Global Positioning System Reference
In-Depth Information
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[32
Figure 9.2
Normal sections on the ellipsoid.
Lin
—
8.1
——
Nor
PgE
di
fferent latitudes. Line 1 is the normal section from
P
1
to
P
2
and line 2 indicates
th
e normal section from
P
2
to
P
1
. It can be readily seen that these two normal
se
ctions do not coincide, because the curvature of the ellipsoidal meridian changes
w
ith latitude. The question is, which of these two normal sections should be adopted
fo
r the computations? Introducing the geodesic, which connects these two points in
a u
nique way, solves this dilemma. There is only one geodesic from
P
1
to
P
2
. Figure
9.
3 shows the approximate geometric relationship between the normal sections and
th
e geodesic. The angular reduction
(
[32
α − α
)
is required to get the azimuth
α
of the
ge
odesic. The expression is listed in Table 9.1 (note that approximate values for the
azimuth
and length
s
of the geodesic are sufficient for expressions on the right-hand
sid
e of Table 9.1).
α
Figure 9.3
Normal section azimuth versus geodesic azimuth.
