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# Earth as a sphere

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• how did we add 55S to 64N? this gives the sum of 119S but the number cant be over 90?

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### Earth as a sphere

1. 1. LATITUDE AND LONGITUDE The coordinate system that we use to locate places on Earth is the terrestrial system. The coordinates in the terrestrial system are Latitude and Longitude. e.g: Kuala Lumpur ( 3 8’ N , 101 42’ E )
2. 2. LONGITUDE Longitude, denoted symbolically by the Greek letter Lambda, is divided in meridians (not parallel to each other, they converge at the poles), which are measured in degrees East or West of the Prime Meridian, also known as Greenwich Meridian The Prime Meridian serves as a starting point for the measurement of degrees in either East or West directions. It marks longitude 0°.
3. 3. LONGITUDE
4. 4. LONGITUDE The Prime Meridian is the meridian (line of longitude) at which the longitude is defined to be 0°. The Prime Meridian and its opposite the 180th meridian (at 180° longitude), which the International Date Line generally follows, form a great circle that divides the Earth into the Eastern and Western Hemispheres.
5. 5. LONGITUDE
6. 6. LONGITUDE Another meridian of great importance is the Dateline Merdian, which marks longitude 180° (either E or W). This meridian is the exact oposite of the Prime Meridian on the globe.
7. 7. LONGITUDEMeridian- is one half of a great circle joining the North and South Poles.Longitude of a meridian- is determined by the angle between its plane and the plane for GM , either to the east or to the west of the GM.
8. 8. LONGITUDE 150 E
9. 9. LONGITUDE Meridians that are opposite to each other and form a great circle, have longitudes x E and ( 180 – x) W or x W and (180-x) E - Great circle is a circle with centre at the centre of the Earth.
10. 10. Longitude
11. 11. The Difference between Two Longitudes If longitudes X and Y are on the same side of the GM, then the difference between X and Y is ( X – Y). If the longitudes X and Y are on the different sides of the GM , then the difference between X and Y is ( X + Y )
12. 12. Longitude
13. 13. LATITUDE
14. 14. LATITUDE Parallels of latitude are circles on the surface of the Earth, parallel to the equator and labeled according to their angular distance from the equator. Parallel of latitudes is NOT a great circle !
15. 15. LATITUDE Latitude is the anglesubtended by a meridianat the centre of the earthbeginning from theequator to the parallel oflatitude which is either tothe North or to the Southof the Equator.
16. 16. LATITUDE
17. 17. LATITUDEDIFFERENCE BETWEEN TWOLATITUDES- If latitudes X and Y are on the same side of the Equator, then the difference between X and Y is ( X – Y). If the latitudes X and Y are on the different sides of the Equator , then the difference between X and Y is ( X + Y )
18. 18. LATITUDECalculate the differencebetween the latitudesbelowi. Latitudes 70 N and64 Nii. Latitudes 64 N and55 S
19. 19. LOCATION OF A PLACEThe location of aplace is determinedby its latitude andlongitude. Based onthe diagram statethe location s of A ,B ,C , D and E
20. 20. LOCATION OF A PLACE
21. 21. DISTANCE ON THE SURFACE OF THE EARTH. The distance between two places on the surface of the Earth is measured in nautical miles. 1 is equal to 60 nautical miles. Any two points on a sphere is always connected by a circular path. The shortest distance between two points is the distance taken along the great circle.
22. 22. DISTANCE BETWEEN TWO POINTS ALONG THE MERIDIANDistance of two points on thesurface of the Earth measuredalong the meridian ( samelongitude, different latitude) isgiven by= ( the difference in latitude X 60’ )=( 60’ )
23. 23. DISTANCE BETWEEN TWO POINTS ALONG THE MERIDIANGiven that P(60 N,30 W)and Q ( 40 S , 30 W) ,find the distance of PQmeasured along themeridian.Answer:Distance = ( 60 + 40 ) 60’ = 100 x 60’ = 6000 nautical miles.
24. 24. DISTANCE BETWEEN TWO POINTS ALONG THE MERIDIANIn the diagram , A ( 45 N ,30 E) and B are two pointson the surface of the earth.Given that the distancebetween A and B is 4800nm measured along thelongitude 30 E . Find thelocation of B
25. 25. DISTANCE ALONG THE EQUATORThe distance between points Pand Q on the Equator ( samelatitude, different longitude) isequivalent to the angle at thecentre of the earth POQ, inminutes.= (difference in longitude ) x 60’
26. 26. DISTANCE ALONG THEEQUATOR Example: Given that P( 0 , 124 W) , Q (0 , 72 W) and R( 0 , 27 E ). Calculate the distance between i. P and Q ii. Q and R
27. 27. DISTANCE ALONG THEEQUATOR Example; Given that P(0 , 160 W) and the distance between P and Q measured along the Equator is 5400 n.m. Find all the possible locations of Q.
28. 28. Relation Between Radius of theEarth and Radius of a Parallelof Latitude OP = OQ = R AQ is parallel to OP POQ = OQA ( alternate angle of two parallel lines) By trigonometric ratio , Cos = r R Therefore, r = R Cos r
29. 29. Relation between the Lengthsof Arcs on the Equator andParallels of Latitude-Let r be the radius of the parallel of latitude and R be the radius of the Equator.-Then , the circumference of the parallel latitude is 2 r and the circumference of the Equator is 2 R
30. 30. Relation between lengths of Arcon the Equator and parallels oflatitude
31. 31. Distance along the parallel oflatitudeDistance of PQ = MN (Cos ) = MON 60 Cos = Diff. in long of PQ 60 Cos(lat of PQ)eg: Find the distance between P( 60 N, 35 W) and Q( 60 N, 45 E).
32. 32.  Find the distance between P( 60 N, 35 W) and Q( 60 N, 45 E).//Dist. of PQ = (diff. in longitude) 60’ Cos = (35 + 45 ) 60 Cos 60 = 2400’ Distance of PQ = 2400 n.m
33. 33. SHORTEST DISTANCEBETWEEN TWO POINTS The shortest distance between two points on the surface of the Earth is the arc on the great circle that passes through the two points. The Equator and all circles passing through the North and South Poles are great circles.
34. 34. SHORTEST DISTANCEa. Along the meridian ( same b. Along the Equator longitude )
35. 35. SHORTEST DISTANCEDistance of two points that passingthrough the North/South Poles* P and Q are on the same greatcircle*The difference in longitudes = 180•The shortest distance of PQ= ( POQ = ) x 60’= ( 180 - lat P – lat Q) 60’
36. 36. Shortest Distance Calculate the shortest distance between P ( 48 N, 45 E) and Q( 53 N, 135 W). = 180PQ ( shortest distance through North pole) = (180 – 48 – 53) x 60’ = 4740’ = 4740 n.m