of the deviation of the vertical, or the angle between the local vertical and the normal to a reference ellipsoid, are about 1 minute of arc. Maximum variations in the height between the reference ellipsoid and mean sea level (also called the geoid or equipotentiaI surface) are about 100 m, as illustrated in Fig. 5-8.

The coordinate transformations given here are intended for use near the Earth's surface to correct for an observer's height above sea level and are valid only for altitudes much less than the radius of the Earth. For satellite altitudes, the coordinates will depend on the definition of the subsatellite point or the method by which geodetic coordinates are extended to high altitudes. For a discussion of geodetic coordinates at satellite altitudes, see Hédman [1970] or Hedgley [1976].

Geodetic and geocentric latitude are related by [H.M. Nautical Almanac Office, 196|]:

tan <J> = tan <f>'/( 1 -/)2« 1.006740 tan <f>'

<f>-<f>' = (/+i /2)sin 2<J> - ( ! /2 + ! /3)sin 4$+1 /3sin 6<f>

where /«1/298.257 is the flattening factor of the Earth as adopted by the IAU in 1976 [Muller and Jappel, 1977],

Let h bé the height of P above the reference ellipsoid in metres; let Rm be the equatorial radius of the Earth in metres; and let d be the distance from P to the center of the Earth in units of Re. Then d and h are related by h = Rb\d-(1 -/)/Vl -/(2-/)cosy ]

«(1.5679 X 10"7)/i+0.998327 + 0.001676 cos 2«f> - 0.000004cos4$

To convert geographic or geodetic coordinates to geocentric rectangular coordinates in units of R9, use the following:

d sin t/>'=( S+h X1.5679 X10" 7)sin <f>

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