UNIT 1 THE EARTH The Earth

Structure 1.1 Introduction

Objectives 1.2 Great Circle 1.3 Geographical Coordinates 1.4 Difference in Latitude and Difference in Longitude 1.5 Units of Distance and Speed 1.6 Summary 1.7 Key Words 1.8 Answers to SAQs

1.1 INTRODUCTION

Earth The earth is one of the planets of the Solar System. Its shape approximates to that of a sphere but could best be described as an oblate spheroid, i.e. bulged at the equator and compressed at the poles. Its equatorial radius is 6378.16 km and the polar radius is 6356.77 km. This difference in diameter is called the earth’s compression. For most practical purposes, we consider the earth to be a true sphere. Navigation is all about knowing where you are on the earth. In this unit, you will be familiarised with various terms which you would be using in Navigation and acquire some knowledge about how the geographical coordinates of a point on earth’s surface are determined. Objectives After studying this unit, you should be able to • define latitude, and longitude, • calculate the differences in latitudes and longitudes between two places, and • acquire knowledge of units of distance and speed.

1.2 GREAT CIRCLE

Axis The axis of the earth is the diameter about which it rotates. Poles The geographic poles of the earth are the two points where the axis meets the surface of the earth. The earth rotates about its axis once each day. This rotation carries each point on the earth’s surface towards East. West is the direction 180° from East, North is the direction 90° to the left of East, and South is the direction 90° to the right of East. The two poles of the earth are designated as North Pole and South Pole, accordingly.

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Terrestrial Navigation Great Circle A Great Circle is a circle on the surface of a sphere, the plane of which passes through the centre of the sphere. There is only one great circle through any two points on the sphere’s surface, except if the points are at the two ends of a diameter when an infinite number of great circles are possible. Examples of great circle are the equator, the ecliptic and the meridians. Small Circle A Small Circle is a circle on the surface of a sphere, the plane of which does not pass through the centre of the sphere. Example is parallel of latitudes. Poles of a great circle are two points on the sphere from where every point on the great circle is 90o away from these points. Every great circle will have two poles which are diametrically opposite.

1.3 GEOGRAPHICAL COORDINATES

We know that every point on the surface of the sphere is equidistant from its center and any point is similar to every other point. As the earth is rotating about its axis therefore the two points where the axis meets the earth’s surface (the two poles of earth) are different from any other points. Thus, grid of great circles passing through the poles (meridians) and circles (parallels of latitude) whose plane is perpendicular to the axis can be drawn on the earth’s sphere. The horizontal and vertical reference grids are the Equator and the Prime meridian. From these references the two coordinates in horizontal and vertical planes are required to pin-point any place on the surface of the earth. The two coordinates are Latitude and Longitude of the place on the surface of the earth and are referred as Geographical coordinates.

Figure 1.1 Equator The equator is a great circle on the surface of the earth, the plane of which is perpendicular to the earth’s axis. The equator divides the earth into the north and the south hemispheres. Latitudes are measured North or South from the equator. Parallels of Latitude Parallels of latitude are small circles on the earth’s surface, the planes of which are parallel to the plane of the equator. All parallels of latitude run East-West. Meridians Meridians are semi-great circles on the surface of the earth, joining the two poles. The other half of the same great circle forms yet another meridian. All meridians intersect the equator and parallels of latitude at 90°. Since the meridians join the 6 poles, all meridians run North-South.

Prime Meridian The Earth Prime meridian is the meridian which passes through Greenwich. The other meridians are named East or West from the prime meridian. Latitude Latitude of a point or an observer is the angle between plane of equator and vertical to the surface at that point. Latitudes are measured from 0° to 90°, and named North or South according to the place being North or South of the equator.

Figure 1.2 Longitude Longitude is the arc of the Equator or the angle at the poles contained between the prime meridian and the meridian through that place. Longitudes are measured from 0° to 180°, and named East or West according to the place being East or West of the prime meridian. In Figure 1.3 • O is centre of the earth, • NOS is the earth’s axis, • N and S are two geographic poles of the earth. (North and South poles respectively),

Figure 1.3 • W GEG’W is equator (also a great circle), • LAL is the parallel of Latitude (also a small circle) passing through point A, • L′BL′ is the parallel of latitude (also small circle) passing through point B, • NAHS is the meridian passing through point A, 7

Terrestrial Navigation • NFBS is the meridian passing through point B, • Angle AOH or arc AH is the latitude of point A, • NOGS is Prime meridian, and • Arc GH or Angle GOH is the longitude of point A.

1.4 DIFFERENCE IN LATITUDE AND DIFFERENCE IN LONGITUDE

Difference in Latitudes (d′lat) The d′lat between two places is the arc of a meridian or angle at the centre of earth contained between the parallels of latitude through the two places. D′lat is named North or South according to the direction from the first place to the second, e.g. d′lat from 20°N to 5°N is 15°S and d′lat from 11°S to 12°N is 23°N. Difference in Longitude (d′long) The d′long between two places is the shorter arc of the equator or the smaller angle at the poles contained between the meridians through the two places. D′long is named East or West according to the direction from the first place to the second place. The following examples will make it more clear. From to d′long 065°E 100°E = 35°E 085°W 010°W = 75°E 020°E 030°W = 50°W 162°W 171°E = 27°W 172°E 175°W = 13°E The shorter arc crosses the 180th Meridian and therefore the d′long is named in the direction of the 180th meridian from the first place. Mean Latitude The Mean latitude between two latitudes is the arithmetic mean between them.

