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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
ᄐ
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
ᄐ
ʾ
new
2
þ ʷ
new
2
minimum,
ð
7
:
29
Þ
or
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