Geology Reference
In-Depth Information
Tabl e 5 . 1
Flattening, ellipsoidal departure and other parameters
computed from three sets of data.
Data sets
(Rapp, 1974)
G. R. S. 1980
G. R. S. 1967
10
6
J
2
±
1,082.635
0.011
1,082.63
1,082.7
10
6
J
4
−
1.6410
±
0.0174
···
···
a
(m)
6,378,128
±
6
6,378,137
6,378,160
10
−
10
GM
(m
3
s
−
2
)
39,860.046
±
0.025
39,860.05
39,860.265
10
5
(rad s
−
1
)
Ω
7.2921151467
7.292115
7.2921151467
Computed values
10
3
m
1
3.461377
3.461391
3.461410
f
1/298.2175
f
e
f
e
10
8
κ
−
78.96
0
0
f
e
1/298.2579
1/298.2579
1/298.2477
10
6
J
4
−
1.641040
−
2.361394
−
2.361747
d
(m)
6,370,994
6,371,000.8
6,371,024
10
3
m
3.449775
3.449786
3.449805
from
m
1
and
f
via expression (5.92). Equatorial gravity is accessible through the
dimensional form of (5.56), which on substituting for δ from (5.73) reduces to
1
2
m
1
21
f
3
f
1
3
f
GM
d
2
3
13
1
2
128
105
κ
+···
g
e
=
−
+
+
+
+
.
(5.100)
A gravity formula is supplied by substituting for δ in equation (5.58). This yields
g
=
g
e
1
5
2
m
1
2
m
−
f
1
14
m
sin
2
3
17
8
7
κ
+
+
+
+
φ
1
8
f
(
f
sin
2
2φ
+···
+
−
5
m
)
−
3κ
.
(5.101)
Through the series (5.83) and expression (5.92), we can convert (5.100) and
(5.101) to depend on
a
and
m
1
instead of
d
and
m
, giving
1
2
m
1
1
7
f
GM
a
2
3
2
16
7
κ
+···
g
e
=
−
+
+
f
(
1
+
f
)
+
,
(5.102)
g
=
g
e
1
5
2
m
1
1
2
m
1
f
1
7
m
1
sin
2
3
26
8
7
κ
+
+
−
+
+
φ
1
sin
2
2φ
+···
8
f
f
5
m
1
+
−
−
3κ
.
(5.103)
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