Geoscience Reference
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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
6,378,137.0000 m
b
6,356,752.3141 m
c
6,399,593.6259 m
f
1/298.257222101
e 2
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
e 2 sin 2 B
p
1
ð
5
:
10
Þ
e 0 2 cos 2 B
V
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
e 2 , a 2
e 0 2 ,
1
b 2
1
þ
ð
5
:
11
Þ
q
1
a
p
e 0 2
b
1
e 2
, a
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
1
and hence:
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