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value of the Ellipsoid GRS80 is defined more precisely (see Nin et al. 2006)], and
also referred to as the IUGG-1980 Ellipsoid. Its geometric parameters are:
a
ᄐ
6,378,137.0000 m
b
ᄐ
6,356,752.3141 m
c
ᄐ
6,399,593.6259 m
f
ᄐ
1/298.257222101
e
2
ᄐ
0.00669438002290
e
02
ᄐ 0.00673949677547
By estimation, the values commonly used are:
a
b
c
6,400 km
f
1/300
e
2
e
02
0.007
1/150
a, b, c, f, e, and e´ are the six geometric parameters often used in the Earth
ellipsoid. To make it simpler to write and convenient to calculate, one can also
introduce the auxiliary functions:
)
,
p
1
W
ᄐ
e
2
sin
2
B
p
1
ð
5
:
10
Þ
e
0
2
cos
2
B
V
ᄐ
þ
where B denotes the geodetic latitude, W is the first auxiliary function, and V is the
second. Both are elliptic functions.
It is quite easy to obtain the relationship between the parameters from the
definition of each parameter.
Relationship Between a and b
It follows from (
5.9
) that:
b
2
a
2
ᄐ
e
2
,
a
2
e
0
2
,
1
b
2
ᄐ
1
þ
ð
5
:
11
Þ
q
1
a
p
e
0
2
b
ᄐ
1
e
2
, a
ᄐ
b
þ
:
ð
5
:
12
Þ
Relationship Between e and e
0
From (
5.11
) it can be found that:
e
0
2
e
2
1
1
þ
ᄐ
1
and hence:
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