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Prepared by Pn Hjh Saripah Ahmad [email_address] H/P: 0133759142 SEK MEN SAINS MUZAFFAR SYAH MELAKA EARTH AS A SPHERE CHAPTER 9
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EARTH AS A SPHERE CHAPTER 9 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
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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 Longitude / Latitude Rap Ron Brown Listen this song
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Watch the video about earth as a sphere from Google Earth
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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.
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The lines of longitude divide the earth into Eastern and Western hemispheres.
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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.
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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. <ul><li>The memory rhyme I use to help remember that lines of longitude denote east-west distance is: </li></ul><ul><ul><li>"Lines of LONGitude are all just as LONG as one another." </li></ul></ul><ul><li>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. </li></ul>
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<ul><li>Learning Outcomes : </li></ul><ul><li>Sketch a great circle through the north and south poles. </li></ul>
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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 . LATITUDE
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parallel Text book Page 253 Sketch a circle parallel to the equator . .
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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. LOCATION OF A PLACE WHERE IS MALAYSIA
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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)
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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) Answer 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.
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Text book Page 259 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.
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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 .
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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.
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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 15 O 15 x 60 900.n.m. EF 45 o 45 x 60 2700.n.m. Arc Angle subtends at earth’s centre Distance computation Distance in nautical miles AB 20 O 20 x 60 1200.n.m. BC 90 o 90 x 60 5400.n.m. CD 50 o 50 x 60 300.n.m
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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' . 1 2 PAGE 263
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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. Step 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 = (73 o 54’ + 47 o 16’)° = 121° 10’ = 121X 60 + 10’ = 7270’ The distance between A and B along the meridian is 7270 nautical miles.
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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 <ul><li>A is north of the equator and B (23°10'S, 50°W) </li></ul><ul><li>is south of the equator. </li></ul><ul><li>Distance A from B along the meridian is 240nautical miles . </li></ul><ul><li>Difference in latitude = 2400 ÷ 60 </li></ul><ul><li>= 40° </li></ul><ul><li>Since A is north of the equator, latitude for A is </li></ul><ul><li>(40° - 23°10')N = 16°50'N </li></ul>
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The distance between 2 points A and B along a great circle = 60 x nautical miles, where is an angle subtended by the arc AB at the center of a great circle. N S W E O A B 60 E 40 W <ul><li>= 40 + 60 </li></ul><ul><li>= 100 </li></ul>The distance between A and B along the equator = 60 x 100 = 6000 nautical miles Great Circle (equator) Horizontal
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N S W E O A 40 N <ul><li>= 40 + 70 </li></ul><ul><li>= 110 </li></ul>The distance between A and B along the meridian = 60 x 110 = 6600 nautical miles Great Circle (meridian) B 70 S Vertical
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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.
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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 = X o . T
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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 Text book Page 271
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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.
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Find the distance of AB measured along parallel of latitude a) A (28 o N, 18 o E), B (28 o N, 107 o E) b) A (37 o S, 108 o W) , B (37 o S, 5 o W)
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The distance between 2 points A and B along the circle of 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 E 40 W N S 50 N <ul><li>= 40 + 50 </li></ul><ul><li>= 90 </li></ul><ul><li>And x = 50 </li></ul>The distance between A and B along latitude 50 N = 60 x x cos x = 60 x 90 x cos 50 = 3471 nautical miles O
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Find the distance of AB measured along parallel of latitude c) A (63 o N, 23 o E), B (63 o N, 74.5 o W) d) A (42 o 5’S, 37 o 14’W),B(42 o 5’S, 94 o 50 ’ E) Text book Page 273
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Finding the longitude of a point given the longitude of another point and the distance between the two points along a parallel of latitude.
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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.
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SPM QUESTION 2003 <ul><li>P(61 o N,10 o E) and Q are two points on the surface of the earth such that PQ is the diameter of a parallel of latitude </li></ul><ul><li>Find the longitude of Q [ 1 mark ] </li></ul><ul><li>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] </li></ul><ul><li>Calculate the shortest distance, in nautical mile, from Q to the North Pole.[ 2 marks ] </li></ul><ul><li>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. </li></ul><ul><li>Calculate </li></ul><ul><li>(i) the distance, in nautical miles, from P to M </li></ul><ul><li>(ii) the longitude of M </li></ul>N S P Equator
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