earthasspere-090822173211-phpapp01-1

7/27/2019 earthasspere-090822173211-phpapp01-1

1/66

Prepared by

Pn Hjh Saripah Ahmad

[email protected]/P: 0133759142

SEK MEN SAINS MUZAFFAR SYAH

MELAKA
mailto:[email protected]:[email protected]


2/66


3/66

Great Circle is a circle on the

surface of earth through the north

and south poles and its centre isin the centre of the earth


4/66

Ive 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...

...Ive got an attitude for latitude and longitude.


The longitude lines travel up and down...



So thats the story about the maps strange grid...





The Longitude / Latitude Rap

Ron BrownListen this

song


5/66


6/66

LONGITUDE

Longitude lines are made by circles that

intersect with both the North and South Poles.

Each longitude can be thought of as dividingthe 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.


7/66

The lines of longitude divide

the earth into Eastern andWestern hemispheres.


8/66

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.


9/66

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 180east and180west 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.


10/66

Learning Outcomes :

i) Sketch a great circle through the north and south poles.


11/66


12/66

(ii) State the longitude of a given poin

Longitude of a Given Point

150o 160o


13/66

80o


14/66

iii) Sketch and label meridian with the longitude given

37oE b) 108o3 W


15/66


16/66


17/66

iv) Find the difference between two longitudes.


18/66


19/66


20/66

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 asthe horizontal rungs of a ladder

("ladder-tude"). Degrees latitude are

numbered from 0to 90north and

south. Zero degrees is the equator,the imaginary line which divides our

planet into the northern and southern

hemispheres. 90north is the North

Pole and 90south 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.


21/66

Sketch a circle parallel to the equator..

parallel


22/66

State the latitude of a given point.


23/66


24/66


25/66

Sketch and label a parallel of latitude.


26/66


27/66


28/66

Find the difference between two latitudes.

(iv).


29/66


30/66

People pinpoint places on the Earth using a pair ofcoordinates known as latitude and longitude. Latitude

describes a locations distance from the Equator.Longitude describes its relative distance east or westof a north-south band called the prime meridian,which runs through Greenwich, England. The latitudeand longitude of any place on Earths surface defineits unique global address.

WHERE IS MALAYSIA


31/66

The diagram shows two points C and D on thesurface of the earth. State their locations.

a) Latitude of C = 72NLongitude of C = 75E

Location of C is (72N, 75E)b) Latitude of D = 80SLongitude of D = (180 - 35)W

= 145WLocation of D is (81S,145W)


32/66


33/66

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 thefollowing points:a)A (68N, 145W)

b) P (71S, 35E)c) C (0S, 75E)

A is the intersection point of latitude 68N

and longitude 145W(from [180 - 35])P is the intersection point of latitude 71Sand longitude 35E.C is the intersection point of latitude 0and longitude 75E.


34/66

Sketching and Labelling the Latitude and

Longitude of a Given Place

If the latitude and longitude of a place is given, we can sketch themeridian and the parallel of latitude on a sphere. The location of thegiven point is the intersection point of the latitude and the longitudeand this can be represented by a point on the sphere.


35/66

Follow the steps given below to sketch and label the point for Q(40N,50W)

STEP 1Sketch a circle to represent

earth with its polar axis NOS.Sketch the equator andthe Greenwich Meridian NGS.

STEP 2Mark angle GOH = 50 on theequator. Sketch and labelthe longitude 50W.

Step 3On the meridian plane of50W, mark angle QOH = 40 from theequator to the north. Sketch and labelthe parallel of latitude that passes throughQ, which is 40N.

Mark the intersection point as N Q.


36/66


37/66

DISTANCE ON THE SURFACE OF THE EARTH

Finding the length of rc of a Great Circle in Nautical Mile

Two placesA and B lie on the equator, withlongitude 23W and 24W respectively.The angle subtends at the centre of theearth, O, is angleAOB and has a value 1.

The distance fromA to B on the surface ofthe earth is equivalent to 60 nauticalmiles. Since 1 = 60',then 1' = 1 nautical mile.The nautical mile is defined as the lengthof arc of a great circle on the earths

surface which subtends an angle of 1' atthe centre of the earth.


38/66

Figure above shows a greatcircle through the plane cuttingacross the polar axis NOS

Figure above shows a globewith WABCED as the equator.

F

Arc Angle subtendsat earths centre DistancecomputationDistance in nautical miles

DE 15O 15 x 60 900.n.m.

EF 45o

45 x 60 2700.n.m.

Arc Angle subtendsat earths 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


39/66

The distance along the equatorbetween J and R is 1234nautical miles. Find the angle

subtended by the arc JR at theearths centre, O.

Distance between J and R = 1234nautical miles. =JOR = 1234'

= 2034'

The angle subtended by the arc JRat the earths centre is 2034'.


40/66

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.

PointsA and B on

longitude 35W.

