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120

CHAPTER

5

EQUIPOTENTIAL ELLIPSOID

z

Ö=const.

-+---~R==~~\,.:..._+- A = const.

x

FIGURE 5.1: Ellipsoidal coordinates. Top: View from the front.

Bottom: View from above.

whose axis coincides with the z-axis, and whose linear excentricity has the constant value E. The co ordinate 11, is the semiminor axis of this "coonlinate ellipsoid",

8

is the complement of the "reduced latitude"

ß

of P with respect to this ellipsoid (for its definition cf. sec. 1.4), and

>.

is the geocentric longitude in the usual sense.

The ellipsoidal coordinates 11"

8, >.

are related to x, y, z by the equations

x ../11,2 +E2sinOcos>.

y ../11,2

+

E2 sin

0

sin

>.

(5-1)

z 11, cosO

which can be read from the figure, considering that ../11,2

+

E2 is the semimajor axis of the ellipsoid whose surface passes through P.

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