 ,130N W
C ( )50 ,50N E
D ( )50 ,130N E
N
Greenwich
Meridian
600
60000
N
S
CO
Greenwich
Meridian
D
A
B
Considering the four points A, B, C and
D, which of these is (600 N, 00 E) ?
Diagram 1
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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
Earth As A Sphere 8
Diagram 3
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 or
D, is located east of X withdifference 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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7. Given that PQ is diameter of the earth. If the location of P is (70 N, 35 W), the
location of Q is
A (70 S, 145 E) C (70 N , 145 E)
B (20 S, 145 E) D (70 S, 35 E)
8. The distance from P(60 S, 60 W) to Q(60 S, 120 W) along the common latitude is A 2700 nm C 5400 nm
B 3600 nm D 6300 nm
9. The shortest distance from London to the North Pole is 2310 nm . The latitude of
London is
A 23.1 N C 66.9 N
B 38.5 N D 51.5 N
10. The shortest distance in nautical miles, from P(75 N, 110 W) to Q(80 N, 70 E)
measured on the earths surface is
A 300 C 2400B 1500 D 9300
11. The shortest distance from P(30 N,70 E) to Q(x N, 110 W) via the north pole is
6600 nm.
Find the value of x.
A 30 C 50
B 40 D 60
12. P(40 N, 120 W) and Q are two points on the earths surface. If Q is 4500 nautical
miles due south of P, find the latitude of Q.
A 10 S C 35 SB 25 S D 65 S
13. M(70 N, 100 W) and N are two points on the earths surface. If the shortestdistance from M to N via the North Pole is 5100 nautical miles, find the latitude of N.
A 15 N C 65 N
B 25 N D 85 N
14. N and S are the North and South Poles respectively. P is (40 N, 10 W) and the two
arc lengths of PQ and QS are equal. Find the latitude of Q
A 15 S C 25 S
B 20 S D 30 S
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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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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 theequator. 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.
Earth As A Sphere 13
400
700
00
S
O
P R
Find the position of point R.
A ( )40 ,70N W
B ( )40 ,70N E
C ( )40 ,110N W
D ( )40 ,110N E
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.
Earth As A Sphere 14
100N
A
Which of the town, A, B, C or D,is located east of X with difference
of 400 in longitude?500N
S
N
D
B
200 E
C
600 W
200 W
400 E
X
The position of point P is
A ( )60 ,80N W
B ( )60 ,100N W
C ( )80 ,60N E
D ( )80 ,100N 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
The position of point P is
A ( )15 ,20S E
B ( )15 ,140S E
C ( )45 ,20S E
D ( )45 ,140S E
Earth As A Sphere 15
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)
Earth As A Sphere 16
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)
Earth As A Sphere 17
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 0f 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
18
O
P
N
S
10o
Greenwich meridian
Q
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ANSWERS
QUESTIONS ACCORDING TO THE SPM FORMAT
1. C 2. A 3. C 4. D
5. B 6. B 7. C 8. B
9. C 10. A 11. C 12. A
13. B 14. D 15. A 16. A
17. B 18. C 19. C 20. C
21. A 22. D 23. B 24. B
25. C
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
Earth As A Sphere 19