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2
4
3
5
sinL
N
cos L
N
0
ð
þ
H
Þ
ð
þ
H
Þ
2
4
3
5
2
4
3
5
ʷ
N
Δ
X 0
Δ
Y 0
cos B
M
sinBcos L
M
sinB sinL
M
Δ
Z 0
þ
H
þ
H
þ
H
new
cos Bcos L cos B sinL
sinB
old
2
4
3
5
2
4
3
5
sinBcos L
sinB sinL
cos B
ʵ X
ʵ Y
ʵ Z
þ
sinL
cos L
0
Ne 2 sinBcos B sinLNe 2 sinBcos Bcos L
0
old
2
4
3
5 Δ
0
N
M e 2 sinBcos B
N 1
þ
m
e 2 sin 2 B
ð
Þ
2
4
3
5
0
0
e 2 sin 2 B
N
M 2
ð
Þ
a e 2 sinBcos B
sinBcos B
da
df
ð
M
þ
H
Þ
ð
M
þ
H
Þ
ð
1
f
Þ
þ
sin 2 B
N
a
M
e 2 sin 2 B
e 2 sin 2 B
1
1
1
f
old
2
3
ð
ʻ
L old
Þ
cos B old
4
5 :
þ
ˆ
B old
N old
ð
7
:
28
Þ
The above is the generalized arc measurement equation, where the unknowns are
Δ
X 0 ,
Δ
Y 0 ,
Δ
Z 0 ,
ʵ X ,
ʵ Y ,
ʵ Z ,
Δ
m,da, and df. In practical cases, the values of
ʵ X ,
ʵ Y ,
ʵ Z ,
and
m are always left out according to conditions 1 and 2 of the ellipsoid
orientation. The new ellipsoidal elements, positioning, and orientation values can
be calculated using the above equation.
Such equations of arc measurement as ( 7.28 ) can be written at every astro-
geodetic point of the astro-geodetic network. Solving the equations based on:
X
Δ
ʾ new 2
þ ʷ new 2
minimum,
ð
7
:
29
Þ
or
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