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height anomaly of the target point, and a
2
is the height of the structure at the target
point.
It follows from (
5.56
) that the correction for skew normals is dependent primar-
ily on the height of the target point.
Let B
2
ﾼ
45
, A
1
ﾼ
45
, and
ˁ
00
/M
2
ﾼ
1/30; when H
2
ﾼ
200 m,
ʴ
2
ﾼ
0.01
00
;
when H
2
ﾼ
0.05
00
. It can be seen that correction for the skew
normals should be taken into consideration in the first- and second-order triangu-
lation and in the third- and fourth-order triangulation at high altitudes.
On the following occasions, the correction for skew normals is zero:
1,000 m,
ʴ
2
ﾼ
1. The target point is on the ellipsoid, i.e., H
2
ﾼ
0
2. The target point and the observation point are at the same longitude or latitude, i.
e., A
1
ﾼ
0; then
ʴ
2
ﾼ
0
,90
, 180
, 270
, then
ʴ
2
ﾼ
0
Correction from Normal Section to Geodesic
Connections between two points on the ellipsoid are referred to the geodesic.
Therefore, in Fig.
5.32
the normal section direction Ab should be converted to the
corresponding geodesic direction, known as the normal section to geodesic correc-
tion, denoted by
ʴ
3
(as illustrated in Fig.
5.33
).
The formula for correction from normal section to geodesic is:
e
2
S
2
00
ˁ
00
3
ﾼ
cos
2
B
1
sin 2A
1
:
ʴ
ð
5
:
57
Þ
12N
1
Obviously, the correction from normal section to geodesic is chiefly concerned
with the distance from the place of observation to the target point.
Set B
1
ﾼ
45
, A
1
ﾼ
45
; when S
0.001
00
; when S
ﾼ
30 km,
ʴ
3
ﾼ
ﾼ
60 km,
ʴ
3
ﾼ
0.005
00
. This serves to show that correction from normal section to geodesic
should generally be applied to the first-order triangulation. However, second- or
lower order triangulation can be carried out irrespective of this correction.
When A
1
ﾼ
0
,90
, 180
, and 270
,
0, i.e., points A and B are on the same
meridian or approximately on the same parallel, and the correction from normal
section to geodesic is zero.
ʴ
3
ﾼ
Computation of the Three Corrections for Horizontal Directions
The three corrections for horizontal directions are theoretical problems in classical
geodesy, indicating the relations between angles on the Earth's surface and on the
ellipsoid. This is still of practical significance in modern geodesy, such as the
reduction of the triangulateration in an engineering control network. While setting
up the azimuth survey monument at the space TT&C (tracking, telemetering, and
command) stations, one needs to convert the difference in geodetic azimuths
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