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C
0
Þ
A
0
B
2
B
0
2
sin2B
2
sin2B
1
þ
4
sin4B
2
sin4B
1
B
1
e
2
X
ﾼ
a 1
ð
ˁ
D
0
6
E
0
F
0
8
sin8B
2
sin8B
1
10
sin10B
2
sin10B
1
þ
ð
sin6B
2
sin6B
1
Þ þ
ð
5
:
39
Þ
This is the general formula for the meridian arc length. In the ensuing terms like
sin8B and sin10B, the greatest value of the term sin8B is only 0.0003 m. Thus,
whether to leave it out is determined by the desired accuracy of computations.
In practical use, the formula for the meridian arc length from the equator to the
point at latitude B is usually applied. In this case, inserting B
ﾼ
0, B
2
ﾼ
B into
(
5.39
) yields:
"
#
B
0
2
sin2B
C
0
4
sin4B
D
0
6
sin6B
E
0
8
sin8B
F
0
10
sin10B
A
0
B
e
2
X
ﾼ
a 1
ˁ
þ
þ
þ
ð
5
:
40
Þ
The formula (
5.40
) gives the meridian arc length from the equator to a given
point along the meridian.
Substituting the defining parameters of the Krassowski Ellipsoid adopted by the
Beijing Geodetic Coordinate System 1954 into the above equation yields:
8611B
X
ﾼ
111134
:
16036
:
4803 sin 2B
þ
16
:
8281 sin 4B
0
:
0220 sin 6B
þ
ð
5
:
41
Þ
Likewise, for the GRS75 Ellipsoid adopted by the Xi'an Goedetic Coordinate
System 1980, we have:
0047B
X
ﾼ
111133
:
16038
:
5282 sin 2B
þ
16
:
8326 sin 4B
0:0220 sin 6B
þ
ð5:42Þ
For the GRS 80 Ellipsoid adopted by CGCS2000, we get:
95254700B
X
ﾼ
111132
:
16038
:
508741268sin2B
þ
16
:
832613326622sin4B
10
5
sin8B
0
:
021984374201268sin6B
þ
3
:
1141625291648
:
ð
5
:
43
Þ
B
o
in (
5.41
), (
5.42
), and (
5.43
) denotes the geodetic latitude in degrees. X is
measured in meters. If the length of the meridian arc X is known, and then the
corresponding geodetic latitude B can be solved by the iteration method.
If we put B
ﾼ
2
, placed in (
5.43
) the length of a quadrant of the meridian Q is
10,001,965 m.
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