The difference in latitudebetweenA and B

= (70 - 35)

= 35 x 60 = 2100'

The distance betweenA

and B along the meridian

is 2100 nautical miles.

PointsA and B on

longitude 123E.

The difference in latitudebetweenA and B

= (65 - 15)

= 50 x 60 = 3000'


and B along the meridian

is 3000 nautical miles.

PointsA and B on

longitude 93W.

The difference in latitude

betweenA and B= (73o54 + 47o16)

= 121 10

= 121X 60 + 10

= 7270


andB

along the meridianis 7270 nautical miles.


41/66

F d h l d f h l d f h d h


42/66

Finding the latitude of a point given the latitude of another point and thedistance between the two points along the same meridian.

If you are given the distance between two points and the latitude of anyone 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 betweenA and B along the meridianis 600 nautical miles and the location of B is(15N, 101E) Difference in latitude = 600 60

= 10SinceA is north of B, latitude forA is (15 + 10)N

= 25N

b) A is north of the equator and B (2310'S, 50W)is south of the equator.

DistanceA from B along the meridian is 240nautical miles.Difference in latitude = 2400 60

= 40SinceA is north of the equator, latitude forA is

(40 - 2310')N = 1650'N


43/66

The distance between 2 points A and B along a greatcircle = 60 x nautical miles, where is an angle

subtended by the arc AB at the center of a great circle.

N

S

W EO

A B

60 E40 W

= 40 + 60

= 100

The distance betweenA and B along theequator

= 60 x 100

= 6000 nautical miles

Great Circle

(equator)

Horizontal


44/66

N

S

W EO

A40

N

= 40 + 70

= 110

The distance between

A and B along themeridian

= 60 x 110


Great Circle(meridian)

B

70 S

Vertical


45/66

Fi di th di t b t t i t d l th


46/66

Finding the distance between two points measured along theequator, given the longitudes of both points.

The only parallel of latitude which is a great circle is the Equator. Thedistance between twopoints on the equator is thedifference in longitude in minutes.

The globe shows 4 points P, G, R and T on theequator. NGS is the Greenwich Meridian. The

diagram below the globe is the cross-sectionalview 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.


47/66

Finding the longitude of a point given the longitude of another point


48/66

Findingthe longitude of a point given the longitude of another pointand the distance between the two points along the equator.


49/66


50/66

Stating the relation between the radius of the earth and the radius of a


51/66

Stating the relation between the radius of the earth and the radius of aparallel 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 latitudebecomes shorter and shorter until the North or South Pole when theradius becomes zero.Observe the point P with latitude X N, and Q is the centre of theparallel of latitude on which P lies. Since angle OPQ and angle POT arealternate, angle OPQ = Xo.

T


52/66

Find the relationship between the radius of the parallel of latitude60N, r, and the radius of the earth, R.

Radius of parallel of latitude 60= Radius of earth x cos 60

r = R cos 60r = R x 0.5

:. r = 0.5 R

Stating the relation between the length of an arc on the equator


53/66

Stating the relation between the length of an arc on the equatorbetween 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 oflatitude , then we can obtain the ratio.


54/66

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)


55/66

The distance between 2 points A and B along the circleof latitude x N or x S = 60 x x cos x nautical mailes,

where is the angle subtended by the arc AB at the

centre of the circle latitude.

A B

50 E40 W

O

N

S

50

N= 40 + 50

= 90

And x= 50

The distance betweenA and B alonglatitude 50 N

= 60 x x cosx

= 60 x 90 x cos 50


Find the distance of AB measured along parallel of latitude


56/66

c) A (63oN, 23oE), B (63oN, 74.5oW) d) A (42o5S, 37o14W),B(42o5S, 94o50E)

Finding the longitude of a point given the longitude of another point


57/66

and the distance between the two points along a parallel of latitude.


58/66


59/66

Finding the shortest distance between two points on the surface of


60/66

g p

the earth.

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


61/66

solving problems involvinga) distance between two points


62/66

a) distance between two points,

b) travelling on the surface of the earth.


63/66


64/66
http://localhost/var/www/apps/conversion/tmp/scratch_3/LATITUDE%20AND%20LONGITUDE%20MENU/index.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_3/f_266.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_3/f_264.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_3/f_260.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_3/f_254.html


65/66

P(61oN,10oE) and Q are two points on the surface of the earth suchthat PQ is the diameter of a parallel of latitude

(a) Find the longitude of Q [ 1 mark ]

(b) PR is the diameter of the earth, On the diagram mark the positionof Q and R , Hence, state the position of R [ 4 marks]

(c) Calculate the shortest distance, in nautical mile, from Q to the

North Pole.[ 2 marks ]

(d) An airplane took off from P and flew due west a long its parallel oflatitude with an average speed of 500 knot. The airplane took 9hours to reach a point M.

(e) Calculate

(i) the distance, in nautical miles, from P to M

(ii) the longitude of M

N

S

P

Equator


66/66

Documents

earthasspere-090822173211-phpapp01-1