EARTH'S SURFACE

Fig. 4-15. Geometry of the Horizon Vector, H, and Surface Normal; N.for an Oblate Earth Because R is a horizon point, H must be perpendicular to N; that is,

EARTH'S SURFACE

Fig. 4-15. Geometry of the Horizon Vector, H, and Surface Normal; N.for an Oblate Earth Because R is a horizon point, H must be perpendicular to N; that is,

Rearranging terms, this becomes

which is the equation for a spheroid of ellipticity/centered at (u/2,v/2,w/2). We call this the horizon spheroid or horizon surface because it contains all possible horizon points (jc,y,z) for an observer at (u,c,w) looking at a spheroidal Earth of ellipticity / and variable sizes. The three principal axes of the horizon spheroid are parallel to those of the Earth spheroid. The intersection of the two surfaces is the Earth's horizon, as shown in Fig. 4-16. By substituting Eq. (4-16) into Eq. (4-20), we obtain u* + oy+ ,°a2 (4-21)

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