P

Mean Latitude L A L between Places A and B D′Lat L′ B L′ Q C Q′

A′ B′

P’ Figure 1.4 Figure 1.4 represents the earth in which C = Centre of the earth, 8 P = North Pole,

P′ = South Pole, The Earth QQ′ = The equator, A and B = Two places on the earth, LAL = Latitude of A, PAA′P′ = Longitude of A, L′BL′ = Latitude of B, PBB′P′ = Longitude of B, and A′CB′ = Difference in longitude between A and B. Example 1.1 Mean lat between 20ºN and 30ºN is 25ºN Mean lat between 10º20′S and 30º30′S is 20º25′S Mean lat from 10º20′S to 30º30′N : D′lat = 40º50′N ½ d′lat = 20º25′N So mean lat = 30º30′N – 20º25′N = 10º05′N or, Mean lat = 20º25′N – 10º20′S = 10º05′N.

1.5 UNITS OF DISTANCE AND SPEED

Various units are used for measuring distances on the surface of the earth. Normally, Nautical mile is the unit used for measuring distances on board ships. International Nautical Mile The international nautical mile or nautical mile at any place is the length of the arc of a meridian subtending an angle of 1' at the centre of curvature of that place. As length of one nautical mile (NM) changes with latitude, mean length of one nautical mile is 1852.3 meters. B N

O

A W E

S

Figure 1.5 In Figure 1.5 • WSEASNB is a meridian. • WOE is equator. • Arc EA is length of 1 Nautical Mile near equator. • Arc NB is length of 1 Nautical Mile near pole. • Arc NB and EA are making same angle of 1 minute at their respective centers. But length of arc NB is greater than length of arc EA. So length of nautical mile depends upon observer’s latitude and is given by the formula : 9

Terrestrial Navigation Nautical mile = 1852.3 – 9.4 cos Latitude (meters) Cable Cable is 1/10th of a nautical mile that means there are 10 cables in one nautical mile and is equal to about 185 m. Knot Knot is the unit of speed and is the speed of ship expressed in nautical miles per hour. Geographical Mile Geographical mile is the length of the arc of the equator subtending an angle of 1' at the centre of the earth. It is constant in length, equal to 1855.3 m. Statute Mile Statute or land mile is an arbitrary measure of length which is equal to 1609.3 meters. Kilometre Kilometre is the unit of length which is equal to 1000 metres and is 1/10,000th of distance from equator to poles. SAQ 1 (a) Find and write position of Little Basses Reef (East Coast of Ceylon) in Latitude and longitude. (b) Find d′lat and mean lat in following cases :

From To

(i) 7° 10′ N 10° 15′ N

(ii) 15° 10′ N 10° 15′ N

(iii) 16° 10′ N 18° 15′ N

(iv) 30° 10′ N 10° 15′ N

(c) Find d′long in following cases :

From To

(i) 60° 10′ N 70° 15′ N

(ii) 57° 10′ N 58° 05′ N

(iii) 178° 17′ N 179° 15′ N

(iv) 10° 10′ N 56° 55′ N

1.6 SUMMARY

Earth is an ellipsoid. Position of any place on earth is known by two co-ordinates – latitude and longitude. Latitude is measured from equator and longitude is measured from prime meridian. At sea, distances are measured in nautical miles and speed in knots. When we say that a ship’s speed is 12 kts, it means that she covers 12 nautical miles in one hour.

1.7 KEY WORDS

Equator : A great circle the plane of which is perpendicular 10 to the earth’s axis. Latitudes are measured from equator.

Prime Meridian : Is the meridian passing through Greenwich from The Earth where Longitudes are measured. Latitude : Angular distance from equator of any place named north or south expressed in degrees and minutes. Longitude : Angular distance from prime meridian of any place named east or west expressed in degrees and minutes. D′lat : Difference in latitude expressed in degrees and minutes. D′long : Difference in longitude expressed in degrees and minutes. Knots : Distance travelled in nautical miles in one hour.

1.8 ANSWERS TO SAQs

SAQ 1 (a) 06° 24.5′ N 081° 43.6′E (b) D′lat lat Mean lat (i) 3° 05′ N (i) 8° 42.5′ N (ii) 5° 05′ S (ii) 12°37.5′ N (iii) 34° 25′ N (iii) 1° 02.5′ N (iv) 19° 55′N (iv) 20′12.5’ S (c) (i) 10° 05′ E (ii) 0° 55′ W (iii) 2 ° 28′ E (iv) 67° 05 E.

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Terrestrial Navigation

N L L A

G’

O

G W H E F B

L’ L’

S

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