INTRODUCTIONOnce the reference

spheroid is defined and oriented, there is a need to integrate this with earth in the sense of defining a unique co-ordinate system. A point on the natural surface is projected on the reference spheroid along the ellipsoidal normal and its horizontal position is determined with respect to the projected point.

Similarly the point is projected on the Geoid along the direction of gravity and the vertical position of the point is determined with respect to the Geoid.

The co-ordinate system will help in locating a point on the surface of the spheroid thus providing a well defined addressing system. Geodetic coordinates refer to a coordinate system defined over the reference spheroid for precise positioning of earth features.

COORDINATE SYSTEMS IN GEODESY

This refers to the well versed latitude and longitude system and is popular in use and frequently referred as the geodetic coordinates. The horizontal coordinates here are geodetic latitude φ/ψ (phi) and geodetic longitude λ (lambda). The vertical location is defined separately with respect to Geoid (M.S.L) as the datum and usually referred in terms of meters above it.

Defining some basic elements on the reference spheroid:Once the spheroid is available we assume that the

rotational axis is made coincident with the semi-minor axis of the spheroid. The North and South poles are the points on the spheroid where the axis of rotation meets it. Now let us define two important terms known as ‘Great Circles’ and ‘Small Circles’. A plane passing through the center of the spheroid cuts the spheroid along a circle known as a Great Circle. Similarly a plane cutting the spheroid without passing through the center generates a small circle on the spheroid.

The particular great circle generated by a plane perpendicular to the axis of rotation of the spheroid (obviously it passes through the center) is called the Equator and the plane itself the Equatorial Plane. This is a unique Great circle on the Spheroid since one and only one plane can pass through the center being perpendicular to axis of rotation. This divides the spheroid in two parts known as the southern and northern hemispheres and used as reference for defining the latitude of a place.

The intersection of a plane perpendicular to the axis of rotation (but not containing the center) generates a small circle named as Parallel of Latitude (latitude circles). There are infinite numbers of parallels of latitudes since infinite number of planes can intersect the spheroid being perpendicular to rotational axis. These are also concentric circles over the reference spheroid with either of the poles as the center.

A plane imagined to be passing through the axis of rotation intersects the spheroid in a great circle named as Meridian Circle. There are an infinite number of meridian circles since an infinite number of planes can be imagined to pass containing the axis of rotation. So every meridian circle contains the North and South poles. These planes are known

as meridian planes. The meridian circle which passes through Greenwich of U.K is named as Prime Meridian or Greenwich Meridian. This is used as reference meridian for defining the longitude of points in subsequent sections.

Defining Latitude and longitude:The latitude of a point is the acute angle

subtended at the center of the spheroid by the arc of the meridian intercepted between the point and the equator. It is expressed in terms of either north or south hemi-sphere. It is sometimes expressed as positive and negative respectively. The latitude of a point lying on the equator is 0º and the latitude of the poles is 90º. There are 90 parallels at 1o interval on each hemisphere, the 90th being the north and south poles respectively. A point on the equator is normally assigned to northern hemisphere

The longitude of a point is the angle made by the meridian plane of the point with the Greenwich meridian/prime meridian and is measured along the arc of the equator between these two meridians. The longitude of any place varies between 0º to 180º and it is reckoned as east or west of Greenwich meridian (also sometimes specified by + or -). A point on the prime meridian is normally assigned to the east eastern hemisphere whereas a point on the 180 meridian is assigned to the western hemisphere. The longitude of a place is closely inter-linked with the time at that place, reckoning from the mean time at Greenwich.

CARTESIAN CO-ORDINATES SYSTEM This system is designed normally with the

origin at the center of the spheroid/ellipsoid. The Z-axis coincides with the semi-minor axis,

the X and Y axis lie on the equatorial plane. Any plane containing the semi minor axis and

cutting the surface of the ellipsoid is called a meridian plane.

The X axis is the line on the equatorial plane which starts at origin and passes through the Greenwich meridian plane.

The Y axis is chosen to form the right handed system and lies in the equatorial plane 90 degree counter-clock wise from the X axis.

The coordinates of a point is defined in terms of X, Y, Z. Here the Z is not the elevation of a point. This can be used to find the spheroidal/ellipsoidal height of the point.

This system is of interest to Geodesists and Researchers where very precise measurements are required.

The WGS 84 Coordinate SystemWGS has been developed by the U.S. Department of

Defense (DoD) since about 1960 in order to define and establish a geocentric terrestrial reference system. WGS 60 was followed by WGS 66, then by WGS 72, and finally by WGS 84. Each realization of the reference system incorporated more data, better computational techniques, a better knowledge of Earth, and improved accuracy (Malys, Slater, 1994; Slater, Malys, 1997; Merrigan et al., 2002). WGS 72 and WGS 84 have been used to compute the operational broadcast ephemeris of Transit Doppler and GPS satellites. As a consequence, coordinates derived from the broadcast ephemeris with Transit or GPS refer to WGS. This is the main reason for the high acceptance of WGS 84 as a primary reference coordinate system.

The WGS 84 Coordinate SystemOrigin The direction of the Conventional Terrestrial Pole (CTP)

for polar motion, as defined by the Bureau International del’Heure (BIH), the basis of the coordinates adopted for theBIH stations.

x-Axis Intersection of the WGS 84 Reference Meridian Plane andthe plane of the CTP’s Equator, the Reference Meridianbeing the Zero Meridian defined by the BIH on the basis

y-Axis Complete a right handed, Earth Centred, Earth Fixed(ECEF) orthogonal coordinate system, measured in theplane of the CTP Equator 900 East of the x-Axis.

The WGS 84 Coordinate SystemThe major parameters of WGS 84 are given in Table

2.1 (cf. NIMA, 2000).

Parameter Name WGS 84semi-major axis a 6 378 137 mflattening f 1/298.257223563angular velocity ω 7.292115

×10−5 rad s−1geocentric GM 398 600.4418 km3

s−2gravitational constant

2nd zonal harmonic C2,0 −484.16685 × 10−6

The WGS 84 Coordinate System