chapter 23 i earth as a sphere (enrichment)

TOPIC : EARTH AS A SPHERE

Enrichment

CHAPTER 23: EARTH AS A SPHERE23.1 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 Greenwich Meridian(ii) its position to the left or to the right of the Greenwich Meridian. The longitude of a given point is written as x0 E or x0 W.

The difference between two longitudes: 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.

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 or x0 S. 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.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.

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.

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

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

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

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

C

B

D

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.

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) via the north pole is

A 600 B 3600 C 4200 D 6600

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

A2700 nm C5400 nm

B3600 nm D6300 nm

9. The shortest distance from London to the North Pole is 2310 nm . The latitude of London is

A23.1 N C66.9 N

B38.5 N D51.5 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

A300C2400

B1500D9300

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.

A30C50

B40 D60

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.

A10 S C35 S

B25 SD65 S

13. M(70 N, 100 W) and N are two points on the earths surface. If the shortest distance from M to N via the North Pole is 5100 nautical miles, find the latitude of N.

A15 N C65 N

B25 ND85 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

A15 S C25 S

B20 S D30 S

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) CC (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 difference in 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

A8 E C72 W

B8 W D152 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

A3480C4080

B3780D5220

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

A14C36

B24 D66

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.A5 E C5 W

B70 E D30 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.A3000C4200

B3600D6600

25. P (60S, 90E) and Q (60S, 90W) 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.

A10800C5400

B7200D3600

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 (400 N, 00 E)?

2. (July 2004, P1, Q19)

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

B

C

D

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 B C

D 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

C

B

D

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.

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.

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.

DIAGRAM 10

The position of point P is

A

B

C

D

O

C

N

00

600

400


A EMBED Equation.DSMT4

B EMBED Equation.DSMT4

C EMBED Equation.DSMT4

D EMBED Equation.DSMT4

Equator

P

600

400 E

200 W

N

S

Q

Equator

The Equator

Q

S

N

P

600 N

400 E

200 W

1000 W

Y

S

500 N

X

400 E

N

O

Q

B

A

C

D

P

D

N

S

500 N

Which of the town, A, B, C or D, is located east of X with difference in longitude of 600 ?

A

100 N

Diagram 3

S

Greenwich

Meridian

00

O

500

P

R

Find the position of point R.





PQ is a diameter of the earth.

PointLocationP( 00, 1000 W )QABCDE

500

700 E

420 N

1000 E

S

N

O

Q

P

PointLocationA( 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 )

Greenwich

Meridian

N

Diagram 5

P

O

S

1000

800

Diagram 4

X

600 E

200 W

600 W

C

B

400 E

100 E

E

N

Diagram 1

Y

A

550 N

P

A

N

EX. 23.7 A2.


State the location of each of the

following points:

PointLocationA( 550N , 660 E )BXY

Considering the four points A, B, C and

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

B

A

D

Greenwich

Meridian

O

C

S

N

00

600

600

550 N

150 W

N

EX. 23.4A 1.


XY is the diameter of the 600 N parallel

of latitude.

Complete the table below :

PointLocationXYRTKL

Y

X

T

O

P

Q

R

S

800 N

K

L

N

EX. 23.5A 1.

PQ, XY and AB are diameters of the

earth.


following points:

PointLocationP( 00 , 1000 E )QABXY

A

750 N

750 N

N

Q

B

O

1000 E

S

800 E

EX. 23.6 A1.



following points:

PointLocationA( 750N , 300 E )XYB

800 E

S

600 E

B

X

O

P

Q

Y

A

N

700 N

EX. 23.5 A 2.

PQ, XY and AB are diameters of the

earth.


following points:

PointLocationP( 00 , 600 E )QABXY

X

B

Q

P

O

X

Y

400

S

300 E

EX. 23.6 A 2.



following points:

PointLocationA( 750N , 300 B )YXB

N

750 N

B

A

EX. 23.7 A1



following points:

PointLocationA( 350N , 420 E )BYX

O

Q

P

500

Y

X

S

300 B

N

350 N

A

B

O

Q

P

500

Y

X

S

420 E

180 W

B

600

Q

P

O

X

Y

660 E

100 E

S

500 W

S

Greenwich

Meridian

D

A

B

Diagram 8

N

S

P

Q

O

R

40o

50O

DIAGRAM 10

700

N

Find the position of point R.





P

R

400

O

00

Greenwich

Meridian

S

Diagram 10

N

Which of the town, A, B, C or D, is located east of X with difference of 400 in longitude?

X

B

A

C

500 N

100 N

D

400 E

600 W

200 E

200 W

S






600

800

S

O

P

Diagram 9

N

Greenwich

Meridian

Equator

O

P

N

R

S

45o

60o

80o E

30o N

PAGE 15Earth As A Sphere

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chapter 23 i earth as a sphere (enrichment)

Documents

earth surface

location of q

given parallel of latitude

location position

location of given points

location of x

location of y

longitude